prompt listlengths 1 27 | label stringlengths 1 23 | metadata dict |
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{
"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 $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
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{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nLet \\(f_{1}(x)=\\sqrt{1-x}\\), and for integers \\(n \\geq 2\\), let \\(f_{n}(x)=f_{n-1}(\\sqrt{n^2 - x})... | -226 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nAn abundant number is a positive integer such that the sum of its proper divisors is greater than the numb... | 20 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nAn abundant number is a positive integer such that the sum of its proper divisors is greater than the numb... | 20 | {
"assistant_turn_index": 2,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nAn abundant number is a positive integer such that the sum of its proper divisors is greater than the numb... | 20 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nAn abundant number is a positive integer such that the sum of its proper divisors is greater than the numb... | 20 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nAn abundant number is a positive integer such that the sum of its proper divisors is greater than the numb... | 20 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nAn abundant number is a positive integer such that the sum of its proper divisors is greater than the numb... | 20 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nAn abundant number is a positive integer such that the sum of its proper divisors is greater than the numb... | 20 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nAn abundant number is a positive integer such that the sum of its proper divisors is greater than the numb... | 20 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nAn abundant number is a positive integer such that the sum of its proper divisors is greater than the numb... | 20 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n设函数 $f(x)=x-\\ln (a x+2 a+1)+2$. 若对于任意 $x \\geqslant-2$, 均有 $f(x) \\geqslant 0$ 恒成立，请给出实数 $a$ 的取值范围端点之和。\n... | 1 | {
"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 $f(x)=x-\\ln (a x+2 a+1)+2$. 若对于任意 $x \\geqslant-2$, 均有 $f(x) \\geqslant 0$ 恒成立，请给出实数 $a$ 的取值范围端点之和。\n... | 1 | {
"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设函数 $f(x)=x-\\ln (a x+2 a+1)+2$. 若对于任意 $x \\geqslant-2$, 均有 $f(x) \\geqslant 0$ 恒成立，请给出实数 $a$ 的取值范围端点之和。\n... | 1 | {
"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 $f(x)=x-\\ln (a x+2 a+1)+2$. 若对于任意 $x \\geqslant-2$, 均有 $f(x) \\geqslant 0$ 恒成立，请给出实数 $a$ 的取值范围端点之和。\n... | 1 | {
"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设函数 $f(x)=x-\\ln (a x+2 a+1)+2$. 若对于任意 $x \\geqslant-2$, 均有 $f(x) \\geqslant 0$ 恒成立，请给出实数 $a$ 的取值范围端点之和。\n... | 1 | {
"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设函数 $f(x)=x-\\ln (a x+2 a+1)+2$. 若对于任意 $x \\geqslant-2$, 均有 $f(x) \\geqslant 0$ 恒成立，请给出实数 $a$ 的取值范围端点之和。\n... | 1 | {
"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 $f(x)=x-\\ln (a x+2 a+1)+2$. 若对于任意 $x \\geqslant-2$, 均有 $f(x) \\geqslant 0$ 恒成立，请给出实数 $a$ 的取值范围端点之和。\n... | 1 | {
"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 sequence of nonnegative integers $F_0, F_1, F_2, \\dots$ is defined recursively as $F_0 = 0$, $F_1 = 1... | 638 | {
"assistant_turn_index": 0,
"total_assistant_turns": 7
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sequence of nonnegative integers $F_0, F_1, F_2, \\dots$ is defined recursively as $F_0 = 0$, $F_1 = 1... | 638 | {
"assistant_turn_index": 0,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sequence of nonnegative integers $F_0, F_1, F_2, \\dots$ is defined recursively as $F_0 = 0$, $F_1 = 1... | 638 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sequence of nonnegative integers $F_0, F_1, F_2, \\dots$ is defined recursively as $F_0 = 0$, $F_1 = 1... | 638 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sequence of nonnegative integers $F_0, F_1, F_2, \\dots$ is defined recursively as $F_0 = 0$, $F_1 = 1... | 638 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sequence of nonnegative integers $F_0, F_1, F_2, \\dots$ is defined recursively as $F_0 = 0$, $F_1 = 1... | 638 | {
"assistant_turn_index": 2,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe sequence of nonnegative integers $F_0, F_1, F_2, \\dots$ is defined recursively as $F_0 = 0$, $F_1 = 1... | 638 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nHow many lattice points are exactly twice as close to $(0,0)$ as they are to $(15,0)$? (A lattice point is... | 12 | {
"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\nHow many lattice points are exactly twice as close to $(0,0)$ as they are to $(15,0)$? (A lattice point is... | 12 | {
"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\nHow many lattice points are exactly twice as close to $(0,0)$ as they are to $(15,0)$? (A lattice point is... | 12 | {
"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\nHow many lattice points are exactly twice as close to $(0,0)$ as they are to $(15,0)$? (A lattice point is... | 12 | {
"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\nHow many lattice points are exactly twice as close to $(0,0)$ as they are to $(15,0)$? (A lattice point is... | 12 | {
"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\nHow many lattice points are exactly twice as close to $(0,0)$ as they are to $(15,0)$? (A lattice point is... | 12 | {
"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\nHow many lattice points are exactly twice as close to $(0,0)$ as they are to $(15,0)$? (A lattice point is... | 12 | {
"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\nIn triangle $ABC$, $AB = BC$, and $\\overline{BD}$ is an altitude. Point $E$ is on the extension of $\\ove... | 53 | {
"assistant_turn_index": 0,
"total_assistant_turns": 9
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, $AB = BC$, and $\\overline{BD}$ is an altitude. Point $E$ is on the extension of $\\ove... | 53 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, $AB = BC$, and $\\overline{BD}$ is an altitude. Point $E$ is on the extension of $\\ove... | 53 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, $AB = BC$, and $\\overline{BD}$ is an altitude. Point $E$ is on the extension of $\\ove... | 53 | {
"assistant_turn_index": 2,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, $AB = BC$, and $\\overline{BD}$ is an altitude. Point $E$ is on the extension of $\\ove... | 53 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, $AB = BC$, and $\\overline{BD}$ is an altitude. Point $E$ is on the extension of $\\ove... | 53 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, $AB = BC$, and $\\overline{BD}$ is an altitude. Point $E$ is on the extension of $\\ove... | 53 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, $AB = BC$, and $\\overline{BD}$ is an altitude. Point $E$ is on the extension of $\\ove... | 53 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nIn triangle $ABC$, $AB = BC$, and $\\overline{BD}$ is an altitude. Point $E$ is on the extension of $\\ove... | 53 | {
"assistant_turn_index": 1,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nThe diagram below shows circles with radii $1$ and $2$ that are externally tangent to each other and inter... | 13 | {
"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\nThe diagram below shows circles with radii $1$ and $2$ that are externally tangent to each other and inter... | 13 | {
"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\nThe diagram below shows circles with radii $1$ and $2$ that are externally tangent to each other and inter... | 13 | {
"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\nThe diagram below shows circles with radii $1$ and $2$ that are externally tangent to each other and inter... | 13 | {
"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 diagram below shows circles with radii $1$ and $2$ that are externally tangent to each other and inter... | 13 | {
"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\nThe diagram below shows circles with radii $1$ and $2$ that are externally tangent to each other and inter... | 13 | {
"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\nThe diagram below shows circles with radii $1$ and $2$ that are externally tangent to each other and inter... | 13 | {
"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\nThe diagram below shows circles with radii $1$ and $2$ that are externally tangent to each other and inter... | 13 | {
"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 $\\triangle A B C$ 中, $A B=6, B C=4$, 边 $A C$ 上的中线长为 $\\sqrt{10}$, 则 $\\sin ^{6} \\frac{A}{2}+\\cos ^{6}... | 467 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在 $\\triangle A B C$ 中, $A B=6, B C=4$, 边 $A C$ 上的中线长为 $\\sqrt{10}$, 则 $\\sin ^{6} \\frac{A}{2}+\\cos ^{6}... | 467 | {
"assistant_turn_index": 1,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在 $\\triangle A B C$ 中, $A B=6, B C=4$, 边 $A C$ 上的中线长为 $\\sqrt{10}$, 则 $\\sin ^{6} \\frac{A}{2}+\\cos ^{6}... | 467 | {
"assistant_turn_index": 2,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在 $\\triangle A B C$ 中, $A B=6, B C=4$, 边 $A C$ 上的中线长为 $\\sqrt{10}$, 则 $\\sin ^{6} \\frac{A}{2}+\\cos ^{6}... | 467 | {
"assistant_turn_index": 0,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在 $\\triangle A B C$ 中, $A B=6, B C=4$, 边 $A C$ 上的中线长为 $\\sqrt{10}$, 则 $\\sin ^{6} \\frac{A}{2}+\\cos ^{6}... | 467 | {
"assistant_turn_index": 1,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在 $\\triangle A B C$ 中, $A B=6, B C=4$, 边 $A C$ 上的中线长为 $\\sqrt{10}$, 则 $\\sin ^{6} \\frac{A}{2}+\\cos ^{6}... | 467 | {
"assistant_turn_index": 3,
"total_assistant_turns": 6
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在 $\\triangle A B C$ 中, $A B=6, B C=4$, 边 $A C$ 上的中线长为 $\\sqrt{10}$, 则 $\\sin ^{6} \\frac{A}{2}+\\cos ^{6}... | 467 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在 $\\triangle A B C$ 中, $A B=6, B C=4$, 边 $A C$ 上的中线长为 $\\sqrt{10}$, 则 $\\sin ^{6} \\frac{A}{2}+\\cos ^{6}... | 467 | {
"assistant_turn_index": 1,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在 $\\triangle A B C$ 中, $A B=6, B C=4$, 边 $A C$ 上的中线长为 $\\sqrt{10}$, 则 $\\sin ^{6} \\frac{A}{2}+\\cos ^{6}... | 467 | {
"assistant_turn_index": 0,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\n在 $\\triangle A B C$ 中, $A B=6, B C=4$, 边 $A C$ 上的中线长为 $\\sqrt{10}$, 则 $\\sin ^{6} \\frac{A}{2}+\\cos ^{6}... | 467 | {
"assistant_turn_index": 0,
"total_assistant_turns": 5
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$Answer} where $Answer is the answer to the problem.\n\nA number is called \"cool\" if the sum of its digits is a multiple of $17$, and the sum of the digits of i... | 8899 | {
"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\nA number is called \"cool\" if the sum of its digits is a multiple of $17$, and the sum of the digits of i... | 8899 | {
"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 number is called \"cool\" if the sum of its digits is a multiple of $17$, and the sum of the digits of i... | 8899 | {
"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\nA number is called \"cool\" if the sum of its digits is a multiple of $17$, and the sum of the digits of i... | 8899 | {
"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 number is called \"cool\" if the sum of its digits is a multiple of $17$, and the sum of the digits of i... | 8899 | {
"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 number is called \"cool\" if the sum of its digits is a multiple of $17$, and the sum of the digits of i... | 8899 | {
"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\nA number is called \"cool\" if the sum of its digits is a multiple of $17$, and the sum of the digits of i... | 8899 | {
"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 number is called \"cool\" if the sum of its digits is a multiple of $17$, and the sum of the digits of i... | 8899 | {
"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 number is called \"cool\" if the sum of its digits is a multiple of $17$, and the sum of the digits of i... | 8899 | {
"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 number is called \"cool\" if the sum of its digits is a multiple of $17$, and the sum of the digits of i... | 8899 | {
"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\nThe sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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\nThe sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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\nThe sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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 sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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 sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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 sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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\nThe sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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\nThe sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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\nThe sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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 sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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\nThe sum of the product and the sum of two positive integers is $454$. Find the largest possible value of t... | 33840 | {
"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 $f(n)$ be the number of times you have to hit the $\\sqrt{}$ key on a calculator to get a number less ... | 242 | {
"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\nLet $f(n)$ be the number of times you have to hit the $\\sqrt{}$ key on a calculator to get a number less ... | 242 | {
"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 $f(n)$ be the number of times you have to hit the $\\sqrt{}$ key on a calculator to get a number less ... | 242 | {
"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 $f(n)$ be the number of times you have to hit the $\\sqrt{}$ key on a calculator to get a number less ... | 242 | {
"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\nLet $f(n)$ be the number of times you have to hit the $\\sqrt{}$ key on a calculator to get a number less ... | 242 | {
"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 $f(n)$ be the number of times you have to hit the $\\sqrt{}$ key on a calculator to get a number less ... | 242 | {
"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 $f(n)$ be the number of times you have to hit the $\\sqrt{}$ key on a calculator to get a number less ... | 242 | {
"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 $f(n)$ be the number of times you have to hit the $\\sqrt{}$ key on a calculator to get a number less ... | 242 | {
"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 $f(n)$ be the number of times you have to hit the $\\sqrt{}$ key on a calculator to get a number less ... | 242 | {
"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 $0 \\leqslant x_{... | 3 | {
"assistant_turn_index": 1,
"total_assistant_turns": 2
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$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 $0 \\leqslant x_{... | 3 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$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 $0 \\leqslant x_{... | 3 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$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 $0 \\leqslant x_{... | 3 | {
"assistant_turn_index": 2,
"total_assistant_turns": 4
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$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 $0 \\leqslant x_{... | 3 | {
"assistant_turn_index": 0,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$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 $0 \\leqslant x_{... | 3 | {
"assistant_turn_index": 1,
"total_assistant_turns": 3
} |
[
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: \\boxed{$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
} |
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