context listlengths 2 2 | gen_kwargs dict | repeat_idx int64 0 0 | request_idx int64 0 499 | task_name stringclasses 1
value | metadata dict | model_outputs stringlengths 2.34k 111k |
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[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
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} | <|begin_of_thought|>
Okay, let's try to solve this magic square problem. First, I need to recall what a magic square is. From what I remember, a magic square is a grid where the numbers in each row, each column, and the two main diagonals all add up to the same number, called the magic constant. The goal here is to fi... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
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} | 0 | 132 | MATH500 | {
"expected_answer": "",
"problem_id": "",
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} | <|begin_of_thought|>
Okay, let's try to figure out this problem step by step. So, Rick is thinking of a positive factor of 14, and Steve is thinking of a positive factor of 42. The question is asking how many possible numbers they could be thinking of if they both end up choosing the same number. Hmm, right. So we nee... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
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} | 0 | 472 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's see. The problem is asking: At 50 miles per hour, how far would a car travel in 2 and 3/4 hours? And they want the answer as a mixed number. Hmm. Alright, first, I need to remember the basic formula for distance. Distance equals speed multiplied by time. So, distance = speed × time. Th... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 46 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to figure out the smallest positive integer n such that all the roots of the equation z⁴ + z² + 1 = 0 are n-th roots of unity. Hmm, so first, I need to understand what the roots of this equation are, and then determine the least common multiple of their orders to find n.
Wait, ro... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 40 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's see. The problem says a regular octagon has the same perimeter as a regular hexagon with a side length of 16 cm. I need to find the length of each side of the octagon. Hmm, alright. Let me start by recalling what a regular octagon and a regular hexagon are. Both are regular polygons, m... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
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} | 0 | 232 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to tackle this problem. So, the question is: If ω^1997 = 1 and ω ≠ 1, then evaluate the sum 1/(1 + ω) + 1/(1 + ω^2) + ... + 1/(1 + ω^1997). Hmm, interesting. Alright, let's start by understanding what ω is here. Since ω^1997 = 1 and ω ≠ 1, ω must be a primitive 1997th root of unity... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 45 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's see. I need to find tan A in a right triangle ABC where angle B is 90 degrees, and sin A is twice cos A. Hmm. Let me start by recalling some trigonometric identities and relationships in a right triangle.
First, in a right triangle, the sine of an angle is the ratio of the opposite si... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
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"temperature": 0.7
} | 0 | 428 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, so I need to find the minimum value of the expression 1/a + 1/b + 4/c + 16/d, given that a, b, c, d are positive real numbers and their sum is 1. Hmm, let's start by recalling some optimization techniques. Since there's a constraint a + b + c + d = 1, maybe I can use the method of Lagrange m... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
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"temperature": 0.7
} | 0 | 326 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to solve this problem: Evaluate \(\sin (\arcsin 0.4 + \arcsin 0.5) \cdot \sin (\arcsin 0.5 - \arcsin 0.4)\). Hmm, that looks a bit complicated with all the arcsin and sin functions. Let me break it down step by step.
First, I remember that \(\arcsin a\) gives an angle whose sine i... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 159 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's see. I need to convert the quadratic equation x² + 2.6x + 3.6 into the form (x + b)² + c, and then find the sum of b and c. Hmm, right. This is about completing the square, I remember. Let me think step by step.
First, the standard form of a quadratic is ax² + bx + c, and here, a is 1... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 291 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to figure out how many points with integer coordinates are strictly inside the rectangle defined by the vertices (5,4), (-5,4), (-5,-4), and (5,-4). Hmm, first, I need to visualize this rectangle. The vertices are given, so maybe plotting them would help. Let me think: the points (... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 235 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's see. I need to compute 0.\overline{7} minus 0.\overline{4} plus 0.\overline{2}, and then express the result as a common fraction. Hmm, repeating decimals can sometimes be tricky, but I remember that there's a way to convert them into fractions by using algebra or some formula. Let me t... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 453 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to figure out this problem step by step. So, the 7th grade has 520 students, and the 8th grade has 650 students. Together, they need to have 18 representatives on the Student Council. The question is asking how many representatives the 8th grade should have if the representation is... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 107 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to figure out this problem. So the question is asking: How many elements are in the intersection of the set of all the prime numbers less than 30 and the set of all the odd numbers greater than zero? Hmm, let me break this down step by step.
First, I need to understand what the in... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 367 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to figure out this problem. So, we have a function f and its inverse f⁻¹. The question is asking for f⁻¹(f⁻¹(6)). Hmm, let's break this down step by step. First, I need to recall what an inverse function does. The inverse function essentially "undoes" what the original function doe... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 115 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's see. I need to find the number of ways to arrange the letters in the word ELLIPSE. Hmm. Alright, first, I remember that when dealing with permutations of letters in a word, if all the letters are distinct, the formula is just factorial of the number of letters. But ELLIPSE has some rep... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 280 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to solve this problem step by step. The question is: Given two different prime numbers a and b, both greater than 2, how many whole-number divisors does the integer a(2a + b) - 2a² + ab have? Hmm, primes greater than 2 are all odd numbers, right? Because 2 is the only even prime. S... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 357 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to figure out this problem. So, we have a deck of 54 cards, and we need to deal all of them to x players, each getting y cards. The conditions are that x is at least 2 and y is at least 5. We need to find how many possible values of x there are. Hmm, let's break this down step by s... |
[
{
"content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 185 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's see. I need to find the value of k in the equation (3^k)^6 equals 3^6. Hmm, right. Let me start by recalling some exponent rules because that's probably where I need to apply them here.
First, the equation is (3^k)^6 = 3^6. So, the left side is (3^k) raised to the 6th power, and the r... |
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