prompt listlengths 1 27 | label stringlengths 1 23 | metadata dict |
|---|---|---|
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n给定正整数 $n$. 求最小的实数 $\\lambda$, 使得存在区间 $[0,1]$ 内的实数 $a_{1}, a_{2}$, $\\cdots, a_{n}$, 对于满足 $0 \\leqslant x_{... | 3 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n两人轮流投掷股子，每人每次投掷两颗，第一个使两颗股子点数和大于 6 者为胜，否则轮由另一人投郑。先投郑人的获胜概率是原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\n... | 29 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n两人轮流投掷股子，每人每次投掷两颗，第一个使两颗股子点数和大于 6 者为胜，否则轮由另一人投郑。先投郑人的获胜概率是原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\n... | 29 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n两人轮流投掷股子，每人每次投掷两颗，第一个使两颗股子点数和大于 6 者为胜，否则轮由另一人投郑。先投郑人的获胜概率是原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\n... | 29 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n两人轮流投掷股子，每人每次投掷两颗，第一个使两颗股子点数和大于 6 者为胜，否则轮由另一人投郑。先投郑人的获胜概率是原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\n... | 29 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n两人轮流投掷股子，每人每次投掷两颗，第一个使两颗股子点数和大于 6 者为胜，否则轮由另一人投郑。先投郑人的获胜概率是原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\n... | 29 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n两人轮流投掷股子，每人每次投掷两颗，第一个使两颗股子点数和大于 6 者为胜，否则轮由另一人投郑。先投郑人的获胜概率是原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\n... | 29 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n两人轮流投掷股子，每人每次投掷两颗，第一个使两颗股子点数和大于 6 者为胜，否则轮由另一人投郑。先投郑人的获胜概率是原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\n... | 29 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n两人轮流投掷股子，每人每次投掷两颗，第一个使两颗股子点数和大于 6 者为胜，否则轮由另一人投郑。先投郑人的获胜概率是原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\n... | 29 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n两人轮流投掷股子，每人每次投掷两颗，第一个使两颗股子点数和大于 6 者为胜，否则轮由另一人投郑。先投郑人的获胜概率是原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\n... | 29 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n两人轮流投掷股子，每人每次投掷两颗，第一个使两颗股子点数和大于 6 者为胜，否则轮由另一人投郑。先投郑人的获胜概率是原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\n... | 29 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nJar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red butt... | 9 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nJar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red butt... | 9 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nJar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red butt... | 9 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nJar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red butt... | 9 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nJar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red butt... | 9 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nJar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red butt... | 9 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nJar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red butt... | 9 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nJar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red butt... | 9 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nJar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red butt... | 9 | {
"assistant_turn_index": 1,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(ABC\\) be a triangle with \\(m(\\widehat{A})=90^\\circ\\), \\(|AB|=4\\), and \\(|AC|=3\\). Let \\(D... | 19 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(ABC\\) be a triangle with \\(m(\\widehat{A})=90^\\circ\\), \\(|AB|=4\\), and \\(|AC|=3\\). Let \\(D... | 19 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(ABC\\) be a triangle with \\(m(\\widehat{A})=90^\\circ\\), \\(|AB|=4\\), and \\(|AC|=3\\). Let \\(D... | 19 | {
"assistant_turn_index": 0,
"total_assistant_turns": 11
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(ABC\\) be a triangle with \\(m(\\widehat{A})=90^\\circ\\), \\(|AB|=4\\), and \\(|AC|=3\\). Let \\(D... | 19 | {
"assistant_turn_index": 6,
"total_assistant_turns": 11
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(ABC\\) be a triangle with \\(m(\\widehat{A})=90^\\circ\\), \\(|AB|=4\\), and \\(|AC|=3\\). Let \\(D... | 19 | {
"assistant_turn_index": 0,
"total_assistant_turns": 10
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(ABC\\) be a triangle with \\(m(\\widehat{A})=90^\\circ\\), \\(|AB|=4\\), and \\(|AC|=3\\). Let \\(D... | 19 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(ABC\\) be a triangle with \\(m(\\widehat{A})=90^\\circ\\), \\(|AB|=4\\), and \\(|AC|=3\\). Let \\(D... | 19 | {
"assistant_turn_index": 0,
"total_assistant_turns": 9
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 1,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 1,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 3,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 1,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe graph of \\( y = x^2 + 2x - 15 \\) intersects the \\( x \\)-axis at points \\( A \\) and \\( C \\) and... | 11 | {
"assistant_turn_index": 4,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数$f(x)=x^{3}+a x^{2}+b x+c$（$a, b, c$均为非零整数），若 $f(a)=a^{3}, f(b)=b^{3}$，则 $c$ 的值是多少？\n\nRemember to put ... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 1
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数$f(x)=x^{3}+a x^{2}+b x+c$（$a, b, c$均为非零整数），若 $f(a)=a^{3}, f(b)=b^{3}$，则 $c$ 的值是多少？\n\nRemember to put ... | 16 | {
"assistant_turn_index": 1,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数$f(x)=x^{3}+a x^{2}+b x+c$（$a, b, c$均为非零整数），若 $f(a)=a^{3}, f(b)=b^{3}$，则 $c$ 的值是多少？\n\nRemember to put ... | 16 | {
"assistant_turn_index": 2,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数$f(x)=x^{3}+a x^{2}+b x+c$（$a, b, c$均为非零整数），若 $f(a)=a^{3}, f(b)=b^{3}$，则 $c$ 的值是多少？\n\nRemember to put ... | 16 | {
"assistant_turn_index": 1,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数$f(x)=x^{3}+a x^{2}+b x+c$（$a, b, c$均为非零整数），若 $f(a)=a^{3}, f(b)=b^{3}$，则 $c$ 的值是多少？\n\nRemember to put ... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数$f(x)=x^{3}+a x^{2}+b x+c$（$a, b, c$均为非零整数），若 $f(a)=a^{3}, f(b)=b^{3}$，则 $c$ 的值是多少？\n\nRemember to put ... | 16 | {
"assistant_turn_index": 2,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数$f(x)=x^{3}+a x^{2}+b x+c$（$a, b, c$均为非零整数），若 $f(a)=a^{3}, f(b)=b^{3}$，则 $c$ 的值是多少？\n\nRemember to put ... | 16 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数$f(x)=x^{3}+a x^{2}+b x+c$（$a, b, c$均为非零整数），若 $f(a)=a^{3}, f(b)=b^{3}$，则 $c$ 的值是多少？\n\nRemember to put ... | 16 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 1,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 2,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 3,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 4,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 1,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 3,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the remainder when $2024^{2023^{2022^{2021 \\ldots^{3^{2}}}}} + 2025^{2021^{2017^{2013 \\ldots^{5^{1}... | 17 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 1,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 1,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA circle rests in the interior of the parabola with equation $y = x^2,$ so that it is tangent to the parab... | 3 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet $S_i$ be the set of all integers $n$ such that $100i\\leq n < 100(i + 1)$ . For example, $S_4$ is the ... | 708 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet $S_i$ be the set of all integers $n$ such that $100i\\leq n < 100(i + 1)$ . For example, $S_4$ is the ... | 708 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet $S_i$ be the set of all integers $n$ such that $100i\\leq n < 100(i + 1)$ . For example, $S_4$ is the ... | 708 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet $S_i$ be the set of all integers $n$ such that $100i\\leq n < 100(i + 1)$ . For example, $S_4$ is the ... | 708 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet $S_i$ be the set of all integers $n$ such that $100i\\leq n < 100(i + 1)$ . For example, $S_4$ is the ... | 708 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet $S_i$ be the set of all integers $n$ such that $100i\\leq n < 100(i + 1)$ . For example, $S_4$ is the ... | 708 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet $S_i$ be the set of all integers $n$ such that $100i\\leq n < 100(i + 1)$ . For example, $S_4$ is the ... | 708 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet $S_i$ be the set of all integers $n$ such that $100i\\leq n < 100(i + 1)$ . For example, $S_4$ is the ... | 708 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在平面直角坐标系 $x O y$ 中, 设 $A B$ 是抛物线 $y^{2}=4 x$ 的过点 $F(1,0)$ 的弦, $\\triangle A O B$ 的外接圆交抛物线于点 $P$ (不同于点 $O, ... | 14 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在平面直角坐标系 $x O y$ 中, 设 $A B$ 是抛物线 $y^{2}=4 x$ 的过点 $F(1,0)$ 的弦, $\\triangle A O B$ 的外接圆交抛物线于点 $P$ (不同于点 $O, ... | 14 | {
"assistant_turn_index": 0,
"total_assistant_turns": 1
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在平面直角坐标系 $x O y$ 中, 设 $A B$ 是抛物线 $y^{2}=4 x$ 的过点 $F(1,0)$ 的弦, $\\triangle A O B$ 的外接圆交抛物线于点 $P$ (不同于点 $O, ... | 14 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在平面直角坐标系 $x O y$ 中, 设 $A B$ 是抛物线 $y^{2}=4 x$ 的过点 $F(1,0)$ 的弦, $\\triangle A O B$ 的外接圆交抛物线于点 $P$ (不同于点 $O, ... | 14 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在平面直角坐标系 $x O y$ 中, 设 $A B$ 是抛物线 $y^{2}=4 x$ 的过点 $F(1,0)$ 的弦, $\\triangle A O B$ 的外接圆交抛物线于点 $P$ (不同于点 $O, ... | 14 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the greatest positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your ... | 36 | {
"assistant_turn_index": 0,
"total_assistant_turns": 8
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the greatest positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your ... | 36 | {
"assistant_turn_index": 2,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the greatest positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your ... | 36 | {
"assistant_turn_index": 3,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the greatest positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your ... | 36 | {
"assistant_turn_index": 3,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the greatest positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your ... | 36 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the greatest positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your ... | 36 | {
"assistant_turn_index": 1,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the greatest positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your ... | 36 | {
"assistant_turn_index": 2,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the greatest positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your ... | 36 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the greatest positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your ... | 36 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nFind the greatest positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your ... | 36 | {
"assistant_turn_index": 3,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n将 1,2,3,4,5,6 随机排成一行，记为 a, b, c, d, e, f，则 abc+def 是偶数的概率为________.原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m ... | 19 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n将 1,2,3,4,5,6 随机排成一行，记为 a, b, c, d, e, f，则 abc+def 是偶数的概率为________.原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m ... | 19 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n将 1,2,3,4,5,6 随机排成一行，记为 a, b, c, d, e, f，则 abc+def 是偶数的概率为________.原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m ... | 19 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
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