messages listlengths 2 2 | dataset_source stringclasses 1 value | id stringlengths 46 51 |
|---|---|---|
[
{
"content": "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?",
"role": "user"
},
{
"conte... | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_0 |
[
{
"content": "If $x^4 + 3x^3 - 5x^2 + rx + s$ is divisible by $(x^2 + 2x + 1)(x - 1),$ find the ordered pair $(r,s).$",
"role": "user"
},
{
"content": "<think> Okay, so I have this problem here: I need to find the ordered pair (r, s) such that the polynomial x⁴ + 3x³ - 5x² + r x + s is divisible by ... | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_1 |
[
{
"content": "A linear function $f(x) = ax + b$ is defined on the interval $[-10, 10]$ such that the sum of the absolute values of $f(x)$ at $100$ evenly spaced points in the interval is equal to $1000$. Let $M$ be the maximum possible value of $|f(0)|$ and let $m$ be the minimum possible value of $|f(0)|$. Wha... | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_2 |
[{"content":"In a mathematical competition, six teams are participating, and each team has four memb(...TRUNCATED) | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_3 |
[{"content":"The number $x$ can be expressed as a three-place decimal $0.abc,$ where $a, b,$ and $c$(...TRUNCATED) | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_4 |
[{"content":"A kite is flying at an altitude of 25 meters, and its shadow on the ground is 15 meters(...TRUNCATED) | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_5 |
[{"content":"Let $f(x) = x^3 + ax^2 + bx + c$ be a cubic polynomial with rational coefficients, and (...TRUNCATED) | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_6 |
[{"content":"Suppose that the equation \\[\\frac{2x}{x^2+2x+1}=\\frac{A}{x+1}+\\frac{Bx+C}{x^2+1}\\](...TRUNCATED) | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_7 |
[{"content":"The vertices of a regular tetrahedron have coordinates $A=(x_1, y_1, z_1), B=(x_2, y_2,(...TRUNCATED) | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_8 |
[{"content":"In a round-robin chess tournament, each player earns a certain number of points for eac(...TRUNCATED) | saumyamalik/OpenThoughts3-full-filtered-math-decontam-v2 | OpenThoughts3-full-filtered-math-decontam-v2_9 |
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