Datasets:
system stringclasses 2
values | conversations listlengths 2 2 |
|---|---|
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "Given real numbers \\( a, b, c \\) and a positive number \\( \\lambda \\) such that the polynomial \\( f(x) = x^3 + a x^2 + b x + c \\) has three real roots \\( x_1, x_2, x_3 \\), and the conditions \\( x_2 - x_1 = \\lambda \\) and \\( x_3 > \\frac{1}{2}(x_1 + x_2) \\) are satisf... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "Let \\( p = 2^{3009}, q = 3^{2006}, \\) and \\( r = 5^{1003} \\). Which of the following statements is true?\n(A) \\( p < q < r \\)\n(B) \\( p < r < q \\)\n(C) \\( q < p < r \\)\n(D) \\( r < p < q \\)\n(E) \\( q < r < p \\)"
},
{
"from": "assistant",
"value": "<think>... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "Suppose that $A, B, C, D$ are four points in the plane, and let $Q, R, S, T, U, V$ be the respective midpoints of $AB, AC, AD, BC, BD, CD$. If $QR = 2001$, $SU = 2002$, and $TV = 2003$, find the distance between the midpoints of $QU$ and $RV$."
},
{
"from": "assistant",
... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "Find all prime numbers \\( p \\) such that for any prime number \\( q < p \\), if \\( p = kq + r \\) with \\( 0 \\leq r < q \\), then there does not exist an integer \\( a > 1 \\) such that \\( a^2 \\) divides \\( r \\)."
},
{
"from": "assistant",
"value": "<think>\nO... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "Let \\( a, b, c \\) be given complex numbers, with \\( |a+b| = m \\) and \\( |a-b| = n \\). Given that \\( m \\cdot n \\neq 0 \\), prove that:\n$$\n\\max \\{|ac+b|, |a+bc|\\} \\geqslant \\frac{mn}{\\sqrt{m^2 + n^2}}\n$$"
},
{
"from": "assistant",
"value": "<think>\nOk... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "Determine the value of\n\n$$\nz=a \\sqrt{a} \\sqrt[4]{a} \\sqrt[8]{a} \\ldots \\sqrt[2^{n}]{a} \\ldots\n$$\n\nif \\( n \\) is infinitely large."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the value of z, which is this infinite product of a mu... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "A game begins with seven coins lined up on a table, all showing heads up. To win the game, you need to flip some coins such that, in the end, two adjacent coins always show different faces. The rule of the game is to flip two adjacent coins in each move. What is the minimum numbe... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "Find the function $F(x)$, whose graph passes through the point $M_{0}(3 ;-2)$, given that $F'(x) = 4x^{2} + 9x^{-2}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the function F(x) whose graph passes through the point M₀(3, -2), and we know th... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "Find the variance of the discrete random variable $X$ that is distributed according to the Poisson distribution:\n\n$$\n\\begin{array}{ccccccc}\nX & 0 & 1 & 2 & \\cdots & k & \\cdots \\\\\nP & \\mathrm{e}^{-\\lambda} & \\lambda \\mathrm{e}^{-\\lambda} / 1! & \\lambda^{2} \\mathrm... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "Calculate the volume of the body bounded above by the surface \\(z = xy^2\\) and below by the rectangle \\(0 \\leq x \\leq 1\\), \\(0 \\leq y \\leq 2\\)."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the volume bounded above by the surface z = ... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "\nVasya cut a triangle out of cardboard and numbered its vertices with the digits $1, 2, 3$. It turned out that if Vasya rotates the triangle 12 times clockwise around its vertex numbered 1 by an angle equal to the angle at this vertex, it will return to its original position. If... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "What is the largest result we can find when we divide a 2-digit number by the sum of its digits?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the largest result when dividing a two-digit number by the sum of its digits. Let me start by underst... |
You are a helpful math assistant. When solving problems, provide clear, step-by-step solutions with logical reasoning. Please structure your response into two main sections: Thought and Solution. In the Thought section, first think step by step inside <think>...</think> tags. Each step should include detailed considera... | [
{
"from": "user",
"value": "Let \\( a_{1}, a_{2}, \\ldots, a_{2000} \\) be real numbers in the interval \\([0,1]\\). Find the maximum possible value of\n\\[ \n\\sum_{1 \\leq i < j \\leq 2000}(j - i) \\left| a_{j} - a_{i} \\right| \n\\]"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I nee... |
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openthoughts_merged_think_39k
Merged think-format SFT dataset (ShareGPT-style: system + conversations with
from/value), 39,874 examples, for OLMo SFT.
Composition (concatenation of two decontaminated think-format sources):
- open-thoughts114k_math_20k_decontam_think — 20,000 examples sampled from OpenThoughts-114k math, decontaminated against the OpenThoughts3 set below.
- openthoughts3_math_decontam_resp_lt8192_think — 19,874 examples from
saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2, keeping responses shorter than 4096... (see note) tokens under the OLMo-2 tokenizer.
Each assistant turn contains <think>...</think> reasoning followed by a solution
ending in \boxed{}.
Note: the two sources currently carry different system prompts (the 114k slice uses a "helpful math assistant" think-structured prompt; the OpenThoughts3 slice uses the long OpenThoughts thinking prompt).
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