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id string | conversations list |
|---|---|
d60e2d1580a1f682364fee1ef6968383 | [
{
"from": "system",
"value": "<|think|>\nYou are a knowledgeable math and science tutor. Show your work clearly."
},
{
"from": "human",
"value": "Anna and Zs贸fi take turns rolling a die, and the number rolled is always added to the sum of the numbers rolled so far. The person who first makes the... |
5c6390265c069f64f6b9c9bdbb48a2c7 | [
{
"from": "system",
"value": "<|think|>"
},
{
"from": "human",
"value": "Let $\\Gamma$ be a circle with center $O$ and $P$ a point outside the circle. Let $A \\in \\Gamma$ such that the line segment $PA$ is tangent to $\\Gamma$, and let $B$ be the point diametrically opposite to $A$. Let $\\Delt... |
9d2a7243d51f1260870b365729debc39 | [
{
"from": "system",
"value": "<|think|>"
},
{
"from": "human",
"value": "If $\\varepsilon _{k}, k=1,2,...,2013$ are all $2013^{th}$ roots of unity, evaluate the product: \\[ \\prod_{k=1}^{2013}(2-\\varepsilon _{k}^{2}). \\] Let's think step by step and output the final answer within \\boxed{}."
... |
aabeda49a325025d0e4d86d51c25d3b2 | [
{
"from": "system",
"value": "<|think|>"
},
{
"from": "human",
"value": "Arrange the arithmetic operation signs and parentheses in the expression consisting of the three numbers $\\frac{1}{8} \\ldots \\frac{1}{9} \\ldots \\frac{1}{28}$ so that the result of the calculations is equal to $\\frac{1... |
ef316dee16e03eb10e9962bc478a03bf | [
{
"from": "system",
"value": "<|think|>\nYou are a helpful assistant that provides clear and concise answers with detailed reasoning."
},
{
"from": "human",
"value": "Let \\( p \\in \\mathbb{N} \\) and \\( f \\in \\mathbb{Z}[X] \\) such that \\( f(p) = 6 \\), \\( f(p+1) = 18 \\), and \\( f(p+2) ... |
421f9aa267588a535c7e8ff4c000d350 | [{"from":"system","value":"<|think|>\nYou are an expert problem solver. Break down complex problems (...TRUNCATED) |
c5f9e6630de19966bf4539c81559bd65 | [{"from":"system","value":"<|think|>\nYou are a smart and capable assistant. Provide well-structured(...TRUNCATED) |
aa2a24ef2d9d2f54722436ede2092450 | [{"from":"system","value":"<|think|>"},{"from":"human","value":"Calculate the integral \\[ \\int \\f(...TRUNCATED) |
1e6529709f1c75ce6bdb02e31dd33e0a | [{"from":"system","value":"<|think|>\nYou are a helpful assistant."},{"from":"human","value":"Determ(...TRUNCATED) |
82595070d45b1a9d9d886d165d0189b3 | [{"from":"system","value":"<|think|>"},{"from":"human","value":"Find the functions \\( f: \\mathbb{R(...TRUNCATED) |
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