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tangram_perception_count_3x3_inst51_var1_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_inst51/irregular_assembly/3x3_inst51invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst51/irregular_assembly/3x3_inst51invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst51/irregular_assembly/3x3_inst51invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece A with its lower-left corner at (x,y) = (-1, 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": [1, 3, 1, 3], "angle": 0, "flip": "none", "color": [0.40689195324775196, 0.7058968636250846, 0.663090640236535], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 1]], "angle": 30, "flip": "none", "color": [0.13194803812894373, 0.9500586037165758, 0.32796267315159777], "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_count_4x4_inst25_var2_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"2",
"5",
"4",
"3"
] |
{"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_3x3_inst3_var2_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"5",
"3",
"4",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_part/3x3_inst3perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_part/3x3_inst3perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_part/3x3_inst3perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_part/3x3_inst3perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_part/3x3_inst3perturbed_part_assembly_step_4.png"], "instructions": ["", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "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).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "", "Over board"], "valid": false, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.17413619213984544, 0.539393258896573, 0.7469777807902688]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.16349340438282878, 0.21139582589822659, 0.2570028333453004]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.3390410963415108, 0.7053312771029449, 0.11207793212756367]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 4, "w": 2.8660254037844384, "h": 3.964101615137755, "label": "1x4", "piece": [1, 5, 0, 1], "color": [0.39620311885379433, 0.3597929969599728, 0.413678806220555]}], "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\n\nPiece B:\n11\n\nPiece C:\n1\n1\n1\n1\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_rotation_3x3_inst13_var1_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
|
[
"45 degrees counterclockwise",
"60 degrees counterclockwise",
"75 degrees counterclockwise",
"30 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_part/3x3_inst13perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_part/3x3_inst13perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_part/3x3_inst13perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_part/3x3_inst13perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_part/3x3_inst13perturbed_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, 2).", "Rotate piece D by about 90 degrees clockwise, and place piece D 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, 3).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "", "", "", "Overlap"], "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]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.4122246781876865, 0.46099712359888834, 0.029808170513958232]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 1, 3], "color": [0.4167436538845991, 0.3774938048911445, 0.3463506332117947]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.5025023117046901, 0.20679137664564085, 0.35368716180716764]}], "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\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_inst0_var4_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"6",
"5",
"3",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_5.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 D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (4, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4)."], "results": ["", "", "", "", "Over board", "Over board"], "valid": false, "config": [{"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.6408366795251199, 0.44684470588581293, 0.7884302557046777], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.4580368292258854, 0.8158453451238444, 0.9632351452602854], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.6587979169912652, 0.844257398556249, 0.15584553214536334], "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": [2, 4, 3, 4], "color": [0.7898276832817946, 0.4878925327916963, 0.09710359553248094], "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, 2, 4], "color": [0.25876504303189696, 0.6936112618438536, 0.14086831103305852], "cell_center": [5.598076211353316, 1.8660254037844388]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_4x4_inst69_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_v2/4x4_inst69/irregular_assembly/4x4_inst69invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst69/irregular_assembly/4x4_inst69invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst69/irregular_assembly/4x4_inst69invalid_irregular_assembly_step_2.png"], "instructions": ["", " Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 4).", "Rotate piece A by about 60 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, 4, 0, 4], [0, 2, 0, 1]], "angle": 0, "flip": "vertical", "color": [0.012658647225970321, 0.393591315142342, 0.7068412804669196], "is_merged": true}, {"index": 0, "shape": [0, 2, 1, 4], "angle": 60, "flip": "none", "color": [0.32272952714353553, 0.6432733817714507, 0.8096626665340618], "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:\n111\n111\n\nPiece B:\n0100\n0100\n1111\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_inst19_var1_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"6",
"5",
"3",
"4"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_5.png"], "instructions": ["", "Place piece B 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, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D 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) = (1, 1).", "Place piece C with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.8415274483290549, 0.46286374035661404, 0.8797592115225641]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.4978586459293345, 0.5976559765313394, 0.14086452934263438]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.8916148044641335, 0.3781423287870871, 0.36352922300777135]}, {"index": 4, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [2, 3, 1, 3], "color": [0.568589415325386, 0.5333890295436079, 0.9833430947635076]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.3223902645479415, 0.8258414522110806, 0.3821764742442382]}], "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:\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_4x4_inst1_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"5",
"4",
"7",
"6"
] |
{"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_inst0_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"3",
"6",
"4",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/assembly/4x4_inst0assembly_step_5.png"], "instructions": ["", "Place piece D 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) = (2, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E 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, 2)."], "valid": true, "config": [{"index": 3, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.4580368292258854, 0.8158453451238444, 0.9632351452602854], "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, 2, 4], "color": [0.25876504303189696, 0.6936112618438536, 0.14086831103305852], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.6587979169912652, 0.844257398556249, 0.15584553214536334], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.7898276832817946, 0.4878925327916963, 0.09710359553248094], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [2, 4, 0, 1], "color": [0.6408366795251199, 0.44684470588581293, 0.7884302557046777], "cell_center": [9.330127018922195, 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:\n11\n11\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n11\n11\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": "assembly"}
|
|
tangram_perception_rotation_3x3_inst3_var2_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
|
[
"45 degrees counterclockwise",
"90 degrees counterclockwise",
"30 degrees counterclockwise",
"0 degrees (not rotated)"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_part/3x3_inst3perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_part/3x3_inst3perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_part/3x3_inst3perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_part/3x3_inst3perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/perturbed_part/3x3_inst3perturbed_part_assembly_step_4.png"], "instructions": ["", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "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).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "", "Over board"], "valid": false, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.17413619213984544, 0.539393258896573, 0.7469777807902688]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.16349340438282878, 0.21139582589822659, 0.2570028333453004]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.3390410963415108, 0.7053312771029449, 0.11207793212756367]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 4, "w": 2.8660254037844384, "h": 3.964101615137755, "label": "1x4", "piece": [1, 5, 0, 1], "color": [0.39620311885379433, 0.3597929969599728, 0.413678806220555]}], "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\n\nPiece B:\n11\n\nPiece C:\n1\n1\n1\n1\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_rotation_4x4_inst8_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>
|
C
|
rotation
|
[
"75 degrees counterclockwise",
"60 degrees counterclockwise",
"90 degrees counterclockwise",
"105 degrees counterclockwise"
] |
{"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_rotation_4x4_inst3_var4_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)",
"30 degrees counterclockwise",
"90 degrees counterclockwise",
"45 degrees counterclockwise"
] |
{"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_rotation_4x4_inst17_var4_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
|
[
"30 degrees counterclockwise",
"45 degrees counterclockwise",
"15 degrees counterclockwise",
"60 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_part/4x4_inst17perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_part/4x4_inst17perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_part/4x4_inst17perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_part/4x4_inst17perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_part/4x4_inst17perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_part/4x4_inst17perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).", "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 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "Over board", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.8024254343287276, 0.5212933415712149, 0.6519422431117098]}, {"index": 4, "angle": 30, "orig_width": 4, "orig_height": 1, "w": 3.964101615137755, "h": 2.8660254037844384, "label": "4x1", "piece": [2, 3, 2, 6], "color": [0.09830256447954788, 0.3396191061459677, 0.9867290956314256]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3209357623770135, 0.4919116750200321, 0.05254088833875614]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.06114350981419958, 0.30119771230277814, 0.1293300317914955]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 0, 2], "color": [0.9578521580074713, 0.8815921980787345, 0.19295089472973515]}], "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\n\nPiece D:\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_size_count_4x4_inst40_var4_q_only
|
How many blocks (cells) are in piece B in the tangram puzzle shown below?
<image_0>
|
B
|
size_count
|
[
"5",
"10",
"9",
"11"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst40/irregular_assembly/4x4_inst40invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst40/irregular_assembly/4x4_inst40invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst40/irregular_assembly/4x4_inst40invalid_irregular_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 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 3], "angle": 60, "flip": "none", "color": [0.9306636850349022, 0.09874831235672099, 0.7356310587347471], "is_merged": false}, {"index": 1, "shape": [[2, 4, 0, 4], [0, 2, 3, 4]], "angle": 30, "flip": "none", "color": [0.45980852671857286, 0.49464127963619375, 0.4191284231456216], "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\n\nPiece B:\n1111\n1111\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_inst38_var0_q+steps
|
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_inst38/irregular_assembly/3x3_inst38invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst38/irregular_assembly/3x3_inst38invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst38/irregular_assembly/3x3_inst38invalid_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).", "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": [0.2640373819201658, 0.23801220505274123, 0.0902448886427546], "is_merged": false}, {"index": 0, "shape": [1, 3, 1, 3], "angle": 0, "flip": "none", "color": [0.8335762701827948, 0.8840202519453446, 0.5496566700702556], "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:\n010\n010\n111\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_size_count_4x4_inst15_var2_q_only
|
How many blocks (cells) are in piece C in the tangram puzzle shown below?
<image_0>
|
C
|
size_count
|
[
"4",
"3",
"2",
"5"
] |
{"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_size_count_4x4_inst63_var2_q_only
|
How many blocks (cells) are in piece A in the tangram puzzle shown below?
<image_0>
|
B
|
size_count
|
[
"4",
"2",
"5",
"1"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst63/irregular_assembly/4x4_inst63invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst63/irregular_assembly/4x4_inst63invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst63/irregular_assembly/4x4_inst63invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst63/irregular_assembly/4x4_inst63invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst63/irregular_assembly/4x4_inst63invalid_irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 2).", "Place piece D with its upper-left corner at (x,y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its lower-left corner at (x,y) = (1, 5)."], "results": ["", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 3, 4], "angle": 60, "flip": "none", "color": [0.5260628033584828, 0.7555766413569492, 0.6421281201612757], "is_merged": false}, {"index": 1, "shape": [2, 4, 0, 1], "angle": 60, "flip": "none", "color": [0.8687307880419107, 0.3658278575519862, 0.030634220537594792], "is_merged": false}, {"index": 3, "shape": [[2, 4, 1, 4], [0, 2, 1, 3]], "angle": 0, "flip": "none", "color": [0.8858464357869126, 0.1733480687938419, 0.34062506371142165], "is_merged": false}, {"index": 2, "shape": [0, 2, 0, 1], "angle": 90, "flip": "none", "color": [0.37795065269759365, 0.3712615852452913, 0.14893548595674522], "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:\n1\n1\n\nPiece B:\n1\n1\n\nPiece C:\n1100\n1100\n1111\n0011\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 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_rotation_3x3_inst8_var0_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
|
[
"45 degrees counterclockwise",
"0 degrees (not rotated)",
"30 degrees counterclockwise",
"90 degrees counterclockwise"
] |
{"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_3x3_inst1_var2_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"3",
"5",
"2",
"4"
] |
{"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_rotation_3x3_inst13_var1_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>
|
B
|
rotation
|
[
"45 degrees counterclockwise",
"60 degrees counterclockwise",
"75 degrees counterclockwise",
"30 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_part/3x3_inst13perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_part/3x3_inst13perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_part/3x3_inst13perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_part/3x3_inst13perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/perturbed_part/3x3_inst13perturbed_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, 2).", "Rotate piece D by about 90 degrees clockwise, and place piece D 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, 3).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "", "", "", "Overlap"], "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]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.4122246781876865, 0.46099712359888834, 0.029808170513958232]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 1, 3], "color": [0.4167436538845991, 0.3774938048911445, 0.3463506332117947]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.5025023117046901, 0.20679137664564085, 0.35368716180716764]}], "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\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_rotation_3x3_inst7_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>
|
C
|
rotation
|
[
"105 degrees counterclockwise",
"75 degrees counterclockwise",
"90 degrees counterclockwise",
"60 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst7/assembly/3x3_inst7assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/assembly/3x3_inst7assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/assembly/3x3_inst7assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/assembly/3x3_inst7assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/assembly/3x3_inst7assembly_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, 1).", "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) = (2, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 1)."], "valid": true, "config": [{"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.5214492117729866, 0.6446553823041661, 0.06936597519800336], "cell_center": [1.8660254037844386, 1.8660254037844386]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.73843051684633, 0.04893125943557952, 0.5781887360388885], "cell_center": [1.8660254037844386, 5.598076211353316]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 2, 3], "color": [0.8890167433678454, 0.8396728997385756, 0.6423378141699023], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.10779093077082336, 0.9663519770282707, 0.08719575355451004], "cell_center": [5.598076211353316, 1.8660254037844386]}], "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\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_4x4_inst21_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>
|
D
|
rotation
|
[
"105 degrees counterclockwise",
"60 degrees counterclockwise",
"75 degrees counterclockwise",
"90 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst21/perturbed_part/4x4_inst21perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/perturbed_part/4x4_inst21perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/perturbed_part/4x4_inst21perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/perturbed_part/4x4_inst21perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/perturbed_part/4x4_inst21perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece C by about 30 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) = (0, 1).", "Place piece A with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 30, "orig_width": 2, "orig_height": 3, "w": 3.232050807568877, "h": 3.598076211353316, "label": "2x3", "piece": [0, 3, 2, 4], "color": [0.9226983536502249, 0.3780541609495376, 0.9449843452750281]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [1, 2, 0, 2], "color": [0.13844656237050856, 0.09373377464750454, 0.41854255601994583]}, {"index": 3, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.5273830110431585, 0.9977137852794107, 0.9524770845988989]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 3, "w": 3.0, "h": 2.0, "label": "3x2", "piece": [0, 3, 0, 2], "color": [0.4773278399576071, 0.4179807901546365, 0.3658306231917948]}], "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:\n11\n11\n11\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_4x4_inst24_var1_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_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).", "Rotate piece B by about 90 degrees clockwise. Flip piece B vertically. Place piece B with its upper-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) = (3, 2).", "Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 2, "shape": [0, 2, 3, 4], "angle": 60, "flip": "none", "color": [0.3941478645364662, 0.07242735131670541, 0.6221981028733828], "is_merged": false}, {"index": 1, "shape": [2, 3, 1, 4], "angle": 90, "flip": "vertical", "color": [0.34499076168116316, 0.3941488900507818, 0.035379367870832845], "is_merged": true}, {"index": 0, "shape": [3, 4, 0, 4], "angle": 30, "flip": "none", "color": [0.34673327216917005, 0.3823052678152453, 0.04807869538996756], "is_merged": false}, {"index": 3, "shape": [[0, 3, 0, 1], [0, 2, 1, 3]], "angle": 60, "flip": "none", "color": [0.667451459773487, 0.609690672977065, 0.9690305764874845], "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:\n1111\n\nPiece B:\n110\n110\n111\n\nPiece C:\n1\n1\n\nPiece D:\n100\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": "irregular_assembly"}
|
|
tangram_perception_rotation_3x3_inst12_var0_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
|
[
"60 degrees counterclockwise",
"75 degrees counterclockwise",
"105 degrees counterclockwise",
"90 degrees counterclockwise"
] |
{"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_rotation_4x4_inst16_var1_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
|
[
"75 degrees counterclockwise",
"60 degrees counterclockwise",
"30 degrees counterclockwise",
"45 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_step/4x4_inst16perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_step/4x4_inst16perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_step/4x4_inst16perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_step/4x4_inst16perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_step/4x4_inst16perturbed_step_assembly_step_4.png"], "instructions": ["", "Place piece D with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2).", "Place piece B with its upper-left corner at (x, y) = (1, 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"], "valid": false, "config": [{"index": 3, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.28731779180264194, 0.03647956859760171, 0.15648045527389287], "cell_center": [2.299038105676658, 6.348076211353315]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 2, "w": 3.598076211353316, "h": 3.232050807568877, "label": "3x2", "piece": [2, 4, 0, 3], "color": [0.10552732137168419, 0.7961088453102383, 0.6833810431216795], "cell_center": [6.897114317029974, 6.348076211353315]}, {"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], "cell_center": [2.299038105676658, 2.1160254037844384]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.2906409364547665, 0.18966064628256707, 0.16656066606481745], "cell_center": [6.897114317029974, 2.1160254037844384]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_3x3_inst15_var2_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"4",
"6",
"3",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_5.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 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 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "", "", "Overlap", "Overlap"], "valid": false, "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]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 0, 1], "color": [0.2824781693183691, 0.4391634637062619, 0.8730414057719783]}, {"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]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 2, 3], "color": [0.678651528421504, 0.2548722306191047, 0.7768283693786211]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.31213979887651133, 0.6376277262292271, 0.2961764771058485]}], "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:\n1\n1\n\nPiece D:\n11\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 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_rotation_3x3_inst15_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>
|
D
|
rotation
|
[
"45 degrees counterclockwise",
"15 degrees counterclockwise",
"60 degrees counterclockwise",
"30 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/perturbed_part/3x3_inst15perturbed_part_assembly_step_5.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 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 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "", "", "Overlap", "Overlap"], "valid": false, "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]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 0, 1], "color": [0.2824781693183691, 0.4391634637062619, 0.8730414057719783]}, {"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]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 2, 3], "color": [0.678651528421504, 0.2548722306191047, 0.7768283693786211]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.31213979887651133, 0.6376277262292271, 0.2961764771058485]}], "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:\n1\n1\n\nPiece D:\n11\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 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst18_var4_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"4",
"5",
"3",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst18/assembly/3x3_inst18assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/assembly/3x3_inst18assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/assembly/3x3_inst18assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/assembly/3x3_inst18assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/assembly/3x3_inst18assembly_step_4.png"], "instructions": ["", "Place piece C with its upper-left corner at (x, y) = (0, 2).", "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).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "valid": true, "config": [{"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.17693734122658056, 0.6003726390211623, 0.25113789613439574], "cell_center": [1.6160254037844386, 1.5]}, {"index": 3, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.010600729886533378, 0.8500375523210303, 0.41713905454049915], "cell_center": [4.848076211353316, 1.5]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.21606549856304313, 0.2484660411194164, 0.5092478714383866], "cell_center": [1.6160254037844386, 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": [0.11654719097461486, 0.3924294240647598, 0.5378042635188506], "cell_center": [4.848076211353316, 4.5]}], "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\n\nPiece B:\n11\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": "assembly"}
|
|
tangram_perception_rotation_4x4_inst5_var4_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
|
[
"60 degrees counterclockwise",
"90 degrees counterclockwise",
"75 degrees counterclockwise",
"105 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_8.png"], "instructions": ["", "Place piece D with its upper-left corner at (x, y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 60 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) = (2, 3).", "Rotate piece H by about 90 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (2, 1).", "Place piece C with its upper-left corner at (x, y) = (2, 4).", "Place piece G 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) = (1, 4)."], "results": ["", "", "", "", "Over board", "Over board", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.9240533250960073, 0.9819349600532725, 0.6747134014128692]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.7349991584173213, 0.6699660472482647, 0.43315305080703437]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 1, 2], "color": [0.22291133685432907, 0.48383465028816663, 0.5699125213630748]}, {"index": 5, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [1, 2, 2, 6], "color": [0.5397844496723473, 0.05872496894813528, 0.15399180068950846]}, {"index": 7, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [3, 4, 2, 4], "color": [0.48160700821724445, 0.60931785491179, 0.22992601917545952]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.6297825243848936, 0.49093541919773, 0.6669745716275061]}, {"index": 6, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.6662381683077349, 0.4371576487638136, 0.8074652784518175]}, {"index": 1, "angle": 90, "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]}], "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\n\nPiece C:\n11\n\nPiece D:\n1\n1\n\nPiece E:\n11\n\nPiece F:\n1111\n\nPiece G:\n11\n\nPiece H:\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_inst2_var0_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"5",
"8",
"7",
"6"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst2/perturbed_step/4x4_inst2perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/perturbed_step/4x4_inst2perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/perturbed_step/4x4_inst2perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/perturbed_step/4x4_inst2perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/perturbed_step/4x4_inst2perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/perturbed_step/4x4_inst2perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/perturbed_step/4x4_inst2perturbed_step_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/perturbed_step/4x4_inst2perturbed_step_assembly_step_7.png"], "instructions": ["", "Place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece C by about 60 degrees clockwise, and place piece C 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, 4).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 1).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece E by about 60 degrees clockwise, and place piece E 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) = (2, 1)."], "results": ["", "", "", "", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.6569014157009531, 0.2313466861102611, 0.010872417072518958], "cell_center": [1.8660254037844388, 9.330127018922193]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.5214964160883804, 0.14197386071806894, 0.6150886066496369], "cell_center": [5.598076211353316, 9.330127018922193]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.4909418154450287, 0.8295599853485568, 0.8848537987406436], "cell_center": [9.330127018922195, 9.330127018922193]}, {"index": 5, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [3, 4, 1, 2], "color": [0.09465920484769241, 0.5230886510184202, 0.29886511441981023], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.6355020062380002, 0.8225754659177894, 0.9905175449642316], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.4062185845144768, 0.82080352213676, 0.12435592468962808], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 6, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.3036862549445286, 0.2573646344972037, 0.48565653763236827], "cell_center": [1.8660254037844388, 1.8660254037844388]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_4x4_inst19_var3_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
A
|
count
|
[
"4",
"5",
"3",
"2"
] |
{"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:\n11\n\nPiece B:\n0011\n1111\n1100\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": "irregular_assembly"}
|
|
tangram_perception_size_count_4x4_inst38_var2_q_only
|
How many blocks (cells) are in piece B in the tangram puzzle shown below?
<image_0>
|
B
|
size_count
|
[
"4",
"2",
"5",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise. Place piece D 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, 2).", " Flip piece C horizontally. Place piece C with its upper-left corner at (x,y) = (0, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 2)."], "results": ["", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 3, "shape": [[2, 4, 1, 4], [0, 2, 2, 4]], "angle": 30, "flip": "none", "color": [0.12093478898180199, 0.6866466715293956, 0.13252558682790772], "is_merged": false}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 60, "flip": "none", "color": [0.2834887826212631, 0.8656741309640128, 0.6531975744498982], "is_merged": false}, {"index": 2, "shape": [0, 2, 1, 2], "angle": 0, "flip": "horizontal", "color": [0.9282782748507362, 0.48858656271077405, 0.05954200460972181], "is_merged": true}, {"index": 1, "shape": [2, 4, 0, 1], "angle": 30, "flip": "none", "color": [0.16003991378313354, 0.02014673951971968, 0.3479685371859973], "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:\n1\n1\n\nPiece C:\n0111\n0111\n1100\n1100\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 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"}
|
|
tangram_perception_size_count_4x4_inst25_var0_q_only
|
How many blocks (cells) are in piece B in the tangram puzzle shown below?
<image_0>
|
B
|
size_count
|
[
"12",
"10",
"5",
"7"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its lower-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) = (0, 4)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 3, 4], "angle": 90, "flip": "none", "color": [0.46767221164754547, 0.4767504561709347, 0.15453668427780887], "is_merged": false}, {"index": 1, "shape": [2, 4, 0, 2], "angle": 90, "flip": "none", "color": [0.2200316360246839, 0.16174837472242654, 0.08603563855101859], "is_merged": true}, {"index": 2, "shape": [[0, 2, 0, 3], [2, 4, 2, 4]], "angle": 90, "flip": "none", "color": [0.25574162196635564, 0.51986659658632, 0.7369240379748156], "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\n\nPiece B:\n1100\n1111\n0011\n0011\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 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"}
|
|
tangram_perception_count_4x4_inst27_var4_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_v2/4x4_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_inst72_var1_q+steps
|
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_inst72/irregular_assembly/3x3_inst72invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst72/irregular_assembly/3x3_inst72invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst72/irregular_assembly/3x3_inst72invalid_irregular_assembly_step_2.png"], "instructions": ["", " Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (1, 4).", "Rotate piece B by about 30 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": "horizontal", "color": [0.8721773622006816, 0.41303145576010014, 0.7791921499016435], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 30, "flip": "none", "color": [0.5908631975774135, 0.17639180955650813, 0.08214364632741677], "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:\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_invalid_assembly"}
|
|
tangram_perception_count_3x3_inst28_var2_q+steps
|
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_inst28/irregular_assembly/3x3_inst28irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28irregular_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) = (0, 3)."], "valid": true, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 0, "flip": "none", "color": [0.5629568688202203, 0.21307617484959096, 0.3881604215827764], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 90, "flip": "none", "color": [0.24874432956275316, 0.10459104781785566, 0.290015710844736], "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:\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_inst25_var3_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_v2/3x3_inst25/perturbed_part/3x3_inst25perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/perturbed_part/3x3_inst25perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/perturbed_part/3x3_inst25perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/perturbed_part/3x3_inst25perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/perturbed_part/3x3_inst25perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece C by about 30 degrees clockwise, and place piece C 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).", "Place piece B with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.9467768577560671, 0.1122469286147828, 0.23084305152189044]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.04014975225319073, 0.7060719947405601, 0.7632273797026523]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3682140433334865, 0.08970897647428389, 0.502425376239822]}, {"index": 1, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.5344029398630591, 0.9891697464278887, 0.21703088700988227]}], "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:\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_rotation_4x4_inst11_var3_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>
|
B
|
rotation
|
[
"60 degrees counterclockwise",
"90 degrees counterclockwise",
"105 degrees counterclockwise",
"75 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst11/perturbed_part/4x4_inst11perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/perturbed_part/4x4_inst11perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/perturbed_part/4x4_inst11perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/perturbed_part/4x4_inst11perturbed_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) = (3, 4).", "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 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "Over board"], "valid": false, "config": [{"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.2617125427976732, 0.3180100977057472, 0.9938777587600973]}, {"index": 0, "angle": 60, "orig_width": 3, "orig_height": 2, "w": 3.2320508075688776, "h": 3.598076211353316, "label": "3x2", "piece": [0, 2, 0, 3], "color": [0.590194494564307, 0.8146086514121477, 0.17186877412793822]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 4, "w": 4.0, "h": 2.0000000000000004, "label": "4x2", "piece": [2, 6, 0, 2], "color": [0.21016152453789094, 0.9415963033779045, 0.8255857971856693]}], "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:\n1111\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_inst11_var0_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",
"45 degrees counterclockwise",
"15 degrees counterclockwise",
"60 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_inst12_var3_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"2",
"4",
"1",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst12/irregular_assembly/3x3_inst12irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/irregular_assembly/3x3_inst12irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/irregular_assembly/3x3_inst12irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/irregular_assembly/3x3_inst12irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 3)."], "valid": true, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 60, "flip": "none", "color": [0.9103403361123941, 0.38267590340608304, 0.7632217986287583], "is_merged": false}, {"index": 1, "shape": [0, 1, 0, 1], "angle": 90, "flip": "horizontal", "color": [0.946796380694129, 0.7835046474330913, 0.11945153897003868], "is_merged": true}, {"index": 2, "shape": [[1, 3, 0, 2], [0, 1, 1, 3]], "angle": 90, "flip": "none", "color": [0.4602759030241912, 0.5263411433589661, 0.5878592840681638], "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\n\nPiece B:\n110\n111\n001\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": "irregular_assembly"}
|
|
tangram_perception_count_4x4_inst13_var1_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_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_6.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise, and place piece C 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) = (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 D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).", "Rotate piece F by about 30 degrees clockwise, and place piece F 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) = (2, 4)."], "results": ["", "", "", "", "", "Overlap", "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, 0, 2], "color": [0.2805251122858946, 0.9715538225079458, 0.3810974789090861], "cell_center": [1.8660254037844386, 5.598076211353316]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.7966424419178151, 0.9680914967906663, 0.866954291693426], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [0, 1, 0, 2], "color": [0.08091420612656075, 0.9562651224873678, 0.23051757819828445], "cell_center": [9.330127018922193, 5.598076211353316]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.13663939469484443, 0.7631849020052232, 0.6462586504062603], "cell_center": [1.8660254037844386, 1.8660254037844386]}, {"index": 5, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.29384131363027277, 0.3163325797949277, 0.007829642754902055], "cell_center": [5.598076211353316, 1.8660254037844386]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.9400983497113293, 0.32605090347507637, 0.5045925067978794], "cell_center": [9.330127018922193, 1.8660254037844386]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_4x4_inst24_var1_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_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).", "Rotate piece B by about 90 degrees clockwise. Flip piece B vertically. Place piece B with its upper-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) = (3, 2).", "Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 2, "shape": [0, 2, 3, 4], "angle": 60, "flip": "none", "color": [0.3941478645364662, 0.07242735131670541, 0.6221981028733828], "is_merged": false}, {"index": 1, "shape": [2, 3, 1, 4], "angle": 90, "flip": "vertical", "color": [0.34499076168116316, 0.3941488900507818, 0.035379367870832845], "is_merged": true}, {"index": 0, "shape": [3, 4, 0, 4], "angle": 30, "flip": "none", "color": [0.34673327216917005, 0.3823052678152453, 0.04807869538996756], "is_merged": false}, {"index": 3, "shape": [[0, 3, 0, 1], [0, 2, 1, 3]], "angle": 60, "flip": "none", "color": [0.667451459773487, 0.609690672977065, 0.9690305764874845], "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\n\nPiece B:\n110\n110\n111\n\nPiece C:\n1\n1\n1\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": "irregular_assembly"}
|
|
tangram_perception_count_4x4_inst4_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"3",
"5",
"4",
"6"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_5.png"], "instructions": ["", "Place piece B with its upper-left corner at (x,y) = (2, 3).", "Rotate piece E by about 60 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 4).", "Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 1, "shape": [1, 3, 2, 4], "angle": 0, "flip": "none", "color": [0.3298784267001694, 0.4254879586883913, 0.8323218982811694], "is_merged": false}, {"index": 4, "shape": [[0, 2, 0, 2], [0, 1, 2, 4]], "angle": 60, "flip": "none", "color": [0.9516920847941206, 0.09192754978443096, 0.034011632485778764], "is_merged": false}, {"index": 0, "shape": [2, 3, 0, 2], "angle": 30, "flip": "vertical", "color": [0.1486163972137372, 0.09099753565850044, 0.9804276633019189], "is_merged": true}, {"index": 2, "shape": [3, 4, 0, 2], "angle": 30, "flip": "none", "color": [0.6633151367722326, 0.05563697103144172, 0.996308043298854], "is_merged": false}, {"index": 3, "shape": [3, 4, 2, 4], "angle": 30, "flip": "none", "color": [0.7873704671604125, 0.6920579729169158, 0.06370548134717746], "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:\n1111\n1100\n\nPiece B:\n11\n11\n\nPiece C:\n11\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_size_count_4x4_inst57_var1_q_only
|
How many blocks (cells) are in piece B in the tangram puzzle shown below?
<image_0>
|
A
|
size_count
|
[
"10",
"5",
"12",
"13"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst57/irregular_assembly/4x4_inst57invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst57/irregular_assembly/4x4_inst57invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst57/irregular_assembly/4x4_inst57invalid_irregular_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, 3).", "Rotate piece B by about 90 degrees clockwise. 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, 2], "angle": 60, "flip": "none", "color": [0.8963129871799862, 0.8739017178590482, 0.6532480183560629], "is_merged": false}, {"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 2, 4]], "angle": 90, "flip": "none", "color": [0.4469059665785543, 0.04348811865815583, 0.4077037879174834], "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:\n11\n11\n11\n\nPiece B:\n0111\n1111\n1000\n1000\n1000\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_inst0_var4_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"1",
"4",
"3",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst0/irregular_assembly/3x3_inst0irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/irregular_assembly/3x3_inst0irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/irregular_assembly/3x3_inst0irregular_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) = (0, 3).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2)."], "valid": true, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 30, "flip": "vertical", "color": [0.3256280422330665, 0.5203129240964942, 0.7395819324105462], "is_merged": true}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 30, "flip": "none", "color": [0.5107935611666639, 0.5856039458335469, 0.7112698396749424], "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:\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_4x4_inst29_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"4",
"6",
"5",
"7"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_6.png"], "instructions": ["", "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 D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).", "Place piece C with its upper-left corner at (x, y) = (3, 4).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "", "", "Over board", "Over board", "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": [0.9543183423703964, 0.16273279693061327, 0.4214676188543469], "cell_center": [2.0, 6.0]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.5891291035296236, 0.3497096728096557, 0.9163403319569924], "cell_center": [6.0, 6.0]}, {"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], "cell_center": [10.0, 6.0]}, {"index": 5, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.6488651399575482, 0.3550425908569148, 0.6083596641075071], "cell_center": [2.0, 2.0]}, {"index": 2, "angle": 0, "orig_width": 1, "orig_height": 3, "w": 1.0, "h": 3.0, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.5990452770695724, 0.8191791111282444, 0.6830708139237405], "cell_center": [6.0, 2.0]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.9906664263285482, 0.5961649832123572, 0.09772349038033212], "cell_center": [10.0, 2.0]}], "variant": "perturbed_step"}
|
|
tangram_perception_count_4x4_inst6_var0_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"7",
"6",
"8",
"9"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst6/perturbed_part/4x4_inst6perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/perturbed_part/4x4_inst6perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/perturbed_part/4x4_inst6perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/perturbed_part/4x4_inst6perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/perturbed_part/4x4_inst6perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/perturbed_part/4x4_inst6perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/perturbed_part/4x4_inst6perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/perturbed_part/4x4_inst6perturbed_part_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/perturbed_part/4x4_inst6perturbed_part_assembly_step_8.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece D with its upper-left corner at (x, y) = (1, 3).", "Place piece B with its upper-left corner at (x, y) = (3, 4).", "Place piece E with its upper-left corner at (x, y) = (2, 3).", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 60 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 F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 3)."], "results": ["", "", "", "", "Overlap", "Overlap", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.5642191206300475, 0.5266511236435065, 0.01583621582154371]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.4742989639644474, 0.909668014873498, 0.8681758927696834]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 3, 4], "color": [0.13437439136796736, 0.27065887983250636, 0.2175623391262027]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.5266413491581361, 0.1750305330495292, 0.268226050316132]}, {"index": 6, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.1635602218612643, 0.9092079607736911, 0.9337866032490502]}, {"index": 2, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.36824799770838956, 0.17303561687252822, 0.932534384866424]}, {"index": 7, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.021174254868769782, 0.46011262673044473, 0.5504395610307828]}, {"index": 5, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.04043697446808392, 0.08054772670054255, 0.40755271819790273]}], "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\n\nPiece C:\n1\n1\n\nPiece D:\n11\n11\n\nPiece E:\n11\n11\n\nPiece F:\n1\n\nPiece G:\n1\n1\n\nPiece H:\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_inst7_var4_q_only
|
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_inst7/assembly/3x3_inst7assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/assembly/3x3_inst7assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/assembly/3x3_inst7assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/assembly/3x3_inst7assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/assembly/3x3_inst7assembly_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, 1).", "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) = (2, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 1)."], "valid": true, "config": [{"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.5214492117729866, 0.6446553823041661, 0.06936597519800336], "cell_center": [1.8660254037844386, 1.8660254037844386]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.73843051684633, 0.04893125943557952, 0.5781887360388885], "cell_center": [1.8660254037844386, 5.598076211353316]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 2, 3], "color": [0.8890167433678454, 0.8396728997385756, 0.6423378141699023], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.10779093077082336, 0.9663519770282707, 0.08719575355451004], "cell_center": [5.598076211353316, 1.8660254037844386]}], "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\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_inst17_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>
|
A
|
rotation
|
[
"0 degrees (not rotated)",
"30 degrees counterclockwise",
"45 degrees counterclockwise",
"90 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_part/3x3_inst17perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_part/3x3_inst17perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_part/3x3_inst17perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_part/3x3_inst17perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_part/3x3_inst17perturbed_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) = (1, 2).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Place piece A with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "Over board", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 3, "angle": 0, "orig_width": 1, "orig_height": 4, "w": 1.0, "h": 4.0, "label": "1x4", "piece": [1, 5, 1, 2], "color": [0.14133289160513685, 0.7931598690282321, 0.18641685245599515]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.5019930741412741, 0.012559332865545225, 0.17639361210978133]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [0, 1, 2, 3], "color": [0.5781587086361871, 0.8308911842343512, 0.6376093319739924]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 0, 2], "color": [0.3661900859965067, 0.7558139235341418, 0.8335971471271846]}], "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:\n1\n1\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 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"}
|
|
tangram_perception_count_4x4_inst7_var4_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"3",
"5",
"4",
"6"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_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) = (1, 2).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 60 degrees clockwise, and place piece C 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": ["", "", "", "", "Overlap", "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": [0.0038464181562460897, 0.5456025205471018, 0.8316288348193334]}, {"index": 4, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [2, 4, 1, 4], "color": [0.982403612127845, 0.027469345943991863, 0.7361933309757964]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.19476840970141396, 0.68707522398946, 0.14366332946109706]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.18526689525137774, 0.6222333081082303, 0.3116245006929087]}, {"index": 1, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 1, 4], "color": [0.5883107006707854, 0.8743059263428191, 0.51136848550568]}], "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\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n\nPiece E:\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": "perturbed_part"}
|
|
tangram_perception_count_3x3_inst66_var4_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"1",
"4",
"3",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst66/irregular_assembly/3x3_inst66invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst66/irregular_assembly/3x3_inst66invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst66/irregular_assembly/3x3_inst66invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece A with its upper-left corner at (x,y) = (1, 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, 1, 3], "angle": 0, "flip": "none", "color": [0.06174887048418565, 0.2337215698672812, 0.4202173017455749], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 30, "flip": "none", "color": [0.9339236099476395, 0.07222480453355551, 0.7957829886255944], "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:\n111\n010\n010\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_inst18_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
|
[
"0 degrees (not rotated)",
"45 degrees counterclockwise",
"90 degrees counterclockwise",
"30 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_7.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Place piece G with its upper-left corner at (x, y) = (2, 1).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Rotate piece F by about 60 degrees clockwise, and place piece F 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).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "", "", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"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]}, {"index": 6, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 2, 3], "color": [0.20448500268098213, 0.7476839464016675, 0.4118171950672438]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.1356106596338602, 0.9006559215808044, 0.9720273788893483]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [1, 4, 3, 4], "color": [0.19883839915334045, 0.19820963751580922, 0.4332106091628175]}, {"index": 5, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.6952002937385011, 0.5451393144090627, 0.3598069443124001]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.3429060563864845, 0.9039302662351224, 0.4769621469089005]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.8949499330157833, 0.9775042345165299, 0.9215521124499638]}], "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:\n1\n1\n\nPiece E:\n1\n1\n1\n\nPiece F:\n111\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": "perturbed_part"}
|
|
tangram_perception_size_count_4x4_inst75_var4_q_only
|
How many blocks (cells) are in piece A in the tangram puzzle shown below?
<image_0>
|
B
|
size_count
|
[
"4",
"6",
"5",
"9"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst75/irregular_assembly/4x4_inst75invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst75/irregular_assembly/4x4_inst75invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst75/irregular_assembly/4x4_inst75invalid_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) = (0, 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, 0, 2], "angle": 30, "flip": "none", "color": [0.9793998578171987, 0.9812459526092574, 0.9427181798334795], "is_merged": false}, {"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 2, 4]], "angle": 60, "flip": "horizontal", "color": [0.9040775368572661, 0.57772211434449, 0.26938305630573245], "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:\n11\n11\n11\n\nPiece B:\n01111\n11000\n11000\n11000\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_4x4_inst27_var2_q_only
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"2",
"1",
"4",
"3"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst27/assembly/4x4_inst27assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/assembly/4x4_inst27assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/assembly/4x4_inst27assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/assembly/4x4_inst27assembly_step_3.png"], "instructions": ["", "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, 4).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "valid": true, "config": [{"index": 2, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.24455951613028104, 0.36845158724774063, 0.3057028634543797], "cell_center": [2.549038105676658, 2.549038105676658]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 3, "w": 3.0, "h": 1.0000000000000002, "label": "3x1", "piece": [0, 3, 0, 1], "color": [0.7760512609454071, 0.23147233408575651, 0.09518146844402253], "cell_center": [2.549038105676658, 7.647114317029974]}, {"index": 1, "angle": 30, "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], "cell_center": [7.647114317029974, 7.647114317029974]}], "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:\n111\n111\n111\n\nPiece C:\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": "assembly"}
|
|
tangram_perception_count_3x3_inst4_var0_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_v2/3x3_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_rotation_3x3_inst11_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>
|
B
|
rotation
|
[
"90 degrees counterclockwise",
"0 degrees (not rotated)",
"30 degrees counterclockwise",
"45 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst11/assembly/3x3_inst11assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst11/assembly/3x3_inst11assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst11/assembly/3x3_inst11assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst11/assembly/3x3_inst11assembly_step_3.png"], "instructions": ["", "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) = (0, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 0, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.20466808994905894, 0.704066164831489, 0.6231877093078216], "cell_center": [2.0, 4.5]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.10167857717644269, 0.8327584618892119, 0.8500740367164027], "cell_center": [6.0, 4.5]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.727812832035729, 0.9023721118321468, 0.059719741721927844], "cell_center": [2.0, 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:\n111\n\nPiece B:\n1\n1\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_rotation_3x3_inst8_var1_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
|
[
"90 degrees counterclockwise",
"30 degrees counterclockwise",
"0 degrees (not rotated)",
"45 degrees counterclockwise"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst8/assembly/3x3_inst8assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/assembly/3x3_inst8assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/assembly/3x3_inst8assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/assembly/3x3_inst8assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/assembly/3x3_inst8assembly_step_4.png"], "instructions": ["", "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, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D 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)."], "valid": true, "config": [{"index": 2, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.42736045177487814, 0.8513826938670388, 0.8750119894026337], "cell_center": [1.5, 1.6160254037844386]}, {"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], "cell_center": [4.5, 4.848076211353316]}, {"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], "cell_center": [4.5, 1.6160254037844386]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.9121940999636362, 0.4658006204694346, 0.5093386252677216], "cell_center": [1.5, 4.848076211353316]}], "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:\n1\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": "assembly"}
|
|
tangram_perception_count_3x3_inst21_var0_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
C
|
count
|
[
"4",
"1",
"3",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst21/assembly/3x3_inst21assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/assembly/3x3_inst21assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/assembly/3x3_inst21assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/assembly/3x3_inst21assembly_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).", "Place piece C 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) = (0, 2)."], "valid": true, "config": [{"index": 0, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.6165348490517608, 0.47248907820449537, 0.17394439876786527], "cell_center": [1.6830127018922196, 6.147114317029974]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.5750109852621413, 0.4718251861047962, 0.07260160357926093], "cell_center": [1.6830127018922196, 2.049038105676658]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.6140362933411411, 0.9726156360309749, 0.23541658483033545], "cell_center": [5.049038105676659, 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:\n1\n1\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_count_4x4_inst26_var1_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
D
|
count
|
[
"3",
"1",
"4",
"2"
] |
{"images": ["output_dir/Tangram_puzzle_v2/4x4_inst26/irregular_assembly/4x4_inst26invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst26/irregular_assembly/4x4_inst26invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst26/irregular_assembly/4x4_inst26invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 3).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 3, 2, 4], "angle": 60, "flip": "none", "color": [0.2046771522625852, 0.6943746193771417, 0.047460348425434895], "is_merged": false}, {"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 0, 2]], "angle": 90, "flip": "none", "color": [0.31277665174922176, 0.35495538459548914, 0.3185787817539524], "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:\n11\n11\n11\n\nPiece B:\n1000\n1111\n1111\n1000\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_inst18_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"3",
"4",
"2",
"5"
] |
{"images": ["output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_4.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, 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 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.21606549856304313, 0.2484660411194164, 0.5092478714383866]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.17693734122658056, 0.6003726390211623, 0.25113789613439574]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.010600729886533378, 0.8500375523210303, 0.41713905454049915]}, {"index": 1, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 1, 4], "color": [0.11654719097461486, 0.3924294240647598, 0.5378042635188506]}], "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\n\nPiece B:\n11\n11\n11\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_inst24_var3_q+steps
|
How many tangram pieces are available in the puzzle shown below?
<image_0>
|
B
|
count
|
[
"2",
"3",
"4",
"1"
] |
{"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_inst5_var0_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_inst5/irregular_assembly/3x3_inst5invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5invalid_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) = (0, 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, 0, 2], "angle": 30, "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}], "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"}
|
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