conversations list | dataset_index string | completion_tokens int64 |
|---|---|---|
[
{
"from": "user",
"value": "Find the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}."
},
{
"from": "assistant",
"value": "<think>\nI need to find the sum of all integer bases \\( b > 9 \\) such t... | 0 | 6,167 |
[
{
"from": "user",
"value": "On $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be th... | 1 | 13,840 |
[
{
"from": "user",
"value": "The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of pl... | 2 | 16,518 |
[
{
"from": "user",
"value": "Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}."
},
{
"from": "assistant",
"value": "<think>\nI... | 3 | 7,952 |
[
{
"from": "user",
"value": "There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within... | 4 | 11,553 |
[
{
"from": "user",
"value": "An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by ste... | 5 | 3,925 |
[{"from":"user","value":"The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped in(...TRUNCATED) | 6 | 18,413 |
[{"from":"user","value":"Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z(...TRUNCATED) | 7 | 9,691 |
[{"from":"user","value":"The parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ countercloc(...TRUNCATED) | 8 | 20,145 |
[{"from":"user","value":"The 27 cells of a $3\\times9$ grid are filled in using the numbers 1 throug(...TRUNCATED) | 9 | 20,517 |
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