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": "Let φ(n) denote Euler's totient function (the number of positive integers k ≤ n with gcd(k, n) = 1). Determine all pos... | {
"id": "gen-03763ee8be63bc2c",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let φ(n) denote Euler's totient function (the number of positive integers k ≤ n with gcd(k, n) = 1). Determine all positive integers n such that φ(n) = 12.",
"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 the following Python code:\n\n```python\nfuncs = []\nfor i in range(3):\n funcs.append(lambda: i)\nprint([... | {
"id": "gen-6827d4cdf4a624bc",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following Python code:\n\n```python\nfuncs = []\nfor i in range(3):\n funcs.append(lambda: i)\nprint([f() for f in funcs])\n```\n\nWhat is the outpu... |
[
{
"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 program:\n\n```python\ndef fib_sequence(n):\n a, b = 0, 1\n result = []\n for i... | {
"id": "gen-606ed8454af83bc3",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following Python program:\n\n```python\ndef fib_sequence(n):\n a, b = 0, 1\n result = []\n for i in range(n):\n result.append(a)\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 people—Alice, Bob, Carol, and Dave—are each either a knight (who always tells the truth) or a knave (who always l... | {
"id": "gen-0beb9cb70faca735",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Four people—Alice, Bob, Carol, and Dave—are each either a knight (who always tells the truth) or a knave (who always lies). They make the following statements:\n\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 person sits in a closed car holding a helium-filled balloon on a string. The windows are rolled up and the air insid... | {
"id": "gen-27ded22f5f041dfa",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A person sits in a closed car holding a helium-filled balloon on a string. The windows are rolled up and the air inside is still. The car accelerates forward from 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": "The table below shows quarterly sales (in thousands of units) for four regions.\n\n| Region | Q1 | Q2 | Q3 | Q4 |\n|--... | {
"id": "gen-91cbc2e2c61271eb",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows quarterly sales (in thousands of units) for four regions.\n\n| Region | Q1 | Q2 | Q3 | Q4 |\n|--------|----|----|----|----|\n| North | 120 | ... |
[
{
"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 boat floats in a swimming pool with a heavy rock on board. The rock is thrown overboard and sinks to the bottom. Doe... | {
"id": "gen-29fe7bb9383bd2ba",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A boat floats in a swimming pool with a heavy rock on board. The rock is thrown overboard and sinks to the bottom. Does the water level in the pool rise, fall, or s... |
[
{
"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 perfect logicians—Alice, Bob, and Carol—are each wearing a hat with a positive integer written on it. They can s... | {
"id": "gen-e46b107287ccbf8d",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Three perfect logicians—Alice, Bob, and Carol—are each wearing a hat with a positive integer written on it. They can see the numbers on the other two hats but not 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": "Consider the function \\( f(x) = x^3 - 3x + 1 \\). Let \\( R \\) be the region in the \\( xy \\)-plane bounded by the ... | {
"id": "gen-e89d1c41b139bafa",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the function \\( f(x) = x^3 - 3x + 1 \\). Let \\( R \\) be the region in the \\( xy \\)-plane bounded by the graph of \\( y = f(x) \\), the \\( x \\)-axis,... |
[
{
"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-bromo-2-methylbutane is treated with potassium tert-butoxide in tert-b... | {
"id": "gen-028ba8279bc4ce6f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "What is the major organic product formed when 2-bromo-2-methylbutane is treated with potassium tert-butoxide in tert-butanol? Provide the IUPAC name of the product.... |
[
{
"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 salesperson to sell a product. The salesperson can choose high effort (cost = 20 utils) or... | {
"id": "gen-2ed64b9e116a7db9",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A risk-neutral firm hires a salesperson to sell a product. The salesperson can choose high effort (cost = 20 utils) or low effort (cost = 0 utils). With high effort... |
[
{
"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": "Five friends—Alice, Ben, Clara, Dan, and Eva—each own a different type of pet (cat, dog, parrot, rabbit, turtle), pref... | {
"id": "gen-15d58bf848332a03",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Five friends—Alice, Ben, Clara, Dan, and Eva—each own a different type of pet (cat, dog, parrot, rabbit, turtle), prefer a distinct favorite color (red, blue, green... |
[
{
"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 all permutations of the numbers 1, 2, 3, 4, 5, 6, 7. How many of these permutations have the property that fo... | {
"id": "gen-3a119019b1aab58f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider all permutations of the numbers 1, 2, 3, 4, 5, 6, 7. How many of these permutations have the property that for every i from 1 to 6, the number i is not imm... |
[
{
"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 logistics company must deliver packages to four locations (A, B, C, D) using a single truck starting and ending at t... | {
"id": "gen-51d2f67cc18981e6",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A logistics company must deliver packages to four locations (A, B, C, D) using a single truck starting and ending at the depot (O). The truck has a capacity of 10 u... |
[
{
"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, which is intended to compute the sum of the first n Fibonacci numbers (where F... | {
"id": "gen-1f1f16b21865c7fb",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following Python function, which is intended to compute the sum of the first n Fibonacci numbers (where F_1 = 1, F_2 = 1):\n\ndef fib_sum(n):\n if 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": "Consider the following algorithm that processes an array A of length n:\n\nmax = A[1]\nupdates = 0\nfor i = 2 to n:\n ... | {
"id": "gen-9dc33a0bc555cfc0",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following algorithm that processes an array A of length n:\n\nmax = A[1]\nupdates = 0\nfor i = 2 to n:\n if A[i] > max:\n max = A[i]\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": "The following Python function is intended to return the sum of all even integers from 1 to n inclusive, but it contain... | {
"id": "gen-107b197ddef21cc1",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The following Python function is intended to return the sum of all even integers from 1 to n inclusive, but it contains a bug.\n\n```python\ndef sum_even(n):\n 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 single intermediate question about data interpretation from a table. Must be self-contained, with a... | {
"id": "gen-960eb505c1fa89bb",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a single intermediate question about data interpretation from a table. Must be self-contained, with a table included in the question. Must have a s... |
[
{
"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. Let T be the number of flips until the sequence HTH appears for the first time. Fin... | {
"id": "gen-b6acc162a737b599",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A fair coin is flipped repeatedly. Let T be the number of flips until the sequence HTH appears for the first time. Find the expected value of T.",
"reasoning": "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": "Find all prime numbers \\( p \\) such that \\( p^2 + 2 \\) is also prime."
},
{
"from": "gpt",
"value": "<... | {
"id": "gen-1359f567da99516f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Find all prime numbers \\( p \\) such that \\( p^2 + 2 \\) is also prime.",
"reasoning": "We need to find all prime numbers p such that p^2 + 2 is also prime.\n\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": "We need to write a single advanced question about economics and incentives. It must be self-contained, have a single c... | {
"id": "gen-7d0cbbb5d184a2aa",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a single advanced question about economics and incentives. It must be self-contained, have a single correct verifiable answer, solvable through exp... |
[
{
"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 dose of a life‑saving drug. Patient A has a 60% chance of surviving if given the drug, while P... | {
"id": "gen-40569d9a2f3cfff9",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital has only one dose of a life‑saving drug. Patient A has a 60% chance of surviving if given the drug, while Patient B has a 40% chance. If the ethical guid... |
[
{
"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 cylindrical glass of inner radius 4.0 cm contains water at 0°C. A 50 g ice cube at 0°C floats in the water. The ice ... | {
"id": "gen-196e163f75900100",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A cylindrical glass of inner radius 4.0 cm contains water at 0°C. A 50 g ice cube at 0°C floats in the water. The ice cube contains a 10 g steel ball bearing (densi... |
[
{
"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 absolute configuration) formed when (2R,3S)-2-bromo-3-methylpentane is treated wi... | {
"id": "gen-118d60c5283d8d55",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "What is the major product (including absolute configuration) formed when (2R,3S)-2-bromo-3-methylpentane is treated with potassium tert-butoxide in tert-butanol 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": "Consider the following table showing monthly sales (in units) for three products over six months:\n\n| Month | Product... | {
"id": "gen-0980c4bc53cf5ac9",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following table showing monthly sales (in units) for three products over six months:\n\n| Month | Product A | Product B | Product C |\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 seller wishes to sell a single indivisible item via a second-price sealed-bid auction with a reserve price \\( r \\)... | {
"id": "gen-78661d8ce3fe43ab",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A seller wishes to sell a single indivisible item via a second-price sealed-bid auction with a reserve price \\( r \\). There are two potential buyers. Buyer 1's va... |
[
{
"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 sum of all positive integers $n < 100$ such that $n^3 - n$ is divisible by $24$."
},
{
"from": "gpt",... | {
"id": "gen-306678d4f66b8a26",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Find the sum of all positive integers $n < 100$ such that $n^3 - n$ is divisible by $24$.",
"reasoning": "We need to find all positive integers n < 100 such that ... |
[
{
"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 3×10 rectangle is to be tiled using 1×2 dominoes. Each domino covers exactly two adjacent unit squares and may be pl... | {
"id": "gen-e69e3f7c16d105a0",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A 3×10 rectangle is to be tiled using 1×2 dominoes. Each domino covers exactly two adjacent unit squares and may be placed either horizontally or vertically. Domino... |
[
{
"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 elementary number theory. It must be self-contained, have a sing... | {
"id": "gen-5b42fbc3d3aa505f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a single intermediate question about elementary number theory. It must 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": "How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if no digit is repeated and the number mus... | {
"id": "gen-809210346edaf1e6",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if no digit is repeated and the number must be even?",
"reasoning": "We need to count ... |
[
{
"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-ba8fe501f5e530fb",
"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": "Starting from pent-4-en-1-ol, the following sequence of reactions is performed:\n1. Protection of the hydroxyl group u... | {
"id": "gen-dc5c4f036bfbfb37",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Starting from pent-4-en-1-ol, the following sequence of reactions is performed:\n1. Protection of the hydroxyl group using tert-butyldimethylsilyl chloride (TBSCl) ... |
[
{
"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 the function defined by f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0. Is f differentiable at x = 0? If so, what... | {
"id": "gen-71174ee894fe9d0f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let f be the function defined by f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0. Is f differentiable at x = 0? If so, what is f'(0)?",
"reasoning": "We need to determ... |
[
{
"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": "Five tasks A, B, C, D, E have processing times 3, 2, 4, 1, 5 (in arbitrary time units), respectively. The precedence c... | {
"id": "gen-d049e3218f7ccb9d",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Five tasks A, B, C, D, E have processing times 3, 2, 4, 1, 5 (in arbitrary time units), respectively. The precedence constraints are: A must finish before C and D c... |
[
{
"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 geometry/spatial reasoning question. Must be self-contained, single correct answe... | {
"id": "gen-ec1a2b3241e91258",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level geometry/spatial reasoning question. Must be self-contained, single correct 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": "The table below shows the annual sales (in units) of three products from 2018 to 2022.\n\n| Year | Product X (units) |... | {
"id": "gen-43da069392b584a1",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows the annual sales (in units) of three products from 2018 to 2022.\n\n| Year | Product X (units) | Product Y (units) | Product Z (units) |\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 cube is painted on all six faces and then cut into 27 identical smaller cubes. How many of these smaller cubes have ... | {
"id": "gen-c03ab1a9028a4bbc",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A cube is painted on all six faces and then cut into 27 identical smaller cubes. How many of these smaller cubes have paint on exactly two faces?",
"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": "Consider the following pseudocode function that operates on an array `A` of length `n`:\n\n```\nfunction Mystery(A):\n... | {
"id": "gen-947339dea65b1230",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following pseudocode function that operates on an array `A` of length `n`:\n\n```\nfunction Mystery(A):\n n = length(A)\n count = 0\n for 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 products (including absolute configuration) for the ring-opening of (R)-styrene oxide with sodium az... | {
"id": "gen-890c5af7d8510e4e",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Predict the major products (including absolute configuration) for the ring-opening of (R)-styrene oxide with sodium azide under the following two conditions:\n(i) 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": "On an island, there are two types of people: Knights, who always tell the truth, and Knaves, who always lie. You meet ... | {
"id": "gen-f4d7e710ccd51453",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "On an island, there are two types of people: Knights, who always tell the truth, and Knaves, who always lie. You meet three inhabitants: Alice, Bob, and Carol.\n\nA... |
[
{
"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 median of a list of numbers:\n\n```python\ndef find_med... | {
"id": "gen-9268a4c25e0e8357",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following Python function intended to compute the median of a list of numbers:\n\n```python\ndef find_median(values):\n if not values:\n retu... |
[
{
"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 radius of convergence of the power series \\(\\displaystyle \\sum_{n=1}^{\\infty} \\frac{n!}{n^n} x^n\\)."
... | {
"id": "gen-ba0ef1b1c08aa358",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Find the radius of convergence of the power series \\(\\displaystyle \\sum_{n=1}^{\\infty} \\frac{n!}{n^n} x^n\\).",
"reasoning": "We are asked to find the radius... |
[
{
"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 \\( 2^n + 1 \\) is a perfect square."
},
{
"from": "gpt",
"... | {
"id": "gen-5325a098456677b1",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Find all positive integers \\( n \\) such that \\( 2^n + 1 \\) is a perfect square.",
"reasoning": "We are asked: Find all positive integers n such that 2^n + 1 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 competition-level question about debugging a described program. It should be self-contained, have a... | {
"id": "gen-2200e15b5880781a",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a competition-level question about debugging a described program. It should be self-contained, have a single correct verifiable answer, solvable 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": "The table below shows the quarterly revenue (in millions of dollars) and the number of employees for four divisions of... | {
"id": "gen-33f1e7a162f00604",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows the quarterly revenue (in millions of dollars) and the number of employees for four divisions of a company over two years.\n\n| Division | Yea... |
[
{
"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 3,3-dimethyl-1-butene is treated with hydrogen chloride (HCl)? Provide t... | {
"id": "gen-3ab32f68271a0879",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "What is the major organic product formed when 3,3-dimethyl-1-butene is treated with hydrogen chloride (HCl)? Provide the structure and explain the mechanism, includ... |
[
{
"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 projectile is launched from ground level with an initial speed of 20 m/s at an angle of 30° above the horizontal. Ig... | {
"id": "gen-936bdc80529ed59e",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A projectile is launched from ground level with an initial speed of 20 m/s at an angle of 30° above the horizontal. Ignoring air resistance and taking g = 9.8 m/s²,... |
[
{
"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 complete a project. The agent chooses effort \\(e \\in \\{0,1\\... | {
"id": "gen-794d009f82a9fb13",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A risk-neutral principal hires a risk-neutral agent to complete a project. The agent chooses effort \\(e \\in \\{0,1\\}\\), which the principal cannot observe. 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": "Consider the set \\(S = \\{1, 2, 3, \\dots, 12\\}\\). How many 4-element subsets of \\(S\\) have the property that the... | {
"id": "gen-782b69bfff103883",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the set \\(S = \\{1, 2, 3, \\dots, 12\\}\\). How many 4-element subsets of \\(S\\) have the property that the sum of their elements is a multiple of 3?",
... |
[
{
"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 who both need it to survive. Patient X is 25 years old, ... | {
"id": "gen-da803f91f3b4ee9d",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital has only one ventilator available for two patients who both need it to survive. Patient X is 25 years old, has a 70% probability of surviving with the ve... |
[
{
"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 ABCDEFGH be a cube with side length 8. The faces ABCD and EFGH are opposite, and the edges AE, BF, CG, DH are para... | {
"id": "gen-a3bff8cabf2aeaf3",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let ABCDEFGH be a cube with side length 8. The faces ABCD and EFGH are opposite, and the edges AE, BF, CG, DH are parallel. Let M be the midpoint of AB, N be the mi... |
[
{
"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 + 3 \\) divides \\( n^3 + 5n^2 + 7n + 8 \\)."
},
{
... | {
"id": "gen-ea294abc17565e13",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Find all positive integers \\( n \\) such that \\( n^2 + 3n + 3 \\) divides \\( n^3 + 5n^2 + 7n + 8 \\).",
"reasoning": "We are asked: Find all positive integers ... |
[
{
"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 decide which of two patients receives the only available liver for transplant. The co... | {
"id": "gen-85b81f4c3d406b93",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital ethics committee must decide which of two patients receives the only available liver for transplant. The committee operates under a strict charter with 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": "The table below shows the kilograms of three fruits sold at a market stall over five days.\n\n| Day | Apples (kg... | {
"id": "gen-47d05abf5229b544",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows the kilograms of three fruits sold at a market stall over five days.\n\n| Day | Apples (kg) | Oranges (kg) | Bananas (kg) |\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 fair six-sided die is rolled repeatedly. What is the expected number of rolls until the product of the two most rece... | {
"id": "gen-88fa5cd0cc413f37",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A fair six-sided die is rolled repeatedly. What is the expected number of rolls until the product of the two most recent rolls is a perfect square?",
"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": "Starting from (E)-3-methylpent-2-ene, the following sequence is carried out:\n(i) Hydroboration–oxidation (BH₃·THF, th... | {
"id": "gen-427e422cb04e2803",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Starting from (E)-3-methylpent-2-ene, the following sequence is carried out:\n(i) Hydroboration–oxidation (BH₃·THF, then H₂O₂/NaOH)\n(ii) Oxidation with PCC in CH₂C... |
[
{
"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 sold for three products (A, B, C) in two consecutive years.\n\n| Product | 2... | {
"id": "gen-9cfb610a207cca91",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows the number of units sold for three products (A, B, C) in two consecutive years.\n\n| Product | 2022 Sales | 2023 Sales |\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": "Consider the function $f(x) = \\frac{\\sqrt{x+4} - 2}{x}$ for $x \\neq 0$. \nEvaluate $\\lim_{x \\to 0} f(x)$ and det... | {
"id": "gen-4576841287396c73",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the function $f(x) = \\frac{\\sqrt{x+4} - 2}{x}$ for $x \\neq 0$. \nEvaluate $\\lim_{x \\to 0} f(x)$ and determine whether $f$ can be extended to a contin... |
[
{
"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 table showing quarterly units sold and average selling price for three products.\n\n| Quarter |... | {
"id": "gen-450f04be39a7b1f2",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following table showing quarterly units sold and average selling price for three products.\n\n| Quarter | Product A Units | Product A Price | Product 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": "Four people—Alice, Bob, Carol, and Dave—live in four houses numbered 1, 2, 3, and 4 in a row. Each house has a distinc... | {
"id": "gen-f8530798e146b788",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Four people—Alice, Bob, Carol, and Dave—live in four houses numbered 1, 2, 3, and 4 in a row. Each house has a distinct color (red, blue, green, yellow), a distinct... |
[
{
"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 a spring constant of 200 N/m, compressing it by 0.15 m. The ... | {
"id": "gen-ea7e3008c8e9a8fb",
"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 a spring constant of 200 N/m, compressing it by 0.15 m. The block is released from rest on a horizontal su... |
[
{
"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 calculate the factorial of a non-negative integer `n`:\n\n```python... | {
"id": "gen-c2052b1119c19fea",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following Python function intended to calculate the factorial of a non-negative integer `n`:\n\n```python\ndef factorial(n):\n result = 1\n for 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": "Consider the reaction of (2R,3S)-2-bromo-3-methylpentane with sodium ethoxide (NaOEt) in ethanol at 25°C. The reaction... | {
"id": "gen-313a37294886f91b",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the reaction of (2R,3S)-2-bromo-3-methylpentane with sodium ethoxide (NaOEt) in ethanol at 25°C. The reaction produces two major alkene products. One 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": "Consider an initially empty stack `S` and an initially empty queue `Q`. The following sequence of operations is perfor... | {
"id": "gen-6e1ec99e6247c869",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider an initially empty stack `S` and an initially empty queue `Q`. The following sequence of operations is performed:\n\n1. Push 10 onto `S`\n2. Push 20 onto `... |
[
{
"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 function `calculate_discount(price, quantity)` is intended to compute the total cost after applying a volume discoun... | {
"id": "gen-b5163e2b5c02b17a",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A function `calculate_discount(price, quantity)` is intended to compute the total cost after applying a volume discount: 5% off for 10–49 items, 10% off for 50–99 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": "A regular octahedron has vertices at (1,0,0), (-1,0,0), (0,1,0), (0,-1,0), (0,0,1), (0,0,-1). A plane given by the equ... | {
"id": "gen-1188cf0b7bef8fbc",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A regular octahedron has vertices at (1,0,0), (-1,0,0), (0,1,0), (0,-1,0), (0,0,1), (0,0,-1). A plane given by the equation x + y + z = 1/2 intersects the octahedro... |
[
{
"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 students—Alex, Blake, and Casey—each have a different favorite subject (Math, Science, English) and a different ... | {
"id": "gen-3f18e5a7dda2960a",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Three students—Alex, Blake, and Casey—each have a different favorite subject (Math, Science, English) and a different favorite hobby (reading, swimming, coding). Us... |
[
{
"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, Blake, and Casey — each have a different favorite color: red, blue, or green. They also each hav... | {
"id": "gen-561f6b44cb684bfd",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Three friends — Alex, Blake, and Casey — each have a different favorite color: red, blue, or green. They also each have a different pet: cat, dog, or fish.\n\n1. Al... |
[
{
"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 step-by-step planning problems. It must be fully self-contained, hav... | {
"id": "gen-717ac86ae8e1cc17",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to write a single advanced question about step-by-step planning problems. It must be fully self-contained, have a single correct verifiable answer, solvable... |
[
{
"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 frictionlessly at one end and hangs vertically at rest. A ... | {
"id": "gen-64b87f6d717a5408",
"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 frictionlessly at one end and hangs vertically at rest. A bullet of mass \\(m\\), traveling horizontally... |
[
{
"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 program:\n\n```\nn = 24\nwhile True:\n is_prime = True\n for i in range(2, int(n**0.5)):\... | {
"id": "gen-183dc2267495d2f9",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following program:\n\n```\nn = 24\nwhile True:\n is_prime = True\n for i in range(2, int(n**0.5)):\n if n % i == 0:\n is_prime ... |
[
{
"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 a base radius of 5 and a height of 12. A sphere is placed inside the cone so that it is tang... | {
"id": "gen-c7b892afed3394a2",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A right circular cone has a base radius of 5 and a height of 12. A sphere is placed inside the cone so that it is tangent to the base and the lateral surface. A sec... |
[
{
"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 pseudocode function that operates on an array A of n integers:\n\n```\nfunction mystery(A):\n ... | {
"id": "gen-b057d0815c37555b",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following pseudocode function that operates on an array A of n integers:\n\n```\nfunction mystery(A):\n n = length(A)\n if n <= 1:\n retur... |
[
{
"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 a single ventilator that can be used for one patient at a time. Three patients need it: \n- Patient A ... | {
"id": "gen-a5a333b867ea2d3b",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital has a single ventilator that can be used for one patient at a time. Three patients need it: \n- Patient A (age 30) has an 80% chance of surviving the ne... |
[
{
"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 3 cm is painted on all six faces. It is then cut into 27 congruent smaller cubes of side length ... | {
"id": "gen-e14fe7f621da391d",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A cube of side length 3 cm is painted on all six faces. It is then cut into 27 congruent smaller cubes of side length 1 cm. How many of these smaller cubes have pai... |
[
{
"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—Lena, Marco, and Nina—each have a different favorite sport (tennis, swimming, cycling) and a different f... | {
"id": "gen-d256559752907e24",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Three friends—Lena, Marco, and Nina—each have a different favorite sport (tennis, swimming, cycling) and a different favorite snack (chips, fruit, nuts). The follow... |
[
{
"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 debugging a described program. It must be self-contained, have a s... | {
"id": "gen-a822b6fdac21a356",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "We need to produce a single advanced question about debugging a described program. It must be self-contained, have a single correct verifiable answer, solvable thro... |
[
{
"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 perform binary search on a sorted list `arr` and return the index o... | {
"id": "gen-b63e469cc3244660",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following Python function intended to perform binary search on a sorted list `arr` and return the index of `target` if found, otherwise -1.\n\n```pytho... |
[
{
"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": "When (2R,3S)-2-bromo-3-methylpentane is heated with sodium ethoxide in ethanol at 80 °C, what is the major elimination... | {
"id": "gen-ebca94deda187e89",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "When (2R,3S)-2-bromo-3-methylpentane is heated with sodium ethoxide in ethanol at 80 °C, what is the major elimination product? Draw the structure of the alkene for... |
[
{
"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, have a sin... | {
"id": "gen-8d315354081fead3",
"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, have a single correct verifiable answer, solvable throug... |
[
{
"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 program, which implements a custom `Deque` (double-ended queue) class using a doubly-lin... | {
"id": "gen-3682e8c6d9563376",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following Python program, which implements a custom `Deque` (double-ended queue) class using a doubly-linked list with sentinel nodes. The `rotate(k)` ... |
[
{
"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 uses the following protocol to allocate a single available liver for transplant:\n\n1. Cal... | {
"id": "gen-bd79c5e0703a59b8",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A hospital ethics committee uses the following protocol to allocate a single available liver for transplant:\n\n1. Calculate each candidate's expected post-transpla... |
[
{
"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": "In a blocksworld, there are four blocks A, B, C, D and a table. Initially, A is on B, B is on C, C is on D, and D is o... | {
"id": "gen-b65e3f51c718f5b0",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "In a blocksworld, there are four blocks A, B, C, D and a table. Initially, A is on B, B is on C, C is on D, and D is on the table. The goal is to have D on C, C 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": "A block of mass 2.0 kg is attached to a horizontal spring with spring constant 50 N/m on a frictionless surface. The b... | {
"id": "gen-07a2298632b80f06",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A block of mass 2.0 kg is attached to a horizontal spring with spring constant 50 N/m on a frictionless surface. The block is displaced 0.10 m from its equilibrium ... |
[
{
"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 continuously differentiable function such that \\( f(0) = 0 \\) and \\( \\i... | {
"id": "gen-84124d00160fb1ab",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Let \\( f: [0,1] \\to \\mathbb{R} \\) be a continuously differentiable function such that \\( f(0) = 0 \\) and \\( \\int_0^1 (f'(x))^2 \\, dx = 1 \\). Determine 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 uniform ladder of length 5.0 m and mass 20 kg leans against a frictionless vertical wall. The foot of the ladder res... | {
"id": "gen-bb55ee3e3a596961",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A uniform ladder of length 5.0 m and mass 20 kg leans against a frictionless vertical wall. The foot of the ladder rests on rough horizontal ground with a coefficie... |
[
{
"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 a base radius of 3 and a height of 4. A sphere is inscribed in the cone, tangent to the base... | {
"id": "gen-665367e565e3246c",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A right circular cone has a base radius of 3 and a height of 4. A sphere is inscribed in the cone, tangent to the base and the lateral surface. A plane parallel to ... |
[
{
"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 a capacity of 1 and doubles its capacity whenever an insertion would exceed the current ca... | {
"id": "gen-8ca422eeae30a82e",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A dynamic array starts with a capacity of 1 and doubles its capacity whenever an insertion would exceed the current capacity. When a resize occurs, all existing ele... |
[
{
"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 an island, there are three types of inhabitants: Knights, who always tell the truth; Knaves, who always lie; and Sp... | {
"id": "gen-d768ac8951a8fe0a",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "On an island, there are three types of inhabitants: Knights, who always tell the truth; Knaves, who always lie; and Spies, who may either tell the truth or lie. You... |
[
{
"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} \\int_0^1 \\left( x^n + (1-x)^n \\right)^{1/n} \\, dx.\n\\]"
},
{
... | {
"id": "gen-b536a768bea19e9b",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Evaluate the limit:\n\\[\n\\lim_{n\\to\\infty} \\int_0^1 \\left( x^n + (1-x)^n \\right)^{1/n} \\, dx.\n\\]",
"reasoning": "We need to evaluate the limit as n→∞ 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": "The table below shows quarterly performance data for four regional divisions of Apex Dynamics in 2023. All monetary va... | {
"id": "gen-9f4a972574027f6f",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "The table below shows quarterly performance data for four regional divisions of Apex Dynamics in 2023. All monetary values are in millions of dollars.\n\n| Region |... |
[
{
"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-95ff4b3702a7d500",
"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, Bird, Fish). Use the followi... |
[
{
"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 pour two identical cups of hot coffee at the same initial temperature. Into the first cup, you immediately pour a ... | {
"id": "gen-5f592c76fd20615a",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "You pour two identical cups of hot coffee at the same initial temperature. Into the first cup, you immediately pour a tablespoon of cold milk and stir. The second c... |
[
{
"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 10 times. Let \\(H\\) be the total number of heads that appear. Then the first \\(H\\) flips (i... | {
"id": "gen-a0c316390ec39258",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A fair coin is flipped 10 times. Let \\(H\\) be the total number of heads that appear. Then the first \\(H\\) flips (i.e., the outcomes of flips 1 through \\(H\\)) ... |
[
{
"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-4b6bddb6fc79083a",
"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), ... |
[
{
"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 alkene product, including its IUPAC name, formed upon treatment of (2R,3R)-2-bromo-3-methylpentane w... | {
"id": "gen-9b2e8fd0d051bc01",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Predict the major alkene product, including its IUPAC name, formed upon treatment of (2R,3R)-2-bromo-3-methylpentane with potassium tert-butoxide in tert-butanol.",... |
[
{
"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 sum of all positive integers \\( n \\) such that \\( n^2 - 19n + 99 \\) is a perfect square."
},
{
"f... | {
"id": "gen-d6ef0ad36cb83aab",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Find the sum of all positive integers \\( n \\) such that \\( n^2 - 19n + 99 \\) is a perfect square.",
"reasoning": "We need to find all positive integers n such... |
[
{
"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 recursive algorithm that processes an array A of length n:\n\nAlgorithm Mystery(A, n):\n if ... | {
"id": "gen-c7e2ad42f54bbeb4",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Consider the following recursive algorithm that processes an array A of length n:\n\nAlgorithm Mystery(A, n):\n if n ≤ 1:\n return\n k = ⌊√n⌋\n for ... |
[
{
"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 is filled to the brim with water. An ice cube containing a small, dense metal pebble frozen in its center floa... | {
"id": "gen-608d65f4ce1e7c93",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "A glass is filled to the brim with water. An ice cube containing a small, dense metal pebble frozen in its center floats in the glass, causing some water to spill 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": "Find all pairs of positive integers \\((x, y)\\) such that \\(x^3 + y^3 = (x + y)^2\\)."
},
{
"from": "gpt",
... | {
"id": "gen-eed862bd4a0b2228",
"source": "generated",
"model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free",
"effort": "high",
"question": "Find all pairs of positive integers \\((x, y)\\) such that \\(x^3 + y^3 = (x + y)^2\\).",
"reasoning": "We need to find all positive integer pairs (x, y) such tha... |
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