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[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "An autonomous medical triage AI operates under a explicitly programmed \"lexical prioritarian\" principle: it must fir...	{ "id": "gen-500e9122ac3edd4a", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "An autonomous medical triage AI operates under a explicitly programmed \"lexical prioritarian\" principle: it must first maximize the number of lives saved; only if...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A city government is considering two policies to reduce traffic congestion during peak hours:\n\nPolicy A: Implement a...	{ "id": "gen-3b40a16eaa59fce4", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A city government is considering two policies to reduce traffic congestion during peak hours:\n\nPolicy A: Implement a flat $5 congestion fee for all vehicles enter...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A factory pays each worker a base wage of $10 per hour plus a piece‑rate of $0.50 for every unit the worker produces i...	{ "id": "gen-286d91baa3af43f9", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A factory pays each worker a base wage of $10 per hour plus a piece‑rate of $0.50 for every unit the worker produces in that hour. The worker’s marginal cost of eff...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "How many distinct arrangements of the letters in the word \"MATHEMATICS\" have no two identical letters adjacent?" }...	{ "id": "gen-4b2ce98c9d21539a", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "How many distinct arrangements of the letters in the word \"MATHEMATICS\" have no two identical letters adjacent?", "reasoning": "We need to find the number of di...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider the function \\( f \\) defined by \\( f(x) = x^2 \\sin(1/x) \\) for \\( x \\neq 0 \\) and \\( f(0) = 0 \\). C...	{ "id": "gen-3303614a1123808e", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider the function \\( f \\) defined by \\( f(x) = x^2 \\sin(1/x) \\) for \\( x \\neq 0 \\) and \\( f(0) = 0 \\). Compute \\( f'(0) \\) and determine whether \\(...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A hash table with separate chaining has 100 buckets and stores 500 distinct keys. Assuming the hash function distribut...	{ "id": "gen-a90f0c905368d75c", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A hash table with separate chaining has 100 buckets and stores 500 distinct keys. Assuming the hash function distributes keys uniformly at random, what is the expec...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Find the remainder when \\(3^{100}\\) is divided by 7." }, { "from": "gpt", "value": "<think>\nWe need to ...	{ "id": "gen-aad7e9eaba36a160", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Find the remainder when \\(3^{100}\\) is divided by 7.", "reasoning": "We need to find the remainder when 3^100 is divided by 7. This is a modular arithmetic prob...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A uniform rod of mass \\(M\\) and length \\(L\\) is pivoted at one end and can rotate freely in a vertical plane. The ...	{ "id": "gen-5b9b00e20fa7c308", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A uniform rod of mass \\(M\\) and length \\(L\\) is pivoted at one end and can rotate freely in a vertical plane. The rod is held horizontally and released from res...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Let \\( f: [0,1] \\to \\mathbb{R} \\) be a continuous function satisfying\n\\[\nf(x) = 1 + \\int_0^x (x - t) f(t) \\, ...	{ "id": "gen-25c737bb5a6128ce", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Let \\( f: [0,1] \\to \\mathbb{R} \\) be a continuous function satisfying\n\\[\nf(x) = 1 + \\int_0^x (x - t) f(t) \\, dt\n\\]\nfor all \\( x \\in [0,1] \\). Evaluat...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A tetrahedron has three edges of lengths 2, 3, and 6 meeting at a vertex, and these three edges are pairwise perpendic...	{ "id": "gen-ae83fd563be8cee0", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A tetrahedron has three edges of lengths 2, 3, and 6 meeting at a vertex, and these three edges are pairwise perpendicular. Find the radius of the circumscribed sph...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "We need to write an advanced organic chemistry reaction question, self-contained, single correct answer, solvable thro...	{ "id": "gen-448d6da2b18cd7a8", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "We need to write an advanced organic chemistry reaction question, self-contained, single correct answer, solvable through reasoning, no answer or hints. Just the qu...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A glass of water sits on a digital scale, which reads 250 g. An ice cube of mass 20 g is gently placed into the water....	{ "id": "gen-0e9acbfa1f6e0467", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A glass of water sits on a digital scale, which reads 250 g. An ice cube of mass 20 g is gently placed into the water. The ice cube floats, partially submerged. Aft...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "We need to write a competition-level question about step-by-step planning problems. It must be self-contained, have a ...	{ "id": "gen-c22262a7a98559b8", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "We need to write a competition-level question about step-by-step planning problems. It must be self-contained, have a single correct answer, solvable through explic...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "We need to write a single advanced geometry/spatial reasoning question, self-contained, with a definite answer, solvab...	{ "id": "gen-e21dc39cd9eba3d5", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "We need to write a single advanced geometry/spatial reasoning question, self-contained, with a definite answer, solvable by reasoning. No answer, no hints. Just the...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Four friends—Alice, Bob, Carol, and Dave—each have a different favorite color (red, blue, green, yellow) and a differe...	{ "id": "gen-5dc1f1ec4d406d7d", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Four friends—Alice, Bob, Carol, and Dave—each have a different favorite color (red, blue, green, yellow) and a different pet (cat, dog, fish, bird). Using the follo...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Find the smallest positive integer that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5,...	{ "id": "gen-2e1525ff97d9c133", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Find the smallest positive integer that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 2 when divided by 7.", "...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider a directed graph with vertices {0, 1, 2, 3, 4} and the following weighted edges:\n0 → 1 (weight 4)\n0 → 2 (we...	{ "id": "gen-1f79b6969c619ac2", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider a directed graph with vertices {0, 1, 2, 3, 4} and the following weighted edges:\n0 → 1 (weight 4)\n0 → 2 (weight 2)\n1 → 2 (weight 5)\n1 → 3 (weight 10)\n...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "How many 5-digit positive integers have the property that the sum of their digits equals the product of their digits?"...	{ "id": "gen-c8478e15497bd7d1", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "How many 5-digit positive integers have the property that the sum of their digits equals the product of their digits?", "reasoning": "We need to find the number o...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "You have 2 liters of water at 80°C and 3 liters of water at 20°C. You mix them together in a perfectly insulated conta...	{ "id": "gen-0ac4f297c17b98cc", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "You have 2 liters of water at 80°C and 3 liters of water at 20°C. You mix them together in a perfectly insulated container. Assuming no heat loss to the surrounding...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "On the island of Knights and Knaves, knights always tell the truth and knaves always lie. You encounter three inhabita...	{ "id": "gen-3c5d258dd76ba438", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "On the island of Knights and Knaves, knights always tell the truth and knaves always lie. You encounter three inhabitants: Alice, Bob, and Carol. They make the foll...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A wedge of mass \\(M\\) and incline angle \\(\\alpha\\) rests on a horizontal frictionless surface. A particle of mass...	{ "id": "gen-ad57a1abbc87d6c5", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A wedge of mass \\(M\\) and incline angle \\(\\alpha\\) rests on a horizontal frictionless surface. A particle of mass \\(m\\) is placed on the frictionless incline...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "The table below shows monthly customer data for a retail store in the first half of 2023.\n\n\| Month \| Total Customers...	{ "id": "gen-29c0b43262ac13e0", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "The table below shows monthly customer data for a retail store in the first half of 2023.\n\n\| Month \| Total Customers \| Average Transaction Value ($) \| % Returning...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A bakery currently pays its workers a fixed hourly wage of $15 per hour. The owner is considering switching to a piece...	{ "id": "gen-add5b7ecd8ebb6da", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A bakery currently pays its workers a fixed hourly wage of $15 per hour. The owner is considering switching to a piece-rate system paying $2 per loaf of bread produ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "We need to write a competition-level probability/expected value question. It should be self-contained, have a single c...	{ "id": "gen-e65f428f0fda2ab2", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "We need to write a competition-level probability/expected value question. It should be self-contained, have a single correct answer, solvable by reasoning. No answe...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A monopolist faces the inverse demand curve \\(P = 100 - Q\\) and has a constant marginal cost of \\(20\\). The govern...	{ "id": "gen-69c72157426738fa", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A monopolist faces the inverse demand curve \\(P = 100 - Q\\) and has a constant marginal cost of \\(20\\). The government imposes a per-unit tax \\(t\\) on the mon...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Three boxes are labeled \"Apples\", \"Oranges\", and \"Apples and Oranges\". Each label is incorrect. You may draw one...	{ "id": "gen-6e12b926f9b299a4", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Three boxes are labeled \"Apples\", \"Oranges\", and \"Apples and Oranges\". Each label is incorrect. You may draw one fruit from one box without looking inside. Fr...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A uniform chain of length \\(L\\) and mass \\(M\\) is held vertically with its lower end just touching a horizontal ta...	{ "id": "gen-f831099561a7f45e", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A uniform chain of length \\(L\\) and mass \\(M\\) is held vertically with its lower end just touching a horizontal table. The chain is released from rest. Find the...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "We need to write a single advanced question about debugging a described program. Must be self-contained, single correc...	{ "id": "gen-c07279374225c5b7", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "We need to write a single advanced question about debugging a described program. Must be self-contained, single correct verifiable answer, solvable through explicit...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A risk-neutral employer hires a risk-neutral worker for a project. The worker can choose either high effort (cost = $5...	{ "id": "gen-5ce2179d17eee4a8", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A risk-neutral employer hires a risk-neutral worker for a project. The worker can choose either high effort (cost = $50) or low effort (cost = $0). If the worker ch...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A uniform rod of length \\(L\\) and mass \\(M\\) is pivoted at one end and initially hangs vertically at rest. A small...	{ "id": "gen-230cb2d30c4c74d1", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A uniform rod of length \\(L\\) and mass \\(M\\) is pivoted at one end and initially hangs vertically at rest. A small putty of mass \\(m\\), moving horizontally wi...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Let \\( f \\) be a continuous function on the closed interval \\([0,1]\\) satisfying\n\\[\n\\int_0^1 f(x) x^n \\, dx =...	{ "id": "gen-cee9c236c3840df0", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Let \\( f \\) be a continuous function on the closed interval \\([0,1]\\) satisfying\n\\[\n\\int_0^1 f(x) x^n \\, dx = \\frac{1}{n+2}\n\\]\nfor every nonnegative in...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider the following reaction sequence:\n\n1. 1-methylcyclohexene is treated with BH₃·THF, followed by H₂O₂/NaOH.\n2...	{ "id": "gen-f9772b56c1d8ab52", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider the following reaction sequence:\n\n1. 1-methylcyclohexene is treated with BH₃·THF, followed by H₂O₂/NaOH.\n2. The product from step 1 is treated with PCC ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A uniform ladder of length 6 m and mass 20 kg leans against a smooth vertical wall at an angle of 60° to the horizonta...	{ "id": "gen-06371ab5776c5ae9", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A uniform ladder of length 6 m and mass 20 kg leans against a smooth vertical wall at an angle of 60° to the horizontal. The coefficient of static friction between ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "What is the smallest positive integer that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by...	{ "id": "gen-c2cb8c9ab1be259d", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "What is the smallest positive integer that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 4 when divided by 7?", ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Evaluate the definite integral \\( \\int_0^1 \\frac{\\ln(1+x)}{1+x^2} \\, dx \\)." }, { "from": "gpt", "va...	{ "id": "gen-5a68b104a481ae91", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Evaluate the definite integral \\( \\int_0^1 \\frac{\\ln(1+x)}{1+x^2} \\, dx \\).", "reasoning": "We need to evaluate the definite integral I = ∫_0^1 ln(1+x)/(1+x...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A dynamic array starts with capacity 1 and 0 elements. It supports two operations:\n- push(x): if the current size equ...	{ "id": "gen-355ad2d212a29f35", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A dynamic array starts with capacity 1 and 0 elements. It supports two operations:\n- push(x): if the current size equals the capacity, the capacity is doubled and ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "What is the major organic product formed when 2,3-dimethyl-2,3-butanediol (pinacol) is heated with concentrated sulfur...	{ "id": "gen-96258814dc969aee", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "What is the major organic product formed when 2,3-dimethyl-2,3-butanediol (pinacol) is heated with concentrated sulfuric acid?", "reasoning": "We need to determin...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A rectangular wooden block of uniform density floats upright in a large tank of fresh water. A vertical cylindrical ho...	{ "id": "gen-d04aa04d7854cd8d", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A rectangular wooden block of uniform density floats upright in a large tank of fresh water. A vertical cylindrical hole is drilled through the center of the block ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "The table below shows production data for four factories in a given month.\n\n\| Factory \| Units Produced \| Defective U...	{ "id": "gen-92b4c46ef9681917", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "The table below shows production data for four factories in a given month.\n\n\| Factory \| Units Produced \| Defective Units \| Rework Cost per Defective Unit ($) \|\n\|...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Four friends—Alice, Bob, Carol, and Dave—each have a different favorite fruit (apple, banana, cherry, date), a differe...	{ "id": "gen-49420ac05512b72e", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Four friends—Alice, Bob, Carol, and Dave—each have a different favorite fruit (apple, banana, cherry, date), a different favorite color (red, blue, green, yellow), ...