conversations listlengths 3 3 | meta dict |
|---|---|
[
{
"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 elementary number theory. Must be self-contained, single correct ver... | {
"id": "gen-d8178f4e88d4cecc",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a single advanced question about elementary number theory. Must be self-contained, single correct verifiable answer, solvable through explicit reas... |
[
{
"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 recurrence relation \\( T(n) = 2T(n/2) + \\frac{n}{\\log_2 n} \\) for \\( n > 1 \\), with base case \\( T... | {
"id": "gen-8e60ebddb742b752",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the recurrence relation \\( T(n) = 2T(n/2) + \\frac{n}{\\log_2 n} \\) for \\( n > 1 \\), with base case \\( T(1) = 1 \\). What is the asymptotic tight boun... |
[
{
"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 organic chemistry question, self-contained, single correct answer, solvable by re... | {
"id": "gen-97eb800de461af7f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level organic chemistry question, self-contained, single correct answer, solvable by reasoning. No answer or hints. Just the question... |
[
{
"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 \\( n \\) that leaves a remainder of 2 when divided by 3, a remainder of 3 when div... | {
"id": "gen-2de318ebc76c025e",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Find the smallest positive integer \\( n \\) 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 b... |
[
{
"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 200 g aluminum cup (specific heat capacity 0.90 J/g·°C) contains 300 g of water (specific heat capacity 4.18 J/g·°C)... | {
"id": "gen-387944f2e7afbafb",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A 200 g aluminum cup (specific heat capacity 0.90 J/g·°C) contains 300 g of water (specific heat capacity 4.18 J/g·°C) at an initial temperature of 25.0°C. A 50.0 g... |
[
{
"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 cube has a side length of 4 cm. A smaller cube of side length 1 cm is removed from each of the eight corners of the ... | {
"id": "gen-270d859b0652b9b4",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A cube has a side length of 4 cm. A smaller cube of side length 1 cm is removed from each of the eight corners of the larger cube. What is the total surface area of... |
[
{
"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 disaster relief team has exactly one dose of antivenom for a fatal snake bite. Two victims arrive at the same time: ... | {
"id": "gen-bdb250304764fc4b",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A disaster relief team has exactly one dose of antivenom for a fatal snake bite. Two victims arrive at the same time: Victim A is a 10-year-old child who will die w... |
[
{
"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 of size 13 uses open addressing with quadratic probing. The hash function is h(k) = k mod 13, and the pro... | {
"id": "gen-6c482a1cca3bd273",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hash table of size 13 uses open addressing with quadratic probing. The hash function is h(k) = k mod 13, and the probe sequence is defined as (h(k) + i^2) mod 13 ... |
[
{
"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 right circular cone has height 12 and base radius 5. A sphere is inscribed in the cone, tangent to the base and the ... | {
"id": "gen-39a7d8a55c0c19da",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A right circular cone has height 12 and base radius 5. A sphere is inscribed in the cone, tangent to the base and the lateral surface. What is the radius of the 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 a single advanced question about everyday physical reasoning. Must be self-contained, single correct ... | {
"id": "gen-f2f1912ac8854105",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a single advanced question about everyday physical reasoning. Must be self-contained, single correct verifiable answer, solvable through explicit r... |
[
{
"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 cube has side length 4. A plane passes through the midpoints of the three edges that meet at one vertex of the cube.... | {
"id": "gen-93ccc864c1129872",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A cube has side length 4. A plane passes through the midpoints of the three edges that meet at one vertex of the cube. What is the area of the cross-section formed ... |
[
{
"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 all positive integers \\( n \\) such that \\( n^2 + 3n + 2 \\) divides \\( n^3 + 1 \\)."
},
{
"from": "gp... | {
"id": "gen-22f6c64df0cf7f9c",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Find all positive integers \\( n \\) such that \\( n^2 + 3n + 2 \\) divides \\( n^3 + 1 \\).",
"reasoning": "We need to find all positive integers n such that n^2... |
[
{
"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 real-valued function on the interval \\([0,1]\\) such that\n\\[\n\\int_0^1 f(x) \\, dx =... | {
"id": "gen-a9b84299d685e319",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let \\( f \\) be a continuous real-valued function on the interval \\([0,1]\\) such that\n\\[\n\\int_0^1 f(x) \\, dx = 1 \\quad \\text{and} \\quad \\int_0^1 x f(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": "We need to write an advanced question about ethical dilemmas with tradeoffs. Must be self-contained, single correct ve... | {
"id": "gen-af38e0013398bb25",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write an advanced question about ethical dilemmas with tradeoffs. Must be self-contained, single correct verifiable answer, solvable through explicit rea... |
[
{
"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 regular tetrahedron of edge length 6 inscribed in a sphere. A plane passes through the midpoints of the thr... | {
"id": "gen-08b33afe79f1f985",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider a regular tetrahedron of edge length 6 inscribed in a sphere. A plane passes through the midpoints of the three edges that meet at a single vertex of the t... |
[
{
"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 combinatorics question. Must be self-contained, single correct answer, solvable b... | {
"id": "gen-5f8d5fe3b08dc08f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level combinatorics question. Must be self-contained, single correct answer, solvable by reasoning. No answer or hints. Just the ques... |
[
{
"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 differentiable function on \\( \\mathbb{R} \\) such that \\( f(0) = 1 \\) and \\( f'(x) = f(x) + x ... | {
"id": "gen-77779ddce7cd161d",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let \\( f \\) be a differentiable function on \\( \\mathbb{R} \\) such that \\( f(0) = 1 \\) and \\( f'(x) = f(x) + x \\) for all \\( x \\). Find \\( f(1) \\).",
... |
[
{
"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 chiral secondary alcohol, (R)-2-phenyl-1-propanol, is treated with thionyl chloride (SOCl₂) in the presence of pyrid... | {
"id": "gen-a8fc08955cac6be5",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A chiral secondary alcohol, (R)-2-phenyl-1-propanol, is treated with thionyl chloride (SOCl₂) in the presence of pyridine at 0 °C, then the resulting chloride is re... |
[
{
"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 employer (risk-neutral) hires a worker (risk-averse with utility u(w) = √w) for a project. The worker chooses effor... | {
"id": "gen-1eb9463d105d0651",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "An employer (risk-neutral) hires a worker (risk-averse with utility u(w) = √w) for a project. The worker chooses effort: High (cost 10) or Low (cost 0). If High 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": "A right circular cone has height 4 and base radius 3. A sphere is inscribed in the cone, tangent to the base and the l... | {
"id": "gen-5b079cabdaab7934",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A right circular cone has height 4 and base radius 3. A sphere is inscribed in the cone, tangent to the base and the lateral surface. A second sphere is placed insi... |
[
{
"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 the monthly sales (in units) of four products over three months.\n\n| Product | Jan | Feb | Mar ... | {
"id": "gen-d822ee6a68833052",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows the monthly sales (in units) of four products over three months.\n\n| Product | Jan | Feb | Mar |\n|---------|-----|-----|-----|\n| A | ... |
[
{
"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 classical mechanics. It must be self-contained, have a single corr... | {
"id": "gen-5e5bb223d96bd6bf",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level question about classical mechanics. It must be self-contained, have a single correct verifiable 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 produce a single advanced question about algorithms and data structures. Must be self-contained, single cor... | {
"id": "gen-60ffb7cf5a304c6c",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to produce a single advanced question about algorithms and data structures. Must be self-contained, single correct verifiable answer, solvable through expli... |
[
{
"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 fair six-sided die is rolled repeatedly. Let \\(N\\) be the number of rolls required until the sum of the last two r... | {
"id": "gen-d5bd9458b1ee6f7f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A fair six-sided die is rolled repeatedly. Let \\(N\\) be the number of rolls required until the sum of the last two rolls equals 7 for the first time. (For example... |
[
{
"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 hospital ethics committee must allocate a single available liver for transplant among three patients. Patient A (age... | {
"id": "gen-1b2e000a21effb90",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital ethics committee must allocate a single available liver for transplant among three patients. Patient A (age 28) has acute liver failure from acetaminophe... |
[
{
"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 pharmaceutical company has developed a life-saving drug for a rare pediatric disease affecting 500 children worldwid... | {
"id": "gen-9cd85e78b000e814",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A pharmaceutical company has developed a life-saving drug for a rare pediatric disease affecting 500 children worldwide. The drug costs $2 million per treatment cou... |
[
{
"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": "For each nonnegative integer \\( n \\), define \\( a_n = \\int_0^1 x^n e^x \\, dx \\). Evaluate the sum \\( \\sum_{n=0... | {
"id": "gen-d35677fe801ef4b7",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "For each nonnegative integer \\( n \\), define \\( a_n = \\int_0^1 x^n e^x \\, dx \\). Evaluate the sum \\( \\sum_{n=0}^\\infty \\frac{a_n}{n!} \\).",
"reasoning"... |
[
{
"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 firm hires a risk-averse worker to complete a project. The worker's effort level e ∈ [0,1] determines t... | {
"id": "gen-5f65a6b705378318",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A risk-neutral firm hires a risk-averse worker to complete a project. The worker's effort level e ∈ [0,1] determines the probability of success: P(success) = e. 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": "We need to write a single advanced calculus/analysis question, self-contained, with a definite checkable answer, solva... | {
"id": "gen-7a3b3638f8a2250e",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a single advanced calculus/analysis question, self-contained, with a definite checkable answer, solvable by reasoning. No answer, no hints. Just th... |
[
{
"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 fair coin is flipped repeatedly until the sequence HTH (heads, tails, heads) appears for the first time as three con... | {
"id": "gen-f27d7938f03149bc",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A fair coin is flipped repeatedly until the sequence HTH (heads, tails, heads) appears for the first time as three consecutive flips. Let X be the total number of f... |
[
{
"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 economics and incentives. It should be self-contained, have a sing... | {
"id": "gen-5bec1f104aae6463",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level question about economics and incentives. It should be self-contained, have a single correct verifiable answer, solvable through... |
[
{
"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(x) = \\begin{cases} x^2 \\sin(1/x), & x \\neq 0 \\\\ 0, & x = 0 \\end{cases} \\).\n\n(a) Show that \\( f \\)... | {
"id": "gen-a0f821b4c4b32640",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let \\( f(x) = \\begin{cases} x^2 \\sin(1/x), & x \\neq 0 \\\\ 0, & x = 0 \\end{cases} \\).\n\n(a) Show that \\( f \\) is differentiable at \\( x = 0 \\) and comput... |
[
{
"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 product, including its absolute configuration, when (R)-2-bromobutane is treated with sodium cyanide... | {
"id": "gen-627c4ba331af382b",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "What is the major product, including its absolute configuration, when (R)-2-bromobutane is treated with sodium cyanide in dimethyl sulfoxide?",
"reasoning": "We 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": "A hospital has one remaining dose of a life-saving drug. Two patients need it: Patient A is a 25-year-old single paren... | {
"id": "gen-f0b6fb22e96c8f94",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital has one remaining dose of a life-saving drug. Two patients need it: Patient A is a 25-year-old single parent of two young children, with a 90% chance of ... |
[
{
"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 cube of side length 2 has one vertex at the origin and its edges along the positive x-, y-, and z-axes. A plane pass... | {
"id": "gen-0ae7316551ad53f6",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A cube of side length 2 has one vertex at the origin and its edges along the positive x-, y-, and z-axes. A plane passes through the points (2,0,0), (0,2,0), and (0... |
[
{
"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 an initially empty binary search tree (BST). Keys are inserted in the following order: 50, 30, 70, 20, 40, 60... | {
"id": "gen-ee0e3a75058c4a8c",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider an initially empty binary search tree (BST). Keys are inserted in the following order: 50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45. After all insertions, wh... |
[
{
"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 bead of mass \\( m \\) slides without friction on a vertical circular hoop of radius \\( R \\). The hoop rotates wit... | {
"id": "gen-afc9cb643e9a2eea",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A bead of mass \\( m \\) slides without friction on a vertical circular hoop of radius \\( R \\). The hoop rotates with constant angular velocity \\( \\Omega \\) ab... |
[
{
"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 hospital ethics committee must allocate one available liver for transplant. Two candidates are matched:\n\n- Candida... | {
"id": "gen-f72a1db3f0ddfd3c",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital ethics committee must allocate one available liver for transplant. Two candidates are matched:\n\n- Candidate A: 28 years old, acute liver failure from a... |
[
{
"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 set of all permutations of the numbers 1, 2, …, 10. A permutation is called “good” if for every i from 1 ... | {
"id": "gen-1d3eaf243445b7ca",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the set of all permutations of the numbers 1, 2, …, 10. A permutation is called “good” if for every i from 1 to 9, the numbers i and i+1 are not adjacent i... |
[
{
"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": "Predict the major organic product(s) formed when (E)-3-methyl-2-pentene is treated with bromine in water (Br₂/H₂O). In... | {
"id": "gen-be13396dcd3e8c9e",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Predict the major organic product(s) formed when (E)-3-methyl-2-pentene is treated with bromine in water (Br₂/H₂O). Indicate the stereochemistry of the product(s) b... |
[
{
"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 an array of distinct integers sorted in ascending order that has been rotated at some pivot unknown to you be... | {
"id": "gen-db4dd324b54a1cfa",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider an array of distinct integers sorted in ascending order that has been rotated at some pivot unknown to you beforehand (e.g., `[0,1,2,4,5,6,7]` might become... |
[
{
"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 cube of side length 2 has vertices at (0,0,0), (2,0,0), (2,2,0), (0,2,0), (0,0,2), (2,0,2), (2,2,2), (0,2,2). A regu... | {
"id": "gen-9cacc2f1d1ba0410",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A cube of side length 2 has vertices at (0,0,0), (2,0,0), (2,2,0), (0,2,0), (0,0,2), (2,0,2), (2,2,2), (0,2,2). A regular tetrahedron is formed by the vertices (0,0... |
[
{
"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 elementary number theory. It must be self-contained, have a single... | {
"id": "gen-7a0eb92b3ab006de",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level question about elementary number theory. It must be self-contained, have a single correct answer, solvable through reasoning, 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": "Evaluate the limit:\n\\[\n\\lim_{n\\to\\infty} n \\int_0^1 x^n \\arctan(x) \\, dx.\n\\]"
},
{
"from": "gpt",
... | {
"id": "gen-10655e6ee12aee61",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Evaluate the limit:\n\\[\n\\lim_{n\\to\\infty} n \\int_0^1 x^n \\arctan(x) \\, dx.\n\\]",
"reasoning": "We need to evaluate the limit: \\(\\lim_{n\\to\\infty} 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": "A block of mass 2.0 kg is released from rest at the top of a rough inclined plane of length 5.0 m that makes an angle ... | {
"id": "gen-170fbeeca0663b18",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A block of mass 2.0 kg is released from rest at the top of a rough inclined plane of length 5.0 m that makes an angle of 30° with the horizontal. The coefficient of... |
[
{
"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 hash table of size 13 that uses open addressing with quadratic probing. The hash function is \\(h(k, i) = (... | {
"id": "gen-444ea828cab74306",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider a hash table of size 13 that uses open addressing with quadratic probing. The hash function is \\(h(k, i) = (k \\bmod 13 + i^2) \\bmod 13\\), where \\(i = ... |
[
{
"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 classical mechanics. It must be self-contained, have a single correc... | {
"id": "gen-ec3addf1f96fa3d2",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a single advanced question about classical mechanics. It must be self-contained, have a 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": "We need to write a single advanced geometry/spatial reasoning question, self-contained, with a definite checkable answ... | {
"id": "gen-25dfc121d99a83dd",
"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 checkable answer, solvable by reasoning. No answer, no hints... |
[
{
"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 islanders—A, B, C, and D—are each either a knight (who always tells the truth) or a knave (who always lies). They... | {
"id": "gen-71747ff52c679506",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Four islanders—A, B, C, and D—are each either a knight (who always tells the truth) or a knave (who always lies). They make the following statements: \nA says: “B ... |
[
{
"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 wants to reduce traffic congestion during rush hour. It considers two policies:\n\nPolicy A: Charge ... | {
"id": "gen-430d14149adb0e21",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A city government wants to reduce traffic congestion during rush hour. It considers two policies:\n\nPolicy A: Charge a $10 fee for every vehicle entering the downt... |
[
{
"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 all positive integers \\( n \\) such that \\( n^4 + 4 \\) is a prime number."
},
{
"from": "gpt",
"va... | {
"id": "gen-c6f480ee867734ec",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Find all positive integers \\( n \\) such that \\( n^4 + 4 \\) is a prime number.",
"reasoning": "We need to find all positive integers n such that n^4 + 4 is pri... |
[
{
"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 principal hires a risk-averse agent to complete a project. The agent's utility is \\( u(w, e) = \\sqrt{... | {
"id": "gen-8c8d5c991581ede2",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A risk-neutral principal hires a risk-averse agent to complete a project. The agent's utility is \\( u(w, e) = \\sqrt{w} - c(e) \\), where \\( w \\geq 0 \\) is 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": "Let \\( f(x) = \\begin{cases} x^2 \\sin(1/x) & \\text{if } x \\neq 0, \\\\ 0 & \\text{if } x = 0. \\end{cases} \\) Det... | {
"id": "gen-d526c4757185045c",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let \\( f(x) = \\begin{cases} x^2 \\sin(1/x) & \\text{if } x \\neq 0, \\\\ 0 & \\text{if } x = 0. \\end{cases} \\) Determine whether \\( f \\) is differentiable at ... |
[
{
"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 cube with side length 6 has a plane that passes through the midpoints of three edges that meet at a single vertex. W... | {
"id": "gen-9a8a30975b2a4a31",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A cube with side length 6 has a plane that passes through the midpoints of three edges that meet at a single vertex. What is the area of the cross-section formed by... |
[
{
"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 intermediate question about organic chemistry reactions. Must be self-contained, single corr... | {
"id": "gen-be69ac3307b0006c",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a single intermediate question about organic chemistry reactions. Must be self-contained, single correct verifiable 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": "A regular tetrahedron has edge length 6. A plane cuts through the tetrahedron parallel to one of its faces at a distan... | {
"id": "gen-46cc7e7e5a33db5f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A regular tetrahedron has edge length 6. A plane cuts through the tetrahedron parallel to one of its faces at a distance of 2 from that face. What is the area of th... |
[
{
"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(x) = \\begin{cases} ax^2 + 1 & \\text{if } x \\le 1, \\\\ 2x + a & \\text{if } x > 1. \\end{cases} \\)\nFind... | {
"id": "gen-a14dcc2e0daaff35",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let \\( f(x) = \\begin{cases} ax^2 + 1 & \\text{if } x \\le 1, \\\\ 2x + a & \\text{if } x > 1. \\end{cases} \\)\nFind all real values of \\( a \\) for which \\( f ... |
[
{
"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 hospital has only one ventilator available for two patients. Patient X has a 70% probability of survival if given th... | {
"id": "gen-7fcdab68c7d576ab",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital has only one ventilator available for two patients. Patient X has a 70% probability of survival if given the ventilator and a 10% probability without it.... |
[
{
"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 following Python program is intended to evaluate the postfix expression `10 6 - 2 /` (which mathematically equals ... | {
"id": "gen-86c67c9ea5bce731",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The following Python program is intended to evaluate the postfix expression `10 6 - 2 /` (which mathematically equals (10 - 6) / 2 = 2). However, the program contai... |
[
{
"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 shopping cart of mass 15 kg is pushed up a ramp inclined at 10° to the horizontal with an initial speed of 2.5 m/s. ... | {
"id": "gen-d47e5f2a01e9110a",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A shopping cart of mass 15 kg is pushed up a ramp inclined at 10° to the horizontal with an initial speed of 2.5 m/s. The coefficient of kinetic friction between th... |
[
{
"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 delivery robot must transport four packages (A, B, C, D) from a warehouse to their respective drop-off locations (1,... | {
"id": "gen-2f30cdfb7c76e9b1",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A delivery robot must transport four packages (A, B, C, D) from a warehouse to their respective drop-off locations (1, 2, 3, 4) in a single trip. The robot can carr... |
[
{
"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 friends—Alex, Bailey, and Casey—each have a different favorite color (red, blue, green), a different pet (cat, d... | {
"id": "gen-b6eab06176586153",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Three friends—Alex, Bailey, and Casey—each have a different favorite color (red, blue, green), a different pet (cat, dog, fish), and a different favorite drink (cof... |
[
{
"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 7-digit numbers can be formed using each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once such that the number ... | {
"id": "gen-631ce6a7a726535d",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "How many 7-digit numbers can be formed using each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once such that the number is divisible by 11?",
"reasoning": "We need ... |
[
{
"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 user wants a single introductory question about classical mechanics. It must be self-contained, have a single corr... | {
"id": "gen-1fae4d9ba157f1fe",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The user wants a single introductory question about classical mechanics. It must be self-contained, have a single correct answer, be solvable by reasoning, and not ... |
[
{
"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": "Alice, Bob, and Carol each have a different pet (cat, dog, bird) and a different favorite color (red, blue, green). Us... | {
"id": "gen-ef40b85a100a0145",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Alice, Bob, and Carol each have a different pet (cat, dog, bird) and a different favorite color (red, blue, green). Using the clues below, determine who has the cat... |
[
{
"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 hospital has exactly one dose of a life-saving medication. Two patients need it immediately or they will die. Patien... | {
"id": "gen-5f65e8ca3cdbce25",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital has exactly one dose of a life-saving medication. Two patients need it immediately or they will die. Patient X is 30 years old; if treated, they have an ... |
[
{
"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 robot is in a linear corridor of five rooms numbered 1 through 5. The robot starts in room 1. The doors between adja... | {
"id": "gen-1b3fcbf7ca579540",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A robot is in a linear corridor of five rooms numbered 1 through 5. The robot starts in room 1. The doors between adjacent rooms are initially unlocked, except:\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": "A 100 g ice cube at -10°C is placed into 200 g of water at 20°C in a perfectly insulated container. The specific heat ... | {
"id": "gen-19fb66bbc461057f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A 100 g ice cube at -10°C is placed into 200 g of water at 20°C in a perfectly insulated container. The specific heat capacity of ice is 2.09 J/(g·°C), the specific... |
[
{
"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 π be a permutation of the set {1, 2, 3, 4, 5, 6}. We say π is 'admissible' if π(i) ≠ i and π(i) ≠ 7−i for all i = ... | {
"id": "gen-b5e3ffa72eb348df",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let π be a permutation of the set {1, 2, 3, 4, 5, 6}. We say π is 'admissible' if π(i) ≠ i and π(i) ≠ 7−i for all i = 1, 2, 3, 4, 5, 6. How many admissible permutat... |
[
{
"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 organic chemistry question. Must be self-contained, single correct answer, solvab... | {
"id": "gen-9bd6d7ca734bb5f3",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level organic chemistry question. Must be self-contained, single correct answer, solvable by reasoning, no answer or 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": "A 2.0 kg block is pushed against a horizontal spring with spring constant 200 N/m, compressing the spring by 0.15 m fr... | {
"id": "gen-3e2380f532dfbfc4",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A 2.0 kg block is pushed against a horizontal spring with spring constant 200 N/m, compressing the spring by 0.15 m from its equilibrium length. The block is releas... |
[
{
"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 hospital has one remaining dose of a life-saving drug. Five patients need it: Patient A (age 25, 90% survival probab... | {
"id": "gen-4242829c90f89d26",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital has one remaining dose of a life-saving drug. Five patients need it: Patient A (age 25, 90% survival probability with treatment, 0% without), Patient B (... |
[
{
"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 fair coin is flipped. If it lands heads, you win $3; if it lands tails, you lose $2. What is the expected value of y... | {
"id": "gen-72414a0ace557ece",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A fair coin is flipped. If it lands heads, you win $3; if it lands tails, you lose $2. What is the expected value of your net gain from one flip?",
"reasoning": "... |
[
{
"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 are sitting in a parked car holding a helium-filled balloon by a string. The balloon floats upward, tethered by th... | {
"id": "gen-63afd26f24873851",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "You are sitting in a parked car holding a helium-filled balloon by a string. The balloon floats upward, tethered by the string. The car then accelerates forward rap... |
[
{
"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 live in a different one of four houses that stand in a row, numbered... | {
"id": "gen-4a4ccb3001f06f76",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Four friends — Alice, Bob, Carol, and Dave — each live in a different one of four houses that stand in a row, numbered 1 (leftmost) to 4 (rightmost). Each house is ... |
[
{
"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 regional health authority must allocate a single available liver for transplant. Two candidates are evaluated using ... | {
"id": "gen-7565c8f24db70c6d",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A regional health authority must allocate a single available liver for transplant. Two candidates are evaluated using a scoring system that multiplies the probabili... |
[
{
"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 right pyramid has a square base of side length 6 and height 4. A sphere is inscribed in the pyramid, tangent to the ... | {
"id": "gen-3e42bda9e7b0d46a",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A right pyramid has a square base of side length 6 and height 4. A sphere is inscribed in the pyramid, tangent to the base and all four lateral faces. A second sphe... |
[
{
"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 right circular cone has base radius 6 and height 8. A sphere is inscribed in the cone, tangent to the base and the l... | {
"id": "gen-728c92ca9fc9e8da",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A right circular cone has base radius 6 and height 8. A sphere is inscribed in the cone, tangent to the base and the lateral surface. A second sphere is placed insi... |
[
{
"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 project consists of five tasks: A, B, C, D, and E. Each task takes exactly one day to complete. The tasks have the f... | {
"id": "gen-ce94d2a8fd402d04",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A project consists of five tasks: A, B, C, D, and E. Each task takes exactly one day to complete. The tasks have the following dependencies:\n- Task B cannot start ... |
[
{
"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 regional health authority has 70 doses of a vaccine that reduces mortality from a deadly virus. There are two popula... | {
"id": "gen-75ac1d860ae71936",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A regional health authority has 70 doses of a vaccine that reduces mortality from a deadly virus. There are two population groups: Group A consists of 50 individual... |
[
{
"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 the number of students enrolled, number of faculty, and total research grant funding (in thousan... | {
"id": "gen-2d29b354ec776f90",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows the number of students enrolled, number of faculty, and total research grant funding (in thousands of dollars) for four departments at a unive... |
[
{
"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 elementary number theory. It should be self-contained, have a sing... | {
"id": "gen-0fcdfd1f09f2b52e",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level question about elementary number theory. It should be self-contained, have a single correct answer, solvable through reasoning.... |
[
{
"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 principal hires a risk-averse agent to complete a project. The agent's utility function is u(w, e) = √w... | {
"id": "gen-db1b6a0ae53ab5f1",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A risk-neutral principal hires a risk-averse agent to complete a project. The agent's utility function is u(w, e) = √w − e, where w is the wage received and e ∈ {0,... |
[
{
"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 cylindrical block of wood of density 0.9 g/cm³ and height 20 cm floats in a container of water (density 1.0 ... | {
"id": "gen-670ec8a1e8da8610",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A uniform cylindrical block of wood of density 0.9 g/cm³ and height 20 cm floats in a container of water (density 1.0 g/cm³). Oil of density 0.8 g/cm³ is poured on ... |
[
{
"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 the number of units produced and the number of defective units for four factories (A, B, C, D) a... | {
"id": "gen-5ff21a963db5ad8a",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows the number of units produced and the number of defective units for four factories (A, B, C, D) across two shifts.\n\n| Factory | Shift 1 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": "A monopolist faces a consumer with private type θ ∈ {θ_H, θ_L} where θ_H = 10 and θ_L = 6. The prior probabilities are... | {
"id": "gen-d1e2093568944544",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A monopolist faces a consumer with private type θ ∈ {θ_H, θ_L} where θ_H = 10 and θ_L = 6. The prior probabilities are Pr(θ_H) = Pr(θ_L) = 1/2. The consumer's utili... |
[
{
"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 principal hires a risk-neutral agent to produce output. The agent can choose effort \\(e \\in \\{0,1\\}... | {
"id": "gen-bae0889f0a356c40",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A risk-neutral principal hires a risk-neutral agent to produce output. The agent can choose effort \\(e \\in \\{0,1\\}\\). If \\(e=1\\) (high effort), the probabili... |
[
{
"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 the annual financial data for Apex Corp from 2021 to 2023.\n\n| Year | Revenue ($ Millions) | Co... | {
"id": "gen-ac8548561d0df127",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows the annual financial data for Apex Corp from 2021 to 2023.\n\n| Year | Revenue ($ Millions) | Cost of Goods Sold ($ Millions) | Operating Expe... |
[
{
"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": "Determine the greatest common divisor of $2^{100} - 1$ and $2^{120} - 1$."
},
{
"from": "gpt",
"value": "<... | {
"id": "gen-4690baa5d5774d98",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Determine the greatest common divisor of $2^{100} - 1$ and $2^{120} - 1$.",
"reasoning": "We are asked to find the greatest common divisor (gcd) of 2^100 - 1 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": "Four friends—Alice, Bob, Carol, and Dave—each have a distinct favorite color (red, blue, green, yellow), a distinct pe... | {
"id": "gen-ad00cfc52658686a",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Four friends—Alice, Bob, Carol, and Dave—each have a distinct favorite color (red, blue, green, yellow), a distinct pet (cat, dog, fish, bird), and a distinct favor... |
[
{
"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 \\(U_1, U_2, \\dots\\) be independent random variables uniformly distributed on \\((0,1)\\). Define \\(N = \\min\\... | {
"id": "gen-e052d2bb41c256a8",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let \\(U_1, U_2, \\dots\\) be independent random variables uniformly distributed on \\((0,1)\\). Define \\(N = \\min\\{ n \\ge 1 : U_1 + \\dots + U_n > 1 \\}\\). Co... |
[
{
"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 wants to reduce traffic congestion during rush hour. They consider two policies:\n\nPolicy A: Charge... | {
"id": "gen-400a30edb9797ab6",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A city government wants to reduce traffic congestion during rush hour. They consider two policies:\n\nPolicy A: Charge a $10 fee for any vehicle entering the downto... |
[
{
"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 everyday physical reasoning. It must be self-contained, single cor... | {
"id": "gen-179b770abc47a259",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level question about everyday physical reasoning. It must be self-contained, single correct answer, solvable by reasoning, no answer/... |
[
{
"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 vehicle's ethical decision module operates under a strict, prioritized rule set:\n1. Minimize total expe... | {
"id": "gen-2c5cef264b8c0cf5",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "An autonomous vehicle's ethical decision module operates under a strict, prioritized rule set:\n1. Minimize total expected harm, quantified as: 1 fatality = 100 har... |
[
{
"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 Python function intended to compute the sum of all even numbers in a list:\n\n```python\ndef su... | {
"id": "gen-b2d433dc59591705",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following Python function intended to compute the sum of all even numbers in a list:\n\n```python\ndef sum_evens(numbers):\n total = 0\n for i 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 a robot with a single gripper that can hold at most one box at a time. The robot operates between two tables,... | {
"id": "gen-8c0e359305067643",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider a robot with a single gripper that can hold at most one box at a time. The robot operates between two tables, Table1 and Table2, and can move between them ... |
[
{
"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 calculus and analysis. Must be self-contained, single correct veri... | {
"id": "gen-2879d4a502d5bbe6",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level question about calculus and analysis. Must be self-contained, single correct verifiable answer, solvable through explicit reaso... |
[
{
"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 project consists of four tasks: A, B, C, and D. Their durations (in days) are: A = 3, B = 2, C = 4, D = 1. The prece... | {
"id": "gen-571f8cd8468dc035",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A project consists of four tasks: A, B, C, and D. Their durations (in days) are: A = 3, B = 2, C = 4, D = 1. The precedence constraints are: A must finish before B ... |
[
{
"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 data interpretation from a table. It must be self-contained, have a ... | {
"id": "gen-d58f178c878496e6",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a single advanced question about data interpretation from a table. It must be self-contained, have a single correct verifiable answer, solvable thr... |
[
{
"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 the quarterly revenue (in thousands of dollars) for five products over one year.\n\n| Product | ... | {
"id": "gen-7d6805ef269bc5bc",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows the quarterly revenue (in thousands of dollars) for five products over one year.\n\n| Product | Q1 | Q2 | Q3 | Q4 |\n|---------|----|----|----... |
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