difficulty null | source stringclasses 1 value | domain stringclasses 1 value | conversations listlengths 2 2 |
|---|---|---|---|
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "A bookshelf has 5 shelves, and each shelf can hold up to 3 books. In how many ways can 6 distinct books be placed on the bookshelf such that no shelf contains more than 2 books by the same author, and no two books by the same author are on adjacent shelves?"
},
{
"from":... |
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "The greatest common divisor of three integers is 5 and their least common multiple is 100. Two of the integers are 10 and 50. What is the smallest possible value of the third integer?"
},
{
"from": "gpt",
"value": "<think> Okay, so I need to figure out the smallest p... |
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "If $x^4 + 3x^3 - 5x^2 + rx + s$ is divisible by $(x^2 + 2x + 1)(x - 1),$ find the ordered pair $(r,s).$"
},
{
"from": "gpt",
"value": "<think> Okay, so I need to find the ordered pair (r, s) such that the polynomial x⁴ + 3x³ - 5x² + rx + s is divisible by (x² + 2x + ... |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"In a music festival, five bands are scheduled to perform on a single stage(...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"A linear function $f(x) = ax + b$ is defined on the interval $[-10, 10]$ s(...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"In a mathematical competition, six teams are participating, and each team (...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"A sequence of seven distinct positive integers has all of the following pr(...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"In the triangle $ABC$ the circumcircle $\\omega$ is drawn. The radius of $(...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"At a convention, four experts on a certain topic were asked to choose one (...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"Let $P(x)$ be a polynomial of degree four with positive coefficients. The (...TRUNCATED) |
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