prompt_messages listlengths 2 2 | answers sequencelengths 4 4 | gt stringlengths 1 97 | rewards sequencelengths 4 4 |
|---|---|---|---|
[
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning.\n2. Explicitly label each step using the format \"### Step 1\", \"### Step 2\", etc.\n3. Output the final answer within \\boxed{}.\n\nAlways ensure clari... | [
"### Step 1: Define the problem\nWe are given that \\(15a + 16b\\) and \\(16a - 15b\\) are both squares of positive integers. Let:\n\\[\n15a + 16b = m^2\n\\]\n\\[\n16a - 15b = n^2\n\\]\nwhere \\(m\\) and \\(n\\) are positive integers.\n\n### Step 2: Add and subtract the equations\nFirst, add the two equations:\n\\[... | 481^2 | [
-1,
-1,
-1,
-1
] |
[
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning.\n2. Explicitly label each step using the format \"### Step 1\", \"### Step 2\", etc.\n3. Output the final answer within \\boxed{}.\n\nAlways ensure clari... | [
"To solve the given problem, we start with the given equation in the triangle, \\(2b \\cos C = 2a + c\\).\n\n### Step 1: Find the measure of angle \\(B\\)\nUsing the Law of Cosines, we know that \\(\\cos C = \\frac{a^2 + b^2 - c^2}{2ab}\\). Substituting this into the given equation, we get:\n\\[2b \\cdot \\frac{a^2... | \cos C = \frac{12 + 5\sqrt{3}}{26} | [
-1,
-0.5,
-1,
-1
] |
[{"content":"You are a mathematical reasoning assistant. For each problem, follow these steps strict(...TRUNCATED) | ["To solve the given problem, let's start by analyzing the given equation and using trigonometric id(...TRUNCATED) | 2\sqrt{2} | [
-1,
-1,
-1,
-1
] |
[{"content":"You are a mathematical reasoning assistant. For each problem, follow these steps strict(...TRUNCATED) | ["### Step 1: Substitute the point into the equation of the line.\nThe given line is \\(\\frac{x}{a}(...TRUNCATED) | 9 | [
-1,
-1,
-1,
-1
] |
[{"content":"You are a mathematical reasoning assistant. For each problem, follow these steps strict(...TRUNCATED) | ["To find the minimum value of the expression \\(\\frac{a + b + c}{2} -\\frac{[a, b] + [b, c] + [c, (...TRUNCATED) | \frac{3}{2} | [
-1,
-1,
-1,
-1
] |
[{"content":"You are a mathematical reasoning assistant. For each problem, follow these steps strict(...TRUNCATED) | ["To determine how many positive integers divide \\(20!\\), we need to follow these steps:\n\n### St(...TRUNCATED) | 41040 | [
-1,
-1,
-1,
-1
] |
[{"content":"You are a mathematical reasoning assistant. For each problem, follow these steps strict(...TRUNCATED) | ["To determine the length of the longest diagonal of pentagon \\(AXB\\) where square \\(ABCD\\) has (...TRUNCATED) | \sqrt{\sqrt{10}} | [
-1,
-1,
-1,
-0.5
] |
[{"content":"You are a mathematical reasoning assistant. For each problem, follow these steps strict(...TRUNCATED) | ["### Step 1: Rewrite the expression using exponents.\nThe expression \\(\\dfrac{\\sqrt[5]{11}}{\\sq(...TRUNCATED) | \frac{1}{30} | [
1,
1,
1,
1
] |
[{"content":"You are a mathematical reasoning assistant. For each problem, follow these steps strict(...TRUNCATED) | ["To find the maximum number of elements in a collection \\( A \\) of subsets of \\( S = \\{1, 2, \\(...TRUNCATED) | C_n^{\left\lfloor \frac{n}{2} \right\rfloor} | [
-0.5,
-1,
-0.5,
-0.5
] |
[{"content":"You are a mathematical reasoning assistant. For each problem, follow these steps strict(...TRUNCATED) | ["### Step 1: Understand the Problem\n\nWe need to find the number of natural numbers \\( n \\) such(...TRUNCATED) | 48 | [
-1,
-1,
-1,
-1
] |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 34