conversations list | token_answer int64 |
|---|---|
[
{
"meta": {},
"loss_mask": 1,
"name": "",
"content": "Given the operation * defined by \\( a * (b * c) = (a * b)c \\), solve the equation \\( 2016 * (6 * x) = 100 \\).",
"role": "user"
},
{
"meta": {},
"loss_mask": 1,
"name": "",
"content": "The operation \\(*\\) satisfies \\... | 31,029 |
[
{
"meta": {},
"loss_mask": 1,
"name": "",
"content": "Find the number of ordered tuples of natural numbers $(a, b, c, d)$ such that $a + b + c + d = 19$ and $a!b!c!d!$ is not a multiple of $100$.",
"role": "user"
},
{
"meta": {},
"loss_mask": 1,
"name": "",
"content": "The pr... | 12,801 |
[{"meta":{},"loss_mask":1,"name":"","content":"A black hole with mass $ M = 10 M_\\odot $ emits Hawk(...TRUNCATED) | 18,550 |
[{"meta":{},"loss_mask":1,"name":"","content":"Let $A$, $B$, $C$, and $D$ be four distinct points in(...TRUNCATED) | 34,368 |
[{"meta":{},"loss_mask":1,"name":"","content":"Find a positive constant \\( c \\) such that the norm(...TRUNCATED) | 18,732 |
[{"meta":{},"loss_mask":1,"name":"","content":"In rhombus $ABCD$, let $E$ be one of the points of in(...TRUNCATED) | 27,260 |
[{"meta":{},"loss_mask":1,"name":"","content":"Determine the \\(2 \\times 2\\) matrices \\(\\boldsym(...TRUNCATED) | 23,525 |
[{"meta":{},"loss_mask":1,"name":"","content":"In cancer cell migration, the persistent random walk (...TRUNCATED) | 13,442 |
[{"meta":{},"loss_mask":1,"name":"","content":"In triangle \\(ABC\\), let \\( l_a = \\frac{r_a}{w_a (...TRUNCATED) | 35,031 |
[{"meta":{},"loss_mask":1,"name":"","content":"What are the possible values of $\\alpha$ such that t(...TRUNCATED) | 21,876 |
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