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tangram_perception_count_3x3_inst25_var1_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"3",
"4",
"1",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst25/assembly/3x3_inst25assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/assembly/3x3_inst25assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/assembly/3x3_inst25assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/assembly/3x3_inst25assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.3682140433334865, 0.08970897647428389, 0.502425376239822], "cell_center": [1.6830127018922196, 6.147114317029974]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.5344029398630591, 0.9891697464278887, 0.21703088700988227], "cell_center": [5.049038105676659, 6.147114317029974]}, {"index": 2, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.04014975225319073, 0.7060719947405601, 0.7632273797026523], "cell_center": [1.6830127018922196, 2.049038105676658]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_rotation_4x4_inst4_var1_q_only
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece E? Note that the label behind piece E indicates its dimensions (wxh).
<image_0>
|
B
|
rotation
|
[
"90 degrees counterclockwise",
"0 degrees (not rotated)",
"45 degrees counterclockwise",
"30 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst4/perturbed_part/4x4_inst4perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/perturbed_part/4x4_inst4perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/perturbed_part/4x4_inst4perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/perturbed_part/4x4_inst4perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/perturbed_part/4x4_inst4perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/perturbed_part/4x4_inst4perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/perturbed_part/4x4_inst4perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/perturbed_part/4x4_inst4perturbed_part_assembly_step_7.png"], "instructions": ["", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (2, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).", "Place piece F with its upper-left corner at (x, y) = (1, 1).", "Place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 6, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.7026544847856405, 0.46673048477596846, 0.989431536237153]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.1486163972137372, 0.09099753565850044, 0.9804276633019189]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.6633151367722326, 0.05563697103144172, 0.996308043298854]}, {"index": 5, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [3, 4, 1, 2], "color": [0.5159597562042038, 0.7332772521875923, 0.7847260582105081]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 2, 4], "color": [0.3298784267001694, 0.4254879586883913, 0.8323218982811694]}, {"index": 4, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.9516920847941206, 0.09192754978443096, 0.034011632485778764]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.7873704671604125, 0.6920579729169158, 0.06370548134717746]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n11\n\nPiece F:\n1\n\nPiece G:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst20_var2_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"1",
"4",
"3",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst20/irregular_assembly/3x3_inst20irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst20/irregular_assembly/3x3_inst20irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst20/irregular_assembly/3x3_inst20irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst20/irregular_assembly/3x3_inst20irregular_assembly_step_3.png"], "instructions": ["", " Flip piece B vertically. Place piece B with its lower-left corner at (x,y) = (0, 3).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 2).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 1, "shape": [2, 3, 0, 1], "angle": 0, "flip": "vertical", "color": [0.2188625865501932, 0.3982672040489632, 0.24949930857585112], "is_merged": true}, {"index": 0, "shape": [0, 2, 2, 3], "angle": 30, "flip": "none", "color": [0.21514705147792568, 0.4919973529353018, 0.7207131866942781], "is_merged": false}, {"index": 2, "shape": [[0, 2, 0, 2], [2, 3, 1, 3]], "angle": 30, "flip": "none", "color": [0.11933639623212677, 0.6534312470367666, 0.34450218937820265], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n110\n110\n011\n\nPiece C:\n011\n110\n110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_3x3_inst12_var2_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"2",
"4",
"5",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_step/3x3_inst12perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_step/3x3_inst12perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_step/3x3_inst12perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_step/3x3_inst12perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_step/3x3_inst12perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.7158111525953443, 0.3144750396327004, 0.9033798732112359], "cell_center": [1.5, 4.5]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.9103403361123941, 0.38267590340608304, 0.7632217986287583], "cell_center": [4.5, 4.5]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.946796380694129, 0.7835046474330913, 0.11945153897003868], "cell_center": [1.5, 1.5]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.4602759030241912, 0.5263411433589661, 0.5878592840681638], "cell_center": [4.5, 1.5]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_4x4_inst7_var2_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"4",
"2",
"3",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst7/assembly/4x4_inst7assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/assembly/4x4_inst7assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/assembly/4x4_inst7assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/assembly/4x4_inst7assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/assembly/4x4_inst7assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Place piece B with its upper-left corner at (x, y) = (1, 4)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.0038464181562460897, 0.5456025205471018, 0.8316288348193334], "cell_center": [2.299038105676658, 6.348076211353315]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [2, 4, 0, 1], "color": [0.18526689525137774, 0.6222333081082303, 0.3116245006929087], "cell_center": [2.299038105676658, 2.1160254037844384]}, {"index": 3, "angle": 30, "orig_width": 3, "orig_height": 2, "w": 3.598076211353316, "h": 3.232050807568877, "label": "3x2", "piece": [2, 4, 1, 4], "color": [0.19476840970141396, 0.68707522398946, 0.14366332946109706], "cell_center": [6.897114317029974, 2.1160254037844384]}, {"index": 1, "angle": 0, "orig_width": 3, "orig_height": 2, "w": 3.0, "h": 2.0, "label": "3x2", "piece": [0, 2, 1, 4], "color": [0.5883107006707854, 0.8743059263428191, 0.51136848550568], "cell_center": [6.897114317029974, 6.348076211353315]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n111\n111\n\nPiece C:\n11\n\nPiece D:\n111\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_rotation_3x3_inst28_var4_q_only
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece B? Note that the label behind piece B indicates its dimensions (wxh).
<image_0>
|
B
|
rotation
|
[
"30 degrees counterclockwise",
"60 degrees counterclockwise",
"45 degrees counterclockwise",
"75 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst28/assembly/3x3_inst28assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/assembly/3x3_inst28assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/assembly/3x3_inst28assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/assembly/3x3_inst28assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [0, 1, 0, 3], "color": [0.24874432956275316, 0.10459104781785566, 0.290015710844736], "cell_center": [1.8660254037844388, 6.0]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.08038459038445755, 0.7628332166932088, 0.014888669554417922], "cell_center": [1.8660254037844388, 2.0]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.5629568688202203, 0.21307617484959096, 0.3881604215827764], "cell_center": [5.598076211353316, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_3x3_inst14_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"2",
"3",
"1",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst14/assembly/3x3_inst14assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/assembly/3x3_inst14assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/assembly/3x3_inst14assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/assembly/3x3_inst14assembly_step_3.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.7571710444334083, 0.6145865680611448, 0.2092124857635973], "cell_center": [1.6830127018922196, 2.049038105676658]}, {"index": 1, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 0, 1], "color": [0.7375466272024475, 0.7958785429353309, 0.9602750500929624], "cell_center": [5.049038105676659, 6.147114317029974]}, {"index": 0, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.6986416373362043, 0.39103013274436993, 0.7338256355090964], "cell_center": [1.6830127018922196, 6.147114317029974]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_size_count_4x4_inst3_var0_q_only
|
How many blocks (cells) are in piece C in the tangram puzzle shown below?
<image_0>
|
B
|
size_count
|
[
"4",
"2",
"5",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst3/irregular_assembly/4x4_inst3irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/irregular_assembly/4x4_inst3irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/irregular_assembly/4x4_inst3irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/irregular_assembly/4x4_inst3irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/irregular_assembly/4x4_inst3irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/irregular_assembly/4x4_inst3irregular_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/irregular_assembly/4x4_inst3irregular_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/irregular_assembly/4x4_inst3irregular_assembly_step_7.png"], "instructions": ["", "Rotate piece F by about 90 degrees clockwise. Place piece F with its upper-left corner at (x,y) = (2, 4).", "Rotate piece B by about 90 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (1, 2).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3).", "Place piece A with its upper-left corner at (x,y) = (0, 1).", "Place piece D with its upper-left corner at (x,y) = (3, 2).", "Rotate piece E by about 60 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (1, 4).", "Rotate piece G by about 60 degrees clockwise. Place piece G with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 5, "shape": [1, 2, 3, 4], "angle": 90, "flip": "none", "color": [0.4972346165255138, 0.8906984233290346, 0.7562452955907089], "is_merged": false}, {"index": 1, "shape": [2, 4, 2, 4], "angle": 90, "flip": "vertical", "color": [0.7422122588815101, 0.7551189736163385, 0.9234718311827813], "is_merged": true}, {"index": 2, "shape": [0, 1, 0, 1], "angle": 90, "flip": "none", "color": [0.9449625741817751, 0.10699177732051413, 0.906832733107004], "is_merged": false}, {"index": 0, "shape": [2, 4, 1, 2], "angle": 0, "flip": "none", "color": [0.54590476492727, 0.8017288265026836, 0.19702177212746563], "is_merged": false}, {"index": 3, "shape": [1, 3, 0, 1], "angle": 0, "flip": "none", "color": [0.09413549272860999, 0.7680476368577523, 0.4128776322048002], "is_merged": false}, {"index": 4, "shape": [3, 4, 0, 1], "angle": 60, "flip": "none", "color": [0.6840121753279651, 0.8419883108103203, 0.07133341675213412], "is_merged": false}, {"index": 6, "shape": [[0, 1, 1, 4], [1, 2, 1, 3]], "angle": 60, "flip": "none", "color": [0.6703174692655477, 0.09045368054856773, 0.1109174370728383], "is_merged": false}], "results": ["", "", "", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n10\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n\nPiece E:\n11\n\nPiece F:\n11\n11\n\nPiece G:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_3x3_inst17_var4_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"4",
"3",
"2",
"1"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst17/irregular_assembly/3x3_inst17irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/irregular_assembly/3x3_inst17irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/irregular_assembly/3x3_inst17irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/irregular_assembly/3x3_inst17irregular_assembly_step_3.png"], "instructions": ["", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3).", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1)."], "valid": true, "config": [{"index": 2, "shape": [[1, 3, 1, 3], [0, 1, 2, 3]], "angle": 0, "flip": "none", "color": [0.5019930741412741, 0.012559332865545225, 0.17639361210978133], "is_merged": false}, {"index": 1, "shape": [0, 1, 0, 2], "angle": 90, "flip": "none", "color": [0.5781587086361871, 0.8308911842343512, 0.6376093319739924], "is_merged": true}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 60, "flip": "none", "color": [0.3661900859965067, 0.7558139235341418, 0.8335971471271846], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n111\n110\n\nPiece C:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_3x3_inst6_var1_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"3",
"4",
"2",
"1"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_3.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.1586208137251468, 0.12393853736495797, 0.8716693278560734], "cell_center": [1.8660254037844386, 2.0]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 2, 3], "color": [0.6512655327908536, 0.8401929301826332, 0.8460989766654483], "cell_center": [5.598076211353316, 6.0]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.10309243167421278, 0.24076261322195902, 0.2100689922963226], "cell_center": [1.8660254037844386, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_rotation_3x3_inst5_var4_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece A? Note that the label behind piece A indicates its dimensions (wxh).
<image_0>
|
A
|
rotation
|
[
"30 degrees counterclockwise",
"15 degrees counterclockwise",
"60 degrees counterclockwise",
"45 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst5/perturbed_part/3x3_inst5perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/perturbed_part/3x3_inst5perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/perturbed_part/3x3_inst5perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/perturbed_part/3x3_inst5perturbed_part_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 30, "orig_width": 3, "orig_height": 3, "w": 4.098076211353316, "h": 4.098076211353316, "label": "3x3", "piece": [0, 3, 0, 3], "color": [0.07357053851548412, 0.9733870202483494, 0.6618987325140707]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.2058943173019785, 0.3076399768831918, 0.506910472590548]}, {"index": 1, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 2, 3], "color": [0.445111390892756, 0.16653115882702152, 0.8213500363599643]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n111\n\nPiece B:\n11\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst4_var0_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"3",
"6",
"4",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst4/perturbed_part/3x3_inst4perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Place piece E with its upper-left corner at (x, y) = (1, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece C with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.2781238656332754, 0.3149691097007876, 0.8834243520527705]}, {"index": 4, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [2, 3, 1, 3], "color": [0.09541635884526178, 0.9752420367434649, 0.6631387179145616]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.4955604281106083, 0.23218544540889552, 0.750238147366625]}, {"index": 3, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.2926298809515543, 0.23058311511659102, 0.3786033753419644]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [1, 2, 1, 3], "color": [0.6744683957180527, 0.765436016656263, 0.5757777482665812]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n\nPiece E:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst16_var0_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"5",
"4",
"2",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_step/3x3_inst16perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_step/3x3_inst16perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_step/3x3_inst16perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_step/3x3_inst16perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_step/3x3_inst16perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Place piece C with its upper-left corner at (x, y) = (1, 1)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.7676425093614947, 0.24713964046947057, 0.3655219928054467], "cell_center": [1.6160254037844386, 4.5]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.9976490339368843, 0.4943065670172001, 0.5594239487418055], "cell_center": [4.848076211353316, 4.5]}, {"index": 1, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.9048699719372921, 0.07001798964152184, 0.5974823649881674], "cell_center": [1.6160254037844386, 1.5]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.10823406854150919, 0.5033344127325038, 0.9895981043015385], "cell_center": [4.848076211353316, 1.5]}], "variant": "perturbed_step"}
|
|
tangram_perception_size_count_4x4_inst29_var2_q_only
|
How many blocks (cells) are in piece D in the tangram puzzle shown below?
<image_0>
|
C
|
size_count
|
[
"5",
"3",
"2",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 4).", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Place piece B with its upper-left corner at (x,y) = (1, 2).", "Place piece D with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 60, "flip": "none", "color": [0.5891291035296236, 0.3497096728096557, 0.9163403319569924], "is_merged": false}, {"index": 4, "shape": [[0, 3, 3, 4], [2, 3, 0, 3]], "angle": 30, "flip": "none", "color": [0.9906664263285482, 0.5961649832123572, 0.09772349038033212], "is_merged": false}, {"index": 2, "shape": [3, 4, 0, 2], "angle": 0, "flip": "none", "color": [0.5990452770695724, 0.8191791111282444, 0.6830708139237405], "is_merged": true}, {"index": 1, "shape": [0, 2, 1, 3], "angle": 0, "flip": "none", "color": [0.9543183423703964, 0.16273279693061327, 0.4214676188543469], "is_merged": false}, {"index": 3, "shape": [3, 4, 2, 4], "angle": 0, "flip": "none", "color": [0.9741545288927297, 0.34746803917361757, 0.23806606283364473], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1111\n0001\n0001\n\nPiece D:\n11\n\nPiece E:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_rotation_3x3_inst10_var2_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece C? Note that the label behind piece C indicates its dimensions (wxh).
<image_0>
|
C
|
rotation
|
[
"60 degrees counterclockwise",
"75 degrees counterclockwise",
"90 degrees counterclockwise",
"105 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_step/3x3_inst10perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_step/3x3_inst10perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_step/3x3_inst10perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_step/3x3_inst10perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_step/3x3_inst10perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (3, 2)."], "results": ["", "", "", "", "Over board"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.8361559109194318, 0.10012585524596118, 0.741018254845187], "cell_center": [1.6160254037844386, 4.5]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.08300347331815172, 0.9129260346492023, 0.030327958859172166], "cell_center": [4.848076211353316, 4.5]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.3863759873563767, 0.3560346662754732, 0.9984770026551721], "cell_center": [1.6160254037844386, 1.5]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "2x1", "piece": [2, 3, 1, 3], "color": [0.6956976668525877, 0.5614724968196306, 0.20881351979388718], "cell_center": [4.848076211353316, 1.5]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_3x3_inst1_var3_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"5",
"3",
"2",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst1/assembly/3x3_inst1assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/assembly/3x3_inst1assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/assembly/3x3_inst1assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/assembly/3x3_inst1assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/assembly/3x3_inst1assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 1)."], "valid": true, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.256800880301729, 0.03751904073714318, 0.9621217613176958], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.6560169554382161, 0.08892499875961357, 0.2746181042425252], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.4502474416941842, 0.8486047097331468, 0.005901795236425311], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.14881909049605957, 0.9309150666944223, 0.2473442019032891], "cell_center": [5.598076211353316, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_3x3_inst30_var4_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"2",
"4",
"3",
"1"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_3.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "valid": true, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3898459914352054, 0.015125501920735585, 0.9748770770994594], "cell_center": [1.8660254037844388, 6.0]}, {"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.8886986770755988, 0.16381677715556997, 0.3911952313182817], "cell_center": [1.8660254037844388, 2.0]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.9881484609812746, 0.3578709672961633, 0.9546513187032589], "cell_center": [5.598076211353316, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_rotation_3x3_inst26_var3_q_only
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece D? Note that the label behind piece D indicates its dimensions (wxh).
<image_0>
|
B
|
rotation
|
[
"75 degrees counterclockwise",
"90 degrees counterclockwise",
"105 degrees counterclockwise",
"60 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.769985114119021, 0.6023151000208017, 0.43905466192464926]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.8601757328506661, 0.8373920802150087, 0.4098927320047637]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.1762969342918307, 0.2700538547336413, 0.9959210428826512]}, {"index": 3, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.7902874398047327, 0.9053459516385535, 0.6109399886078966]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_size_count_3x3_inst30_var2_q_only
|
How many blocks (cells) are in piece B in the tangram puzzle shown below?
<image_0>
|
D
|
size_count
|
[
"10",
"9",
"5",
"7"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 60, "flip": "none", "color": [0.3898459914352054, 0.015125501920735585, 0.9748770770994594], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 60, "flip": "horizontal", "color": [0.9881484609812746, 0.3578709672961633, 0.9546513187032589], "is_merged": true}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n111\n110\n110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_3x3_inst9_var1_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"3",
"2",
"4",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_step/3x3_inst9perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_step/3x3_inst9perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_step/3x3_inst9perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_step/3x3_inst9perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_step/3x3_inst9perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 1).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece C with its upper-left corner at (x, y) = (0, 0)."], "results": ["", "", "", "", "Over board"], "valid": false, "config": [{"index": 3, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.505830367140229, 0.6887465524089847, 0.4889962320971758], "cell_center": [1.6160254037844386, 4.5]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.1919730202293154, 0.3911833530705978, 0.8454502921977165], "cell_center": [4.848076211353316, 4.5]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.5904030260647292, 0.1502228379867938, 0.09526647902491858], "cell_center": [1.6160254037844386, 1.5]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.5491620960992412, 0.8847398297155372, 0.43877106489933393], "cell_center": [4.848076211353316, 1.5]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_4x4_inst10_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"4",
"7",
"5",
"6"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_6.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3)."], "valid": true, "config": [{"index": 1, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.7647943845442875, 0.521793038303051, 0.22931721031735863], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 5, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.20248606624170273, 0.14080963695668047, 0.6747970029148332], "cell_center": [9.330127018922195, 1.8660254037844388]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.25836663280757977, 0.2609931063406825, 0.8704001126195765], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 0, 2], "color": [0.985913636595184, 0.05054811512912383, 0.006039335896045883], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.6583796654906042, 0.6756935160824654, 0.35383825296178073], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [1, 2, 2, 4], "color": [0.7227327947376154, 0.03867259473351192, 0.7187065902508578], "cell_center": [1.8660254037844388, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n11\n11\n\nPiece F:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_4x4_inst3_var4_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"8",
"7",
"9",
"6"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_8.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Place piece D with its upper-left corner at (x, y) = (1, 3).", "Place piece F with its upper-left corner at (x, y) = (1, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece G by about 90 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (2, 2).", "Rotate piece H by about 30 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 1, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.7422122588815101, 0.7551189736163385, 0.9234718311827813], "cell_center": [6.147114317029974, 8.415063509461097]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.6840121753279651, 0.8419883108103203, 0.07133341675213412], "cell_center": [6.147114317029974, 5.049038105676658]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.09413549272860999, 0.7680476368577523, 0.4128776322048002], "cell_center": [2.049038105676658, 5.049038105676658]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.4972346165255138, 0.8906984233290346, 0.7562452955907089], "cell_center": [10.24519052838329, 5.049038105676658]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.54590476492727, 0.8017288265026836, 0.19702177212746563], "cell_center": [2.049038105676658, 8.415063509461097]}, {"index": 6, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.6703174692655477, 0.09045368054856773, 0.1109174370728383], "cell_center": [2.049038105676658, 1.6830127018922192]}, {"index": 7, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.713590518367683, 0.3036182518548164, 0.1397252722702369], "cell_center": [6.147114317029974, 1.6830127018922192]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.9449625741817751, 0.10699177732051413, 0.906832733107004], "cell_center": [10.24519052838329, 8.415063509461097]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n1\n1\n\nPiece D:\n11\n\nPiece E:\n1\n\nPiece F:\n1\n1\n\nPiece G:\n11\n11\n\nPiece H:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_3x3_inst8_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"2",
"4",
"5",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst8/perturbed_part/3x3_inst8perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/perturbed_part/3x3_inst8perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/perturbed_part/3x3_inst8perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/perturbed_part/3x3_inst8perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/perturbed_part/3x3_inst8perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece D with its upper-left corner at (x, y) = (1, 1).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "Over board", "Over board", "Overlap", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 0, 2], "color": [0.42736045177487814, 0.8513826938670388, 0.8750119894026337]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.9121940999636362, 0.4658006204694346, 0.5093386252677216]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 1, 3], "color": [0.9743504876400423, 0.8767773860180708, 0.6725336937906906]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.20247270312835763, 0.14681033333288918, 0.039265900955547495]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_4x4_inst24_var4_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"3",
"4",
"6",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst24/perturbed_part/4x4_inst24perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/perturbed_part/4x4_inst24perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/perturbed_part/4x4_inst24perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/perturbed_part/4x4_inst24perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/perturbed_part/4x4_inst24perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/perturbed_part/4x4_inst24perturbed_part_assembly_step_5.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "Overlap", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 0, "orig_width": 2, "orig_height": 4, "w": 2.0, "h": 4.0, "label": "2x4", "piece": [0, 4, 0, 2], "color": [0.34673327216917005, 0.3823052678152453, 0.04807869538996756]}, {"index": 1, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.34499076168116316, 0.3941488900507818, 0.035379367870832845]}, {"index": 4, "angle": 90, "orig_width": 4, "orig_height": 1, "w": 1.0000000000000002, "h": 4.0, "label": "1x4", "piece": [3, 4, 0, 4], "color": [0.49317056051473784, 0.9208343917888762, 0.5319936589671153]}, {"index": 2, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.3941478645364662, 0.07242735131670541, 0.6221981028733828]}, {"index": 3, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [2, 3, 1, 4], "color": [0.667451459773487, 0.609690672977065, 0.9690305764874845]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n111\n\nPiece E:\n1\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_rotation_4x4_inst20_var2_q_only
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece C? Note that the label behind piece C indicates its dimensions (wxh).
<image_0>
|
C
|
rotation
|
[
"45 degrees counterclockwise",
"15 degrees counterclockwise",
"30 degrees counterclockwise",
"60 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 90, "orig_width": 4, "orig_height": 1, "w": 1.0000000000000002, "h": 4.0, "label": "1x4", "piece": [3, 4, 0, 4], "color": [0.5744625311503513, 0.40604309103934255, 0.6755080869563523]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 4, "w": 4.464101615137754, "h": 3.7320508075688776, "label": "2x4", "piece": [0, 4, 0, 2], "color": [0.29966205358997233, 0.09697437710727908, 0.8636883692270556]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 1, 4], "color": [0.18485780995210122, 0.8265364443197515, 0.6214626335028112]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 2, "w": 3.2320508075688776, "h": 3.598076211353316, "label": "3x2", "piece": [0, 2, 1, 4], "color": [0.6495522933888194, 0.5813963139566096, 0.8481586539915731]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n11\n\nPiece B:\n111\n111\n\nPiece C:\n111\n\nPiece D:\n1\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst18_var1_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"3",
"4",
"2",
"1"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst18/irregular_assembly/3x3_inst18irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/irregular_assembly/3x3_inst18irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/irregular_assembly/3x3_inst18irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/irregular_assembly/3x3_inst18irregular_assembly_step_3.png"], "instructions": ["", " Flip piece B vertically. Place piece B with its lower-left corner at (x,y) = (1, 3).", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1)."], "valid": true, "config": [{"index": 1, "shape": [0, 1, 0, 1], "angle": 0, "flip": "vertical", "color": [0.11654719097461486, 0.3924294240647598, 0.5378042635188506], "is_merged": true}, {"index": 2, "shape": [[1, 3, 2, 3], [0, 1, 1, 3]], "angle": 0, "flip": "none", "color": [0.17693734122658056, 0.6003726390211623, 0.25113789613439574], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 60, "flip": "none", "color": [0.21606549856304313, 0.2484660411194164, 0.5092478714383866], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n01\n01\n\nPiece C:\n01\n01\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_4x4_inst24_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"3",
"4",
"6",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_5.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "valid": true, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 3, "w": 1.0, "h": 3.0, "label": "1x3", "piece": [0, 3, 0, 1], "color": [0.34673327216917005, 0.3823052678152453, 0.04807869538996756], "cell_center": [1.5, 7.5]}, {"index": 4, "angle": 90, "orig_width": 4, "orig_height": 1, "w": 1.0000000000000002, "h": 4.0, "label": "1x4", "piece": [3, 4, 0, 4], "color": [0.49317056051473784, 0.9208343917888762, 0.5319936589671153], "cell_center": [4.5, 2.5]}, {"index": 3, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 1, 4], "color": [0.667451459773487, 0.609690672977065, 0.9690305764874845], "cell_center": [1.5, 2.5]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 3, 4], "color": [0.3941478645364662, 0.07242735131670541, 0.6221981028733828], "cell_center": [7.5, 7.5]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.34499076168116316, 0.3941488900507818, 0.035379367870832845], "cell_center": [4.5, 7.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n1\n1\n\nPiece E:\n1\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_4x4_inst5_var2_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"6",
"7",
"8",
"9"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_8.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 1).", "Place piece D with its upper-left corner at (x, y) = (0, 3).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 3).", "Rotate piece H by about 90 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (2, 1).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 3).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "", "", "", "Over board", "", "", "Over board"], "valid": false, "config": [{"index": 2, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.6297825243848936, 0.49093541919773, 0.6669745716275061], "cell_center": [1.8660254037844388, 9.330127018922193]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 1, 2], "color": [0.26612579155187954, 0.07055091126826107, 0.08305000539925333], "cell_center": [5.598076211353316, 9.330127018922193]}, {"index": 6, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.6662381683077349, 0.4371576487638136, 0.8074652784518175], "cell_center": [9.330127018922195, 9.330127018922193]}, {"index": 3, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.9240533250960073, 0.9819349600532725, 0.6747134014128692], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 5, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.5397844496723473, 0.05872496894813528, 0.15399180068950846], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 7, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.48160700821724445, 0.60931785491179, 0.22992601917545952], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 1, 2], "color": [0.22291133685432907, 0.48383465028816663, 0.5699125213630748], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.7349991584173213, 0.6699660472482647, 0.43315305080703437], "cell_center": [5.598076211353316, 1.8660254037844388]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_4x4_inst29_var2_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"3",
"5",
"6",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 4).", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Place piece B with its upper-left corner at (x,y) = (1, 2).", "Place piece D with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 60, "flip": "none", "color": [0.5891291035296236, 0.3497096728096557, 0.9163403319569924], "is_merged": false}, {"index": 4, "shape": [[0, 3, 3, 4], [2, 3, 0, 3]], "angle": 30, "flip": "none", "color": [0.9906664263285482, 0.5961649832123572, 0.09772349038033212], "is_merged": false}, {"index": 2, "shape": [3, 4, 0, 2], "angle": 0, "flip": "none", "color": [0.5990452770695724, 0.8191791111282444, 0.6830708139237405], "is_merged": true}, {"index": 1, "shape": [0, 2, 1, 3], "angle": 0, "flip": "none", "color": [0.9543183423703964, 0.16273279693061327, 0.4214676188543469], "is_merged": false}, {"index": 3, "shape": [3, 4, 2, 4], "angle": 0, "flip": "none", "color": [0.9741545288927297, 0.34746803917361757, 0.23806606283364473], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1111\n0001\n0001\n\nPiece D:\n11\n\nPiece E:\n1111\n0001\n0001\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_3x3_inst78_var3_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"1",
"3",
"2",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst78/irregular_assembly/3x3_inst78invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst78/irregular_assembly/3x3_inst78invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst78/irregular_assembly/3x3_inst78invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Flip piece B vertically. Place piece B with its lower-left corner at (x,y) = (0, 4).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 2]], "angle": 60, "flip": "vertical", "color": [0.6699971646227355, 0.03820965495859174, 0.27388372938137795], "is_merged": true}, {"index": 0, "shape": [0, 2, 2, 3], "angle": 30, "flip": "none", "color": [0.09293153893323325, 0.449721548009982, 0.8685946469212077], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n1100\n1100\n0111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_4x4_inst55_var4_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"3",
"4",
"1",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst55/irregular_assembly/4x4_inst55invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst55/irregular_assembly/4x4_inst55invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst55/irregular_assembly/4x4_inst55invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 3).", " Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 3, 0, 3], "angle": 90, "flip": "none", "color": [0.48467087813086074, 0.8333251253686752, 0.226606070023177], "is_merged": false}, {"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 3, 4]], "angle": 0, "flip": "vertical", "color": [0.9643179468173023, 0.2453124036567883, 0.8300162028796063], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n111\n\nPiece B:\n0010\n0010\n0010\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_3x3_inst25_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"3",
"4",
"2",
"1"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst25/irregular_assembly/3x3_inst25irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/irregular_assembly/3x3_inst25irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/irregular_assembly/3x3_inst25irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2)."], "valid": true, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 60, "flip": "horizontal", "color": [0.5344029398630591, 0.9891697464278887, 0.21703088700988227], "is_merged": true}, {"index": 0, "shape": [0, 2, 1, 3], "angle": 90, "flip": "none", "color": [0.3682140433334865, 0.08970897647428389, 0.502425376239822], "is_merged": false}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n111\n001\n001\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_size_count_3x3_inst64_var3_q_only
|
How many blocks (cells) are in piece A in the tangram puzzle shown below?
<image_0>
|
C
|
size_count
|
[
"9",
"6",
"7",
"10"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst64/irregular_assembly/3x3_inst64invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst64/irregular_assembly/3x3_inst64invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst64/irregular_assembly/3x3_inst64invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its lower-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 1, 3]], "angle": 0, "flip": "none", "color": [0.08128382681990354, 0.7391361031316008, 0.09206773157709514], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 90, "flip": "none", "color": [0.8326461279623965, 0.09514434016559481, 0.2644252469133076], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n110\n111\n001\n001\n\nPiece B:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_rotation_4x4_inst3_var2_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece E? Note that the label behind piece E indicates its dimensions (wxh).
<image_0>
|
C
|
rotation
|
[
"45 degrees counterclockwise",
"30 degrees counterclockwise",
"0 degrees (not rotated)",
"90 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_8.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece G by about 60 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (2, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Place piece D with its upper-left corner at (x, y) = (1, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece H by about 30 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).", "Place piece E with its upper-left corner at (x, y) = (3, 3).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "Over board", "Over board", "Over board", "Over board", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 0, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.54590476492727, 0.8017288265026836, 0.19702177212746563]}, {"index": 6, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [2, 3, 2, 6], "color": [0.6703174692655477, 0.09045368054856773, 0.1109174370728383]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 0, 1], "color": [0.9449625741817751, 0.10699177732051413, 0.906832733107004]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.09413549272860999, 0.7680476368577523, 0.4128776322048002]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.7422122588815101, 0.7551189736163385, 0.9234718311827813]}, {"index": 7, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.713590518367683, 0.3036182518548164, 0.1397252722702369]}, {"index": 4, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.6840121753279651, 0.8419883108103203, 0.07133341675213412]}, {"index": 5, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.4972346165255138, 0.8906984233290346, 0.7562452955907089]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n11\n\nPiece D:\n11\n\nPiece E:\n1\n\nPiece F:\n1\n1\n\nPiece G:\n1111\n\nPiece H:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_4x4_inst15_var3_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"6",
"4",
"5",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_5.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2)."], "valid": true, "config": [{"index": 0, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.4523784950258848, 0.5966474216563278, 0.4209460701703134], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.38174873155304245, 0.8750272159825754, 0.7170741611088424], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.4240667615814787, 0.7222327073498909, 0.6054485127949952], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 2, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.13557809727733983, 0.7545597463569302, 0.3732963496374987], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.29106684612422073, 0.3972090277120738, 0.0043544742627775745], "cell_center": [5.598076211353316, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_size_count_4x4_inst0_var1_q_only
|
How many blocks (cells) are in piece D in the tangram puzzle shown below?
<image_0>
|
B
|
size_count
|
[
"3",
"4",
"1",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst0/irregular_assembly/4x4_inst0irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/irregular_assembly/4x4_inst0irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/irregular_assembly/4x4_inst0irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/irregular_assembly/4x4_inst0irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/irregular_assembly/4x4_inst0irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (1, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its lower-left corner at (x,y) = (2, 4).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 0, 2], "angle": 60, "flip": "none", "color": [0.6587979169912652, 0.844257398556249, 0.15584553214536334], "is_merged": false}, {"index": 3, "shape": [[0, 2, 2, 4], [2, 4, 3, 4]], "angle": 90, "flip": "none", "color": [0.4580368292258854, 0.8158453451238444, 0.9632351452602854], "is_merged": false}, {"index": 1, "shape": [2, 4, 0, 1], "angle": 30, "flip": "none", "color": [0.25876504303189696, 0.6936112618438536, 0.14086831103305852], "is_merged": true}, {"index": 2, "shape": [2, 4, 1, 3], "angle": 30, "flip": "none", "color": [0.6408366795251199, 0.44684470588581293, 0.7884302557046777], "is_merged": false}], "results": ["", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n01\n01\n11\n11\n\nPiece C:\n11\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_3x3_inst1_var2_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"4",
"3",
"2",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst1/perturbed_part/3x3_inst1perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/perturbed_part/3x3_inst1perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/perturbed_part/3x3_inst1perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/perturbed_part/3x3_inst1perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/perturbed_part/3x3_inst1perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 1)."], "results": ["", "", "", "", "Over board"], "valid": false, "config": [{"index": 2, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [2, 3, 0, 2], "color": [0.6560169554382161, 0.08892499875961357, 0.2746181042425252]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.4502474416941842, 0.8486047097331468, 0.005901795236425311]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.256800880301729, 0.03751904073714318, 0.9621217613176958]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.14881909049605957, 0.9309150666944223, 0.2473442019032891]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_4x4_inst18_var4_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"6",
"5",
"4",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (3, 4).", "Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 90 degrees clockwise. Flip piece B vertically. Place piece B with its lower-left corner at (x,y) = (1, 4).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1)."], "valid": true, "config": [{"index": 2, "shape": [1, 3, 0, 2], "angle": 90, "flip": "none", "color": [0.3429060563864845, 0.9039302662351224, 0.4769621469089005], "is_merged": false}, {"index": 3, "shape": [0, 1, 0, 1], "angle": 90, "flip": "none", "color": [0.8949499330157833, 0.9775042345165299, 0.9215521124499638], "is_merged": false}, {"index": 1, "shape": [3, 4, 0, 3], "angle": 90, "flip": "vertical", "color": [0.9869982514704612, 0.32281939344324206, 0.8306345483609714], "is_merged": true}, {"index": 4, "shape": [[1, 3, 2, 3], [0, 1, 1, 4]], "angle": 30, "flip": "none", "color": [0.19883839915334045, 0.19820963751580922, 0.4332106091628175], "is_merged": false}, {"index": 0, "shape": [1, 4, 3, 4], "angle": 60, "flip": "none", "color": [0.1356106596338602, 0.9006559215808044, 0.9720273788893483], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\n\nPiece B:\n100\n111\n100\n\nPiece C:\n111\n\nPiece D:\n11\n11\n\nPiece E:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_4x4_inst5_var1_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"8",
"6",
"7",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_7.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (1, 3).", "Place piece A with its upper-left corner at (x,y) = (0, 1).", "Rotate piece G by about 30 degrees clockwise. Place piece G with its upper-left corner at (x,y) = (2, 4).", "Place piece B with its upper-left corner at (x,y) = (1, 1).", "Rotate piece F by about 60 degrees clockwise. Place piece F with its upper-left corner at (x,y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 1).", "Rotate piece E by about 60 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 3)."], "valid": true, "config": [{"index": 3, "shape": [0, 1, 0, 1], "angle": 30, "flip": "none", "color": [0.9240533250960073, 0.9819349600532725, 0.6747134014128692], "is_merged": false}, {"index": 0, "shape": [1, 3, 1, 2], "angle": 0, "flip": "none", "color": [0.7349991584173213, 0.6699660472482647, 0.43315305080703437], "is_merged": false}, {"index": 6, "shape": [[3, 4, 0, 2], [1, 3, 0, 1]], "angle": 30, "flip": "none", "color": [0.6662381683077349, 0.4371576487638136, 0.8074652784518175], "is_merged": false}, {"index": 1, "shape": [1, 3, 2, 4], "angle": 0, "flip": "none", "color": [0.26612579155187954, 0.07055091126826107, 0.08305000539925333], "is_merged": false}, {"index": 5, "shape": [0, 1, 2, 4], "angle": 60, "flip": "none", "color": [0.5397844496723473, 0.05872496894813528, 0.15399180068950846], "is_merged": true}, {"index": 2, "shape": [3, 4, 2, 4], "angle": 30, "flip": "none", "color": [0.6297825243848936, 0.49093541919773, 0.6669745716275061], "is_merged": false}, {"index": 4, "shape": [0, 1, 1, 2], "angle": 60, "flip": "none", "color": [0.22291133685432907, 0.48383465028816663, 0.5699125213630748], "is_merged": false}], "results": ["", "", "", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n\nPiece E:\n1\n\nPiece F:\n11\n10\n10\n\nPiece G:\n11\n10\n10\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_rotation_4x4_inst11_var0_q_only
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece C? Note that the label behind piece C indicates its dimensions (wxh).
<image_0>
|
A
|
rotation
|
[
"90 degrees counterclockwise",
"60 degrees counterclockwise",
"75 degrees counterclockwise",
"105 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.2617125427976732, 0.3180100977057472, 0.9938777587600973], "cell_center": [6.897114317029974, 7.5]}, {"index": 0, "angle": 30, "orig_width": 3, "orig_height": 2, "w": 3.598076211353316, "h": 3.232050807568877, "label": "3x2", "piece": [0, 2, 0, 3], "color": [0.590194494564307, 0.8146086514121477, 0.17186877412793822], "cell_center": [2.299038105676658, 7.5]}, {"index": 2, "angle": 90, "orig_width": 4, "orig_height": 2, "w": 2.0000000000000004, "h": 4.0, "label": "2x4", "piece": [2, 4, 0, 4], "color": [0.21016152453789094, 0.9415963033779045, 0.8255857971856693], "cell_center": [2.299038105676658, 2.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_3x3_inst15_var1_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"4",
"5",
"2",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst15/assembly/3x3_inst15assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/assembly/3x3_inst15assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/assembly/3x3_inst15assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/assembly/3x3_inst15assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/assembly/3x3_inst15assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 0, 2], "color": [0.910380989877349, 0.7228160858320822, 0.7740539608931295], "cell_center": [1.5, 4.5]}, {"index": 1, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 2, 3], "color": [0.5860967147337509, 0.19822060430604183, 0.7985991759604419], "cell_center": [4.5, 4.5]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.2824781693183691, 0.4391634637062619, 0.8730414057719783], "cell_center": [4.5, 1.5]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 0, 1], "color": [0.678651528421504, 0.2548722306191047, 0.7768283693786211], "cell_center": [1.5, 1.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n1\n\nPiece C:\n11\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_rotation_4x4_inst27_var4_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece A? Note that the label behind piece A indicates its dimensions (wxh).
<image_0>
|
A
|
rotation
|
[
"60 degrees counterclockwise",
"75 degrees counterclockwise",
"30 degrees counterclockwise",
"45 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [0, 3, 0, 1], "color": [0.7760512609454071, 0.23147233408575651, 0.09518146844402253]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.24455951613028104, 0.36845158724774063, 0.3057028634543797]}, {"index": 3, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.9816281227015189, 0.5664740351314982, 0.6376532394833729]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 3, "w": 4.098076211353316, "h": 4.098076211353316, "label": "3x3", "piece": [0, 3, 1, 4], "color": [0.3199404465463558, 0.3203558624653322, 0.7504705648122028]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n111\n111\n111\n\nPiece C:\n11\n\nPiece D:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_rotation_4x4_inst27_var4_q_only
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece D? Note that the label behind piece D indicates its dimensions (wxh).
<image_0>
|
A
|
rotation
|
[
"0 degrees (not rotated)",
"30 degrees counterclockwise",
"90 degrees counterclockwise",
"45 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [0, 3, 0, 1], "color": [0.7760512609454071, 0.23147233408575651, 0.09518146844402253]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.24455951613028104, 0.36845158724774063, 0.3057028634543797]}, {"index": 3, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.9816281227015189, 0.5664740351314982, 0.6376532394833729]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 3, "w": 4.098076211353316, "h": 4.098076211353316, "label": "3x3", "piece": [0, 3, 1, 4], "color": [0.3199404465463558, 0.3203558624653322, 0.7504705648122028]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n111\n111\n111\n\nPiece C:\n11\n\nPiece D:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_rotation_4x4_inst19_var2_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece A? Note that the label behind piece A indicates its dimensions (wxh).
<image_0>
|
D
|
rotation
|
[
"30 degrees counterclockwise",
"45 degrees counterclockwise",
"75 degrees counterclockwise",
"60 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.9646222808065529, 0.17286663433434668, 0.9197129911831481]}, {"index": 4, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.15548994568154517, 0.5175640932286619, 0.924036957862598]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.952951108351252, 0.41844418587893295, 0.20783217104778784]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.2136068442754907, 0.9077636730804951, 0.008593383588581083]}, {"index": 3, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [2, 4, 0, 3], "color": [0.8421463017266881, 0.998579446834601, 0.828081664466033]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nPiece D:\n11\n11\n11\n\nPiece E:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_rotation_4x4_inst23_var1_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece F? Note that the label behind piece F indicates its dimensions (wxh).
<image_0>
|
A
|
rotation
|
[
"0 degrees (not rotated)",
"45 degrees counterclockwise",
"30 degrees counterclockwise",
"90 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_6.png"], "instructions": ["", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "Overlap", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.9313701131443723, 0.8577776822629893, 0.1914255443977304]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 3, "w": 3.0, "h": 2.0, "label": "3x2", "piece": [0, 3, 0, 2], "color": [0.25815493806589496, 0.2761207462023175, 0.2168904413637872]}, {"index": 4, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.5986403619608208, 0.29107166733029166, 0.30497019909230927]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 1, 2], "color": [0.6716820917008354, 0.3773450251007877, 0.850605988039298]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.5175730479893074, 0.7209008156630139, 0.8339774749798693]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.2475030415730417, 0.8334016992404263, 0.08403143743189156]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst16_var2_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"3",
"1",
"4",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst16/irregular_assembly/3x3_inst16irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/irregular_assembly/3x3_inst16irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/irregular_assembly/3x3_inst16irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/irregular_assembly/3x3_inst16irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise. Flip piece B horizontally. Place piece B with its lower-left corner at (x,y) = (1, 3)."], "valid": true, "config": [{"index": 0, "shape": [1, 3, 0, 2], "angle": 30, "flip": "none", "color": [0.9976490339368843, 0.4943065670172001, 0.5594239487418055], "is_merged": false}, {"index": 2, "shape": [[1, 3, 2, 3], [0, 1, 1, 3]], "angle": 0, "flip": "none", "color": [0.10823406854150919, 0.5033344127325038, 0.9895981043015385], "is_merged": false}, {"index": 1, "shape": [0, 1, 0, 1], "angle": 30, "flip": "horizontal", "color": [0.9048699719372921, 0.07001798964152184, 0.5974823649881674], "is_merged": true}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n10\n10\n11\n\nPiece C:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_3x3_inst23_var2_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"6",
"4",
"5",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 1).", "Place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 4, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.33940213919128803, 0.15148877406439698, 0.5222835237729154]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.16858591960978841, 0.08544656496515068, 0.11494367118197413]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.6294248924659861, 0.3328326929596823, 0.09034406811739082]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [1, 2, 1, 2], "color": [0.9963442161344365, 0.11387330077903723, 0.2799037066005946]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.02981754658528879, 0.27867823105972955, 0.046516018756367794]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n11\n\nPiece E:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst65_var1_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"4",
"2",
"1",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst65/irregular_assembly/3x3_inst65invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst65/irregular_assembly/3x3_inst65invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst65/irregular_assembly/3x3_inst65invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3).", " Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (-1, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 1]], "angle": 60, "flip": "none", "color": [0.6887305068672642, 0.5235125564164917, 0.0026849863709283994], "is_merged": false}, {"index": 0, "shape": [1, 3, 1, 3], "angle": 0, "flip": "vertical", "color": [0.08381875718667964, 0.3054736611392068, 0.1470810697645728], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n010\n010\n\nPiece B:\n100\n100\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_4x4_inst27_var4_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"2",
"4",
"3",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [0, 3, 0, 1], "color": [0.7760512609454071, 0.23147233408575651, 0.09518146844402253]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.24455951613028104, 0.36845158724774063, 0.3057028634543797]}, {"index": 3, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.9816281227015189, 0.5664740351314982, 0.6376532394833729]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 3, "w": 4.098076211353316, "h": 4.098076211353316, "label": "3x3", "piece": [0, 3, 1, 4], "color": [0.3199404465463558, 0.3203558624653322, 0.7504705648122028]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n111\n111\n111\n\nPiece C:\n11\n\nPiece D:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst12_var0_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"2",
"5",
"3",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_part/3x3_inst12perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_part/3x3_inst12perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_part/3x3_inst12perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_part/3x3_inst12perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_part/3x3_inst12perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.7158111525953443, 0.3144750396327004, 0.9033798732112359]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.4602759030241912, 0.5263411433589661, 0.5878592840681638]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.9103403361123941, 0.38267590340608304, 0.7632217986287583]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 1, 3], "color": [0.946796380694129, 0.7835046474330913, 0.11945153897003868]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst73_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"4",
"3",
"2",
"1"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst73/irregular_assembly/3x3_inst73invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst73/irregular_assembly/3x3_inst73invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst73/irregular_assembly/3x3_inst73invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (-1, 3).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 0, 1], "angle": 60, "flip": "horizontal", "color": [0.28032694240971934, 0.7609637718701273, 0.7319630355183685], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 1, 3]], "angle": 90, "flip": "none", "color": [0.2129128502153539, 0.9356517806615614, 0.9542211766006211], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1100\n1100\n0111\n\nPiece B:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_rotation_3x3_inst26_var3_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece A? Note that the label behind piece A indicates its dimensions (wxh).
<image_0>
|
B
|
rotation
|
[
"105 degrees counterclockwise",
"90 degrees counterclockwise",
"75 degrees counterclockwise",
"60 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.769985114119021, 0.6023151000208017, 0.43905466192464926]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.8601757328506661, 0.8373920802150087, 0.4098927320047637]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.1762969342918307, 0.2700538547336413, 0.9959210428826512]}, {"index": 3, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.7902874398047327, 0.9053459516385535, 0.6109399886078966]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_size_count_3x3_inst40_var4_q_only
|
How many blocks (cells) are in piece B in the tangram puzzle shown below?
<image_0>
|
C
|
size_count
|
[
"2",
"6",
"4",
"7"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst40/irregular_assembly/3x3_inst40invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst40/irregular_assembly/3x3_inst40invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst40/irregular_assembly/3x3_inst40invalid_irregular_assembly_step_2.png"], "instructions": ["", " Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (-1, 2).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 1, 3], "angle": 0, "flip": "vertical", "color": [0.6182029536479532, 0.1028217441783712, 0.6005490533698828], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 1]], "angle": 90, "flip": "none", "color": [0.5687910254987621, 0.5142377944845191, 0.5258868534366733], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n010\n010\n\nPiece B:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_4x4_inst25_var4_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"2",
"5",
"3",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst25/perturbed_part/4x4_inst25perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/perturbed_part/4x4_inst25perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/perturbed_part/4x4_inst25perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/perturbed_part/4x4_inst25perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/perturbed_part/4x4_inst25perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "Over board", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 2, "angle": 90, "orig_width": 1, "orig_height": 4, "w": 4.0, "h": 1.0000000000000002, "label": "4x1", "piece": [2, 6, 0, 1], "color": [0.25574162196635564, 0.51986659658632, 0.7369240379748156]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.2200316360246839, 0.16174837472242654, 0.08603563855101859]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.9690186633818382, 0.9996354505529929, 0.019142756554478946]}, {"index": 0, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 0, 3], "color": [0.46767221164754547, 0.4767504561709347, 0.15453668427780887]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n1111\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_4x4_inst8_var4_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"6",
"7",
"5",
"8"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_7.png"], "instructions": ["", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece F with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 1).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3)."], "valid": true, "config": [{"index": 4, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.7918351590524052, 0.539204813032439, 0.47469005514533036], "cell_center": [6.147114317029974, 6.0]}, {"index": 1, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [0, 1, 1, 4], "color": [0.43734772906443453, 0.7140607992935755, 0.5214252728488368], "cell_center": [6.147114317029974, 10.0]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.6104741962438478, 0.7105984792563446, 0.35533199360146306], "cell_center": [2.049038105676658, 10.0]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.17104429060676052, 0.31991486174124684, 0.7751148512375546], "cell_center": [10.24519052838329, 6.0]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.2306122657446259, 0.821394282823099, 0.040689723719669946], "cell_center": [10.24519052838329, 10.0]}, {"index": 6, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.8441902472414256, 0.8605058939309127, 0.9086859759671123], "cell_center": [2.049038105676658, 2.0]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.4434074109775199, 0.09519571468722166, 0.1803872345266927], "cell_center": [2.049038105676658, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n1\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n1\n\nPiece F:\n1\n1\n\nPiece G:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_3x3_inst60_var2_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"3",
"1",
"4",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst60/irregular_assembly/3x3_inst60invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst60/irregular_assembly/3x3_inst60invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst60/irregular_assembly/3x3_inst60invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its lower-left corner at (x,y) = (-1, 3).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 0, 1], "angle": 60, "flip": "none", "color": [0.5082718059170319, 0.0373284384722552, 0.7317503068798865], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 1, 3]], "angle": 90, "flip": "none", "color": [0.45805212387171346, 0.8946682616964287, 0.9922983731162579], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n0011\n0011\n1110\n\nPiece B:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_rotation_4x4_inst16_var2_q_only
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece E? Note that the label behind piece E indicates its dimensions (wxh).
<image_0>
|
C
|
rotation
|
[
"75 degrees counterclockwise",
"30 degrees counterclockwise",
"60 degrees counterclockwise",
"45 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_5.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece E with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.2906409364547665, 0.18966064628256707, 0.16656066606481745]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.5772308670225175, 0.5432997569378035, 0.6895078587076925]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [1, 2, 1, 2], "color": [0.10552732137168419, 0.7961088453102383, 0.6833810431216795]}, {"index": 3, "angle": 60, "orig_width": 3, "orig_height": 2, "w": 3.2320508075688776, "h": 3.598076211353316, "label": "3x2", "piece": [2, 4, 0, 3], "color": [0.28731779180264194, 0.03647956859760171, 0.15648045527389287]}, {"index": 1, "angle": 0, "orig_width": 3, "orig_height": 2, "w": 3.0, "h": 2.0, "label": "3x2", "piece": [0, 2, 1, 4], "color": [0.6455578112263359, 0.04059609907027828, 0.9406976161672972]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n111\n111\n\nPiece C:\n1\n\nPiece D:\n111\n111\n\nPiece E:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_4x4_inst18_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"6",
"4",
"5",
"7"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_6.png"], "instructions": ["", "Place piece F with its upper-left corner at (x, y) = (0, 1).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 5, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.6952002937385011, 0.5451393144090627, 0.3598069443124001], "cell_center": [10.0, 1.8660254037844386]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.8949499330157833, 0.9775042345165299, 0.9215521124499638], "cell_center": [2.0, 1.8660254037844386]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 3, "w": 3.0, "h": 1.0000000000000002, "label": "3x1", "piece": [1, 4, 3, 4], "color": [0.19883839915334045, 0.19820963751580922, 0.4332106091628175], "cell_center": [6.0, 1.8660254037844386]}, {"index": 1, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.9869982514704612, 0.32281939344324206, 0.8306345483609714], "cell_center": [6.0, 5.598076211353316]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.1356106596338602, 0.9006559215808044, 0.9720273788893483], "cell_center": [2.0, 5.598076211353316]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.3429060563864845, 0.9039302662351224, 0.4769621469089005], "cell_center": [10.0, 5.598076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n111\n\nPiece F:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_3x3_inst30_var0_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"1",
"3",
"4",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst30/perturbed_part/3x3_inst30perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/perturbed_part/3x3_inst30perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/perturbed_part/3x3_inst30perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/perturbed_part/3x3_inst30perturbed_part_assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "Over board", "Overlap", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 60, "orig_width": 3, "orig_height": 3, "w": 4.098076211353316, "h": 4.098076211353316, "label": "3x3", "piece": [0, 3, 1, 4], "color": [0.9881484609812746, 0.3578709672961633, 0.9546513187032589]}, {"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.8886986770755988, 0.16381677715556997, 0.3911952313182817]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3898459914352054, 0.015125501920735585, 0.9748770770994594]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n111\n111\n111\n\nPiece C:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst27_var1_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"4",
"1",
"2",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst27/irregular_assembly/3x3_inst27invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/irregular_assembly/3x3_inst27invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/irregular_assembly/3x3_inst27invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 30, "flip": "vertical", "color": [0.604000330200972, 0.6770340247405751, 0.5551674092714912], "is_merged": true}, {"index": 0, "shape": [0, 2, 1, 3], "angle": 90, "flip": "none", "color": [0.17203857926331845, 0.4970169511811482, 0.5662534091810973], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n010\n010\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_3x3_inst22_var4_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"3",
"2",
"1",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst22/irregular_assembly/3x3_inst22irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/irregular_assembly/3x3_inst22irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/irregular_assembly/3x3_inst22irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/irregular_assembly/3x3_inst22irregular_assembly_step_3.png"], "instructions": ["", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 1).", " Flip piece B vertically. Place piece B with its lower-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 2, "shape": [[1, 3, 1, 3], [0, 1, 0, 2]], "angle": 0, "flip": "none", "color": [0.7857756960096848, 0.6067251586117914, 0.34088809144427157], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 90, "flip": "none", "color": [0.8710687100386045, 0.541800756938831, 0.8463220295003806], "is_merged": false}, {"index": 1, "shape": [0, 1, 2, 3], "angle": 0, "flip": "vertical", "color": [0.7625957197009988, 0.9880404381427733, 0.37197914191274184], "is_merged": true}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n110\n011\n011\n\nPiece C:\n011\n011\n110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_4x4_inst22_var2_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"5",
"3",
"4",
"6"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 3).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.11193829003358746, 0.30617434738153293, 0.40388324801152764]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.23279928245104486, 0.8588011204766025, 0.7142789177710182]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.5252542307964176, 0.9142936793495643, 0.8624907593395256]}, {"index": 0, "angle": 90, "orig_width": 4, "orig_height": 1, "w": 1.0000000000000002, "h": 4.0, "label": "1x4", "piece": [0, 1, 0, 4], "color": [0.482618038040181, 0.6865131363274936, 0.7698501288262459]}, {"index": 2, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [1, 3, 2, 5], "color": [0.9444237233564657, 0.633971880646935, 0.9884764278637307]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n11\n11\n\nPiece D:\n11\n11\n\nPiece E:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_4x4_inst3_var4_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"9",
"7",
"6",
"8"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/assembly/4x4_inst3assembly_step_8.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Place piece D with its upper-left corner at (x, y) = (1, 3).", "Place piece F with its upper-left corner at (x, y) = (1, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece G by about 90 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (2, 2).", "Rotate piece H by about 30 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 1, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.7422122588815101, 0.7551189736163385, 0.9234718311827813], "cell_center": [6.147114317029974, 8.415063509461097]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.6840121753279651, 0.8419883108103203, 0.07133341675213412], "cell_center": [6.147114317029974, 5.049038105676658]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.09413549272860999, 0.7680476368577523, 0.4128776322048002], "cell_center": [2.049038105676658, 5.049038105676658]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.4972346165255138, 0.8906984233290346, 0.7562452955907089], "cell_center": [10.24519052838329, 5.049038105676658]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.54590476492727, 0.8017288265026836, 0.19702177212746563], "cell_center": [2.049038105676658, 8.415063509461097]}, {"index": 6, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.6703174692655477, 0.09045368054856773, 0.1109174370728383], "cell_center": [2.049038105676658, 1.6830127018922192]}, {"index": 7, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.713590518367683, 0.3036182518548164, 0.1397252722702369], "cell_center": [6.147114317029974, 1.6830127018922192]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.9449625741817751, 0.10699177732051413, 0.906832733107004], "cell_center": [10.24519052838329, 8.415063509461097]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n1\n1\n\nPiece D:\n11\n\nPiece E:\n1\n\nPiece F:\n1\n1\n\nPiece G:\n11\n11\n\nPiece H:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_4x4_inst8_var3_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"4",
"7",
"5",
"6"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_6.png"], "instructions": ["", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece F by about 30 degrees clockwise. Place piece F with its upper-left corner at (x,y) = (3, 4).", "Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (3, 2).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 1).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 2, "shape": [0, 1, 1, 4], "angle": 0, "flip": "none", "color": [0.2306122657446259, 0.821394282823099, 0.040689723719669946], "is_merged": false}, {"index": 5, "shape": [[3, 4, 0, 3], [1, 3, 2, 3]], "angle": 30, "flip": "none", "color": [0.17104429060676052, 0.31991486174124684, 0.7751148512375546], "is_merged": false}, {"index": 3, "shape": [1, 2, 3, 4], "angle": 60, "flip": "none", "color": [0.4434074109775199, 0.09519571468722166, 0.1803872345266927], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 90, "flip": "none", "color": [0.6104741962438478, 0.7105984792563446, 0.35533199360146306], "is_merged": false}, {"index": 1, "shape": [0, 1, 0, 1], "angle": 90, "flip": "none", "color": [0.43734772906443453, 0.7140607992935755, 0.5214252728488368], "is_merged": false}, {"index": 4, "shape": [2, 4, 3, 4], "angle": 30, "flip": "none", "color": [0.7918351590524052, 0.539204813032439, 0.47469005514533036], "is_merged": true}], "results": ["", "", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n1\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n1\n\nPiece E:\n111\n001\n001\n\nPiece F:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_size_count_3x3_inst67_var1_q_only
|
How many blocks (cells) are in piece A in the tangram puzzle shown below?
<image_0>
|
A
|
size_count
|
[
"2",
"5",
"1",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst67/irregular_assembly/3x3_inst67invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst67/irregular_assembly/3x3_inst67invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst67/irregular_assembly/3x3_inst67invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 3).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 30, "flip": "horizontal", "color": [0.011555386923828292, 0.38856667577712833, 0.5580544451581476], "is_merged": true}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 30, "flip": "none", "color": [0.610168984685911, 0.8861242806116434, 0.5519982870011023], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n0111\n1100\n1100\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_4x4_inst3_var1_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"6",
"7",
"8",
"9"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_8.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece H by about 60 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Place piece F with its upper-left corner at (x, y) = (1, 2).", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "", "", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.54590476492727, 0.8017288265026836, 0.19702177212746563], "cell_center": [1.8660254037844386, 10.24519052838329]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.7422122588815101, 0.7551189736163385, 0.9234718311827813], "cell_center": [5.598076211353316, 10.24519052838329]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.09413549272860999, 0.7680476368577523, 0.4128776322048002], "cell_center": [9.330127018922193, 10.24519052838329]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.9449625741817751, 0.10699177732051413, 0.906832733107004], "cell_center": [1.8660254037844386, 6.147114317029974]}, {"index": 7, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.713590518367683, 0.3036182518548164, 0.1397252722702369], "cell_center": [5.598076211353316, 6.147114317029974]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.6840121753279651, 0.8419883108103203, 0.07133341675213412], "cell_center": [9.330127018922193, 6.147114317029974]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.4972346165255138, 0.8906984233290346, 0.7562452955907089], "cell_center": [1.8660254037844386, 2.049038105676658]}, {"index": 6, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.6703174692655477, 0.09045368054856773, 0.1109174370728383], "cell_center": [5.598076211353316, 2.049038105676658]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_3x3_inst30_var1_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"1",
"2",
"3",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 0, "flip": "none", "color": [0.3898459914352054, 0.015125501920735585, 0.9748770770994594], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 30, "flip": "none", "color": [0.9881484609812746, 0.3578709672961633, 0.9546513187032589], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n1110\n0011\n0011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_4x4_inst30_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"6",
"5",
"7",
"8"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_7.png"], "instructions": ["", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (1, 1).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 3).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 3).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "", "Overlap", "Overlap", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 6, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [3, 4, 1, 4], "color": [0.3925122716097921, 0.08314977817411329, 0.23188307859675394]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.868250353967598, 0.8718178531170512, 0.8044667206493435]}, {"index": 3, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.8519142300537066, 0.5805075864102989, 0.9259830837764971]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.3656083002105275, 0.47581511365521845, 0.6183891885528554]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.05693842955173811, 0.9065171787135644, 0.309832012336156]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 3, "w": 2.3660254037844384, "h": 3.098076211353316, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.16483746954885847, 0.051758929606153026, 0.12492630379800751]}, {"index": 0, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.9035591471762607, 0.11970560100617034, 0.4855676628213387]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n1\n1\n1\n\nPiece C:\n1\n1\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nPiece F:\n1\n\nPiece G:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst13_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"5",
"4",
"2",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_step/3x3_inst13perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_step/3x3_inst13perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_step/3x3_inst13perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_step/3x3_inst13perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_step/3x3_inst13perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Place piece B with its upper-left corner at (x, y) = (3, 2)."], "results": ["", "", "", "", "Over board"], "valid": false, "config": [{"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.45262734202882937, 0.5605337595606488, 0.8098850090862545], "cell_center": [1.8660254037844386, 5.598076211353316]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.5025023117046901, 0.20679137664564085, 0.35368716180716764], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.4122246781876865, 0.46099712359888834, 0.029808170513958232], "cell_center": [1.8660254037844386, 1.8660254037844386]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.4167436538845991, 0.3774938048911445, 0.3463506332117947], "cell_center": [5.598076211353316, 1.8660254037844386]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_3x3_inst14_var1_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"3",
"4",
"1",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst14/irregular_assembly/3x3_inst14irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/irregular_assembly/3x3_inst14irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/irregular_assembly/3x3_inst14irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 0, "shape": [1, 3, 0, 1], "angle": 30, "flip": "horizontal", "color": [0.6986416373362043, 0.39103013274436993, 0.7338256355090964], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 1, 3]], "angle": 30, "flip": "none", "color": [0.7375466272024475, 0.7958785429353309, 0.9602750500929624], "is_merged": false}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n110\n110\n111\n\nPiece B:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_4x4_inst15_var2_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"4",
"3",
"5",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst15/irregular_assembly/4x4_inst15irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/irregular_assembly/4x4_inst15irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/irregular_assembly/4x4_inst15irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/irregular_assembly/4x4_inst15irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/irregular_assembly/4x4_inst15irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 4).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 2).", "Rotate piece B by about 30 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 4).", "Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (2, 4)."], "valid": true, "config": [{"index": 2, "shape": [2, 4, 2, 4], "angle": 30, "flip": "none", "color": [0.13557809727733983, 0.7545597463569302, 0.3732963496374987], "is_merged": false}, {"index": 0, "shape": [0, 2, 2, 4], "angle": 30, "flip": "none", "color": [0.4523784950258848, 0.5966474216563278, 0.4209460701703134], "is_merged": false}, {"index": 1, "shape": [2, 4, 1, 2], "angle": 30, "flip": "vertical", "color": [0.38174873155304245, 0.8750272159825754, 0.7170741611088424], "is_merged": true}, {"index": 3, "shape": [[0, 2, 0, 2], [2, 4, 0, 1]], "angle": 90, "flip": "none", "color": [0.4240667615814787, 0.7222327073498909, 0.6054485127949952], "is_merged": false}], "results": ["", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n11\n10\n10\n\nPiece C:\n1\n1\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_rotation_4x4_inst25_var2_q_only
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece A? Note that the label behind piece A indicates its dimensions (wxh).
<image_0>
|
A
|
rotation
|
[
"90 degrees counterclockwise",
"60 degrees counterclockwise",
"105 degrees counterclockwise",
"75 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst25/assembly/4x4_inst25assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/assembly/4x4_inst25assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/assembly/4x4_inst25assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/assembly/4x4_inst25assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/assembly/4x4_inst25assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "valid": true, "config": [{"index": 2, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 0, 2], "color": [0.25574162196635564, 0.51986659658632, 0.7369240379748156], "cell_center": [1.8660254037844388, 2.0]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.9690186633818382, 0.9996354505529929, 0.019142756554478946], "cell_center": [5.598076211353316, 2.0]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.2200316360246839, 0.16174837472242654, 0.08603563855101859], "cell_center": [5.598076211353316, 6.0]}, {"index": 0, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 0, 3], "color": [0.46767221164754547, 0.4767504561709347, 0.15453668427780887], "cell_center": [1.8660254037844388, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_4x4_inst1_var0_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"4",
"5",
"6",
"7"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst1/assembly/4x4_inst1assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst1/assembly/4x4_inst1assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst1/assembly/4x4_inst1assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst1/assembly/4x4_inst1assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst1/assembly/4x4_inst1assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst1/assembly/4x4_inst1assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst1/assembly/4x4_inst1assembly_step_6.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 4).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1)."], "valid": true, "config": [{"index": 3, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [2, 3, 1, 4], "color": [0.29597082072739067, 0.44809929338734733, 0.6881087446134356], "cell_center": [2.0, 2.049038105676658]}, {"index": 4, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [3, 4, 0, 2], "color": [0.13799246151005418, 0.8543080443892493, 0.24339036992847662], "cell_center": [6.0, 2.049038105676658]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 3, "w": 3.0, "h": 1.0000000000000002, "label": "3x1", "piece": [0, 3, 0, 1], "color": [0.33356625224597825, 0.8251586315847872, 0.9977506524222988], "cell_center": [2.0, 6.147114317029974]}, {"index": 1, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 1, 2], "color": [0.2708162857112263, 0.34824512961383103, 0.6894047673252708], "cell_center": [6.0, 6.147114317029974]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.37595342334832693, 0.6861020575940404, 0.15051798252162207], "cell_center": [10.0, 6.147114317029974]}, {"index": 5, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [3, 4, 2, 4], "color": [0.269630185073346, 0.43741849728502513, 0.119444847905815], "cell_center": [10.0, 2.049038105676658]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nPiece D:\n111\n\nPiece E:\n1\n1\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_4x4_inst43_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"3",
"4",
"5",
"6"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst43/irregular_assembly/4x4_inst43invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst43/irregular_assembly/4x4_inst43invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst43/irregular_assembly/4x4_inst43invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst43/irregular_assembly/4x4_inst43invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst43/irregular_assembly/4x4_inst43invalid_irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst43/irregular_assembly/4x4_inst43invalid_irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 2).", "Rotate piece D by about 60 degrees clockwise. Flip piece D vertically. Place piece D with its lower-left corner at (x,y) = (-1, 4).", "Place piece A with its upper-left corner at (x,y) = (3, 3).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 2)."], "results": ["", "", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 4, "shape": [[2, 3, 0, 3], [3, 4, 1, 4]], "angle": 30, "flip": "none", "color": [0.8509942939181611, 0.09883955340701012, 0.9289732116702049], "is_merged": false}, {"index": 2, "shape": [0, 2, 2, 3], "angle": 90, "flip": "none", "color": [0.4787266393837585, 0.07786004745984676, 0.1679346694893925], "is_merged": false}, {"index": 3, "shape": [3, 4, 0, 1], "angle": 60, "flip": "vertical", "color": [0.5503005880112162, 0.8722009951957114, 0.6238973504309171], "is_merged": true}, {"index": 0, "shape": [0, 3, 3, 4], "angle": 0, "flip": "none", "color": [0.9038922812005301, 0.0021875078414586024, 0.8961722465924689], "is_merged": false}, {"index": 1, "shape": [0, 2, 0, 2], "angle": 30, "flip": "none", "color": [0.13491365473075523, 0.4983322558083467, 0.5584003125352645], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n11100\n00111\n\nPiece E:\n0111\n1110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_rotation_4x4_inst29_var0_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece D? Note that the label behind piece D indicates its dimensions (wxh).
<image_0>
|
D
|
rotation
|
[
"30 degrees counterclockwise",
"90 degrees counterclockwise",
"45 degrees counterclockwise",
"0 degrees (not rotated)"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_6.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1).", "Place piece C with its upper-left corner at (x, y) = (3, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "Over board", "Overlap", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.5891291035296236, 0.3497096728096557, 0.9163403319569924]}, {"index": 4, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [3, 5, 0, 3], "color": [0.9906664263285482, 0.5961649832123572, 0.09772349038033212]}, {"index": 5, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [3, 4, 2, 4], "color": [0.6488651399575482, 0.3550425908569148, 0.6083596641075071]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 3, "w": 2.3660254037844384, "h": 3.098076211353316, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.5990452770695724, 0.8191791111282444, 0.6830708139237405]}, {"index": 3, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.9741545288927297, 0.34746803917361757, 0.23806606283364473]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.9543183423703964, 0.16273279693061327, 0.4214676188543469]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n1\n\nPiece D:\n111\n\nPiece E:\n11\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_4x4_inst29_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"6",
"7",
"4",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_6.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1).", "Place piece C with its upper-left corner at (x, y) = (3, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "Over board", "Overlap", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.5891291035296236, 0.3497096728096557, 0.9163403319569924]}, {"index": 4, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [3, 5, 0, 3], "color": [0.9906664263285482, 0.5961649832123572, 0.09772349038033212]}, {"index": 5, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [3, 4, 2, 4], "color": [0.6488651399575482, 0.3550425908569148, 0.6083596641075071]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 3, "w": 2.3660254037844384, "h": 3.098076211353316, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.5990452770695724, 0.8191791111282444, 0.6830708139237405]}, {"index": 3, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.9741545288927297, 0.34746803917361757, 0.23806606283364473]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.9543183423703964, 0.16273279693061327, 0.4214676188543469]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n1\n\nPiece D:\n111\n\nPiece E:\n11\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst11_var1_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"1",
"3",
"4",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst11/irregular_assembly/3x3_inst11irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst11/irregular_assembly/3x3_inst11irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst11/irregular_assembly/3x3_inst11irregular_assembly_step_2.png"], "instructions": ["", " Flip piece A horizontally. Place piece A with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3)."], "valid": true, "config": [{"index": 0, "shape": [1, 3, 1, 3], "angle": 0, "flip": "horizontal", "color": [0.20466808994905894, 0.704066164831489, 0.6231877093078216], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 1]], "angle": 60, "flip": "none", "color": [0.10167857717644269, 0.8327584618892119, 0.8500740367164027], "is_merged": false}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n001\n001\n111\n\nPiece B:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_size_count_4x4_inst53_var0_q_only
|
How many blocks (cells) are in piece B in the tangram puzzle shown below?
<image_0>
|
A
|
size_count
|
[
"14",
"13",
"11",
"12"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst53/irregular_assembly/4x4_inst53invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst53/irregular_assembly/4x4_inst53invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst53/irregular_assembly/4x4_inst53invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 4).", "Place piece A with its upper-left corner at (x,y) = (0, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[2, 4, 0, 4], [0, 2, 1, 4]], "angle": 30, "flip": "none", "color": [0.5703411072949541, 0.4675093349253865, 0.059971239841069], "is_merged": true}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 0, "flip": "none", "color": [0.6171011853051268, 0.4159916646382219, 0.32416928134320555], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11110\n11110\n00111\n00111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_3x3_inst39_var3_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"2",
"1",
"4",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst39/irregular_assembly/3x3_inst39invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst39/irregular_assembly/3x3_inst39invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst39/irregular_assembly/3x3_inst39invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its upper-left corner at (x,y) = (0, 3).", "Place piece B with its upper-left corner at (x,y) = (2, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 60, "flip": "horizontal", "color": [0.4889016189467239, 0.8044606918775942, 0.790149600882282], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 2]], "angle": 0, "flip": "none", "color": [0.8739555335428091, 0.4336653277817235, 0.5821465473107338], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n0011\n0011\n1110\n\nPiece B:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_4x4_inst11_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"1",
"4",
"3",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.2617125427976732, 0.3180100977057472, 0.9938777587600973], "cell_center": [6.897114317029974, 7.5]}, {"index": 0, "angle": 30, "orig_width": 3, "orig_height": 2, "w": 3.598076211353316, "h": 3.232050807568877, "label": "3x2", "piece": [0, 2, 0, 3], "color": [0.590194494564307, 0.8146086514121477, 0.17186877412793822], "cell_center": [2.299038105676658, 7.5]}, {"index": 2, "angle": 90, "orig_width": 4, "orig_height": 2, "w": 2.0000000000000004, "h": 4.0, "label": "2x4", "piece": [2, 4, 0, 4], "color": [0.21016152453789094, 0.9415963033779045, 0.8255857971856693], "cell_center": [2.299038105676658, 2.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_4x4_inst15_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"4",
"5",
"7",
"6"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst15/perturbed_part/4x4_inst15perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/perturbed_part/4x4_inst15perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/perturbed_part/4x4_inst15perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/perturbed_part/4x4_inst15perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/perturbed_part/4x4_inst15perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/perturbed_part/4x4_inst15perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/perturbed_part/4x4_inst15perturbed_part_assembly_step_6.png"], "instructions": ["", "Place piece F with its upper-left corner at (x, y) = (2, 2).", "Place piece C with its upper-left corner at (x, y) = (2, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 5, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.8124363601454803, 0.8725077509105843, 0.04463369307200571]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.13557809727733983, 0.7545597463569302, 0.3732963496374987]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [2, 4, 0, 1], "color": [0.4240667615814787, 0.7222327073498909, 0.6054485127949952]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.38174873155304245, 0.8750272159825754, 0.7170741611088424]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.29106684612422073, 0.3972090277120738, 0.0043544742627775745]}, {"index": 0, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.4523784950258848, 0.5966474216563278, 0.4209460701703134]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n11\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n1\n1\n\nPiece F:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_rotation_4x4_inst24_var3_q_only
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece D? Note that the label behind piece D indicates its dimensions (wxh).
<image_0>
|
C
|
rotation
|
[
"60 degrees counterclockwise",
"105 degrees counterclockwise",
"90 degrees counterclockwise",
"75 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/assembly/4x4_inst24assembly_step_5.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "valid": true, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 3, "w": 1.0, "h": 3.0, "label": "1x3", "piece": [0, 3, 0, 1], "color": [0.34673327216917005, 0.3823052678152453, 0.04807869538996756], "cell_center": [1.5, 7.5]}, {"index": 4, "angle": 90, "orig_width": 4, "orig_height": 1, "w": 1.0000000000000002, "h": 4.0, "label": "1x4", "piece": [3, 4, 0, 4], "color": [0.49317056051473784, 0.9208343917888762, 0.5319936589671153], "cell_center": [4.5, 2.5]}, {"index": 3, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 1, 4], "color": [0.667451459773487, 0.609690672977065, 0.9690305764874845], "cell_center": [1.5, 2.5]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 3, 4], "color": [0.3941478645364662, 0.07242735131670541, 0.6221981028733828], "cell_center": [7.5, 7.5]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.34499076168116316, 0.3941488900507818, 0.035379367870832845], "cell_center": [4.5, 7.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n1\n1\n\nPiece E:\n1\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_size_count_3x3_inst69_var4_q_only
|
How many blocks (cells) are in piece A in the tangram puzzle shown below?
<image_0>
|
B
|
size_count
|
[
"4",
"5",
"6",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst69/irregular_assembly/3x3_inst69invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst69/irregular_assembly/3x3_inst69invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst69/irregular_assembly/3x3_inst69invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 0, "flip": "none", "color": [0.8289271958121602, 0.2874252866675162, 0.18696413859663752], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 30, "flip": "vertical", "color": [0.8091960335687763, 0.16612470580039684, 0.5513661647674789], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n010\n010\n\nPiece B:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_3x3_inst23_var4_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"5",
"3",
"2",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst23/assembly/3x3_inst23assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/assembly/3x3_inst23assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/assembly/3x3_inst23assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/assembly/3x3_inst23assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/assembly/3x3_inst23assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 1).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1)."], "valid": true, "config": [{"index": 3, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.16858591960978841, 0.08544656496515068, 0.11494367118197413], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.6294248924659861, 0.3328326929596823, 0.09034406811739082], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.02981754658528879, 0.27867823105972955, 0.046516018756367794], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.9963442161344365, 0.11387330077903723, 0.2799037066005946], "cell_center": [1.8660254037844388, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_rotation_3x3_inst0_var3_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece A? Note that the label behind piece A indicates its dimensions (wxh).
<image_0>
|
C
|
rotation
|
[
"45 degrees counterclockwise",
"30 degrees counterclockwise",
"60 degrees counterclockwise",
"75 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst0/perturbed_part/3x3_inst0perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/perturbed_part/3x3_inst0perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/perturbed_part/3x3_inst0perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/perturbed_part/3x3_inst0perturbed_part_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 2, "orig_height": 3, "w": 3.598076211353316, "h": 3.2320508075688776, "label": "2x3", "piece": [0, 3, 0, 2], "color": [0.5107935611666639, 0.5856039458335469, 0.7112698396749424]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.3256280422330665, 0.5203129240964942, 0.7395819324105462]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.8422134984480056, 0.15250547228228883, 0.5324273953128456]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n\nPiece B:\n11\n11\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_4x4_inst30_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"6",
"4",
"7",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_6.png"], "instructions": ["", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 1).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (3, 3)."], "results": ["", "", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 4, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.3656083002105275, 0.47581511365521845, 0.6183891885528554], "cell_center": [2.0, 6.147114317029974]}, {"index": 0, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.9035591471762607, 0.11970560100617034, 0.4855676628213387], "cell_center": [6.0, 6.147114317029974]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.868250353967598, 0.8718178531170512, 0.8044667206493435], "cell_center": [10.0, 6.147114317029974]}, {"index": 5, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "3x1", "piece": [3, 4, 1, 4], "color": [0.05693842955173811, 0.9065171787135644, 0.309832012336156], "cell_center": [2.0, 2.049038105676658]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 3, "w": 2.3660254037844384, "h": 3.098076211353316, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.16483746954885847, 0.051758929606153026, 0.12492630379800751], "cell_center": [6.0, 2.049038105676658]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.8519142300537066, 0.5805075864102989, 0.9259830837764971], "cell_center": [10.0, 2.049038105676658]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_3x3_inst5_var2_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"4",
"3",
"2",
"1"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", " Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 0, 2], "angle": 90, "flip": "none", "color": [0.07357053851548412, 0.9733870202483494, 0.6618987325140707], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 2, 3]], "angle": 0, "flip": "vertical", "color": [0.445111390892756, 0.16653115882702152, 0.8213500363599643], "is_merged": true}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_3x3_inst14_var1_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"4",
"3",
"1",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst14/irregular_assembly/3x3_inst14irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/irregular_assembly/3x3_inst14irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/irregular_assembly/3x3_inst14irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 0, "shape": [1, 3, 0, 1], "angle": 30, "flip": "horizontal", "color": [0.6986416373362043, 0.39103013274436993, 0.7338256355090964], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 1, 3]], "angle": 30, "flip": "none", "color": [0.7375466272024475, 0.7958785429353309, 0.9602750500929624], "is_merged": false}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n110\n110\n111\n\nPiece B:\n011\n011\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_3x3_inst24_var3_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"1",
"4",
"3",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst24/assembly/3x3_inst24assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/assembly/3x3_inst24assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/assembly/3x3_inst24assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/assembly/3x3_inst24assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [0, 1, 0, 3], "color": [0.7128663156774877, 0.20321597181862183, 0.6465282105669317], "cell_center": [1.8660254037844386, 6.0]}, {"index": 1, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.3668565042280403, 0.7544321568579433, 0.022670156613330716], "cell_center": [5.598076211353316, 6.0]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.2714532942394723, 0.8400670830912441, 0.3547580632505397], "cell_center": [1.8660254037844386, 2.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_3x3_inst28_var4_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"4",
"2",
"1",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst28/assembly/3x3_inst28assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/assembly/3x3_inst28assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/assembly/3x3_inst28assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/assembly/3x3_inst28assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [0, 1, 0, 3], "color": [0.24874432956275316, 0.10459104781785566, 0.290015710844736], "cell_center": [1.8660254037844388, 6.0]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.08038459038445755, 0.7628332166932088, 0.014888669554417922], "cell_center": [1.8660254037844388, 2.0]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.5629568688202203, 0.21307617484959096, 0.3881604215827764], "cell_center": [5.598076211353316, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"}
|
|
tangram_perception_count_4x4_inst8_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"6",
"5",
"7",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/irregular_assembly/4x4_inst8irregular_assembly_step_6.png"], "instructions": ["", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece F by about 30 degrees clockwise. Place piece F with its upper-left corner at (x,y) = (3, 4).", "Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (3, 2).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 1).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 2, "shape": [0, 1, 1, 4], "angle": 0, "flip": "none", "color": [0.2306122657446259, 0.821394282823099, 0.040689723719669946], "is_merged": false}, {"index": 5, "shape": [[3, 4, 0, 3], [1, 3, 2, 3]], "angle": 30, "flip": "none", "color": [0.17104429060676052, 0.31991486174124684, 0.7751148512375546], "is_merged": false}, {"index": 3, "shape": [1, 2, 3, 4], "angle": 60, "flip": "none", "color": [0.4434074109775199, 0.09519571468722166, 0.1803872345266927], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 90, "flip": "none", "color": [0.6104741962438478, 0.7105984792563446, 0.35533199360146306], "is_merged": false}, {"index": 1, "shape": [0, 1, 0, 1], "angle": 90, "flip": "none", "color": [0.43734772906443453, 0.7140607992935755, 0.5214252728488368], "is_merged": false}, {"index": 4, "shape": [2, 4, 3, 4], "angle": 30, "flip": "none", "color": [0.7918351590524052, 0.539204813032439, 0.47469005514533036], "is_merged": true}], "results": ["", "", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n\nPiece C:\n111\n\nPiece D:\n1\n\nPiece E:\n111\n001\n001\n\nPiece F:\n111\n001\n001\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_3x3_inst55_var4_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"2",
"3",
"1",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst55/irregular_assembly/3x3_inst55invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst55/irregular_assembly/3x3_inst55invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst55/irregular_assembly/3x3_inst55invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece A with its lower-left corner at (x,y) = (1, 4).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 0, 2], "angle": 0, "flip": "none", "color": [0.9123528570556101, 0.7630357217740212, 0.9404631597785433], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 60, "flip": "none", "color": [0.23979007488546733, 0.8736367172923079, 0.6619995780562954], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n010\n010\n111\n\nPiece B:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_size_count_3x3_inst2_var1_q_only
|
How many blocks (cells) are in piece A in the tangram puzzle shown below?
<image_0>
|
B
|
size_count
|
[
"2",
"4",
"6",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2).", " Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 1, 3], "angle": 90, "flip": "none", "color": [0.12351699744789202, 0.5664729497490351, 0.624512595749913], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 0, "flip": "vertical", "color": [0.12655138063137172, 0.33097078814054737, 0.7001299158222172], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n010\n010\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_rotation_4x4_inst16_var2_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece E? Note that the label behind piece E indicates its dimensions (wxh).
<image_0>
|
D
|
rotation
|
[
"75 degrees counterclockwise",
"45 degrees counterclockwise",
"30 degrees counterclockwise",
"60 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_5.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece E with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.2906409364547665, 0.18966064628256707, 0.16656066606481745]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.5772308670225175, 0.5432997569378035, 0.6895078587076925]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [1, 2, 1, 2], "color": [0.10552732137168419, 0.7961088453102383, 0.6833810431216795]}, {"index": 3, "angle": 60, "orig_width": 3, "orig_height": 2, "w": 3.2320508075688776, "h": 3.598076211353316, "label": "3x2", "piece": [2, 4, 0, 3], "color": [0.28731779180264194, 0.03647956859760171, 0.15648045527389287]}, {"index": 1, "angle": 0, "orig_width": 3, "orig_height": 2, "w": 3.0, "h": 2.0, "label": "3x2", "piece": [0, 2, 1, 4], "color": [0.6455578112263359, 0.04059609907027828, 0.9406976161672972]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n111\n111\n\nPiece C:\n1\n\nPiece D:\n111\n111\n\nPiece E:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst29_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"2",
"4",
"1",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst29/irregular_assembly/3x3_inst29irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst29/irregular_assembly/3x3_inst29irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst29/irregular_assembly/3x3_inst29irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 30, "flip": "none", "color": [0.5587780227736063, 0.37341366971430356, 0.25392528265228476], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 30, "flip": "vertical", "color": [0.16908974540263644, 0.9028171146233334, 0.20691211710600244], "is_merged": true}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n001\n001\n\nPiece B:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_rotation_3x3_inst6_var0_q+steps
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece B? Note that the label behind piece B indicates its dimensions (wxh).
<image_0>
|
B
|
rotation
|
[
"45 degrees counterclockwise",
"60 degrees counterclockwise",
"75 degrees counterclockwise",
"30 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst6/perturbed_step/3x3_inst6perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/perturbed_step/3x3_inst6perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/perturbed_step/3x3_inst6perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/perturbed_step/3x3_inst6perturbed_step_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece C with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.10309243167421278, 0.24076261322195902, 0.2100689922963226], "cell_center": [2.0, 4.5]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.1586208137251468, 0.12393853736495797, 0.8716693278560734], "cell_center": [6.0, 4.5]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 2, 3], "color": [0.6512655327908536, 0.8401929301826332, 0.8460989766654483], "cell_center": [2.0, 1.5]}], "variant": "perturbed_step"}
|
|
tangram_perception_rotation_4x4_inst23_var1_q_only
|
Looking at the tangram puzzle shown below, what is the approximate rotation angle of piece B? Note that the label behind piece B indicates its dimensions (wxh).
<image_0>
|
D
|
rotation
|
[
"30 degrees counterclockwise",
"90 degrees counterclockwise",
"45 degrees counterclockwise",
"0 degrees (not rotated)"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_part/4x4_inst23perturbed_part_assembly_step_6.png"], "instructions": ["", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "Overlap", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.9313701131443723, 0.8577776822629893, 0.1914255443977304]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 3, "w": 3.0, "h": 2.0, "label": "3x2", "piece": [0, 3, 0, 2], "color": [0.25815493806589496, 0.2761207462023175, 0.2168904413637872]}, {"index": 4, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.5986403619608208, 0.29107166733029166, 0.30497019909230927]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 1, 2], "color": [0.6716820917008354, 0.3773450251007877, 0.850605988039298]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.5175730479893074, 0.7209008156630139, 0.8339774749798693]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.2475030415730417, 0.8334016992404263, 0.08403143743189156]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_4x4_inst19_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"4",
"2",
"5",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst19/irregular_assembly/4x4_inst19irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/irregular_assembly/4x4_inst19irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/irregular_assembly/4x4_inst19irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/irregular_assembly/4x4_inst19irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/irregular_assembly/4x4_inst19irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 1).", "Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).", "Place piece B with its lower-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 0, "shape": [3, 4, 0, 4], "angle": 60, "flip": "none", "color": [0.952951108351252, 0.41844418587893295, 0.20783217104778784], "is_merged": false}, {"index": 2, "shape": [0, 1, 2, 4], "angle": 60, "flip": "none", "color": [0.9646222808065529, 0.17286663433434668, 0.9197129911831481], "is_merged": false}, {"index": 3, "shape": [[0, 2, 0, 2], [1, 3, 2, 4]], "angle": 90, "flip": "none", "color": [0.8421463017266881, 0.998579446834601, 0.828081664466033], "is_merged": false}, {"index": 1, "shape": [2, 3, 0, 2], "angle": 0, "flip": "none", "color": [0.2136068442754907, 0.9077636730804951, 0.008593383588581083], "is_merged": true}], "results": ["", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n0011\n1111\n1100\n\nPiece C:\n11\n\nPiece D:\n110\n110\n011\n011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_4x4_inst27_var0_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"4",
"2",
"3",
"1"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst27/irregular_assembly/4x4_inst27invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/irregular_assembly/4x4_inst27invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/irregular_assembly/4x4_inst27invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 3).", "Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 3, 1, 4], "angle": 30, "flip": "none", "color": [0.7760512609454071, 0.23147233408575651, 0.09518146844402253], "is_merged": false}, {"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 0, 1]], "angle": 60, "flip": "horizontal", "color": [0.3199404465463558, 0.3203558624653322, 0.7504705648122028], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n111\n\nPiece B:\n1111\n0010\n0010\n0010\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_count_3x3_inst5_var2_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"3",
"2",
"1",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", " Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 0, 2], "angle": 90, "flip": "none", "color": [0.07357053851548412, 0.9733870202483494, 0.6618987325140707], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 2, 3]], "angle": 0, "flip": "vertical", "color": [0.445111390892756, 0.16653115882702152, 0.8213500363599643], "is_merged": true}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
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