source null | domain null | llama8b_solve_rate float64 | data_source stringclasses 2
values | prompt listlengths 1 1 | ability stringclasses 1
value | apply_chat_template bool 1
class | reward_model dict | extra_info dict | is_unique bool 1
class | solution stringlengths 0 11.1k ⌀ | qwen2.5_7b_pass_rate float64 -1 1 | qwen3_30b_pass_rate float64 0 1 | chat_input listlengths 1 1 | ground_truth stringlengths 0 3.83k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
null | null | null | math__deepscaler_preview | [
{
"content": "Let $ABCD$ be a rectangle such that $\\overline{AB}=\\overline{CD}=30$, $\\overline{BC}=\\overline{DA}=50$ and point $E$ lies on line $AB$, 20 units from $A$. Find the area of triangle $BEC$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "1000",
"style": "rule"
} | {
"index": 12522,
"original_question": "Let $ABCD$ be a rectangle such that $\\overline{AB}=\\overline{CD}=30$, $\\overline{BC}=\\overline{DA}=50$ and point $E$ lies on line $AB$, 20 units from $A$. Find the area of triangle $BEC$.",
"reward_metric": null,
"split": "train"
} | true | 0 | 0 | [
{
"content": "Let $ABCD$ be a rectangle such that $\\overline{AB}=\\overline{CD}=30$, $\\overline{BC}=\\overline{DA}=50$ and point $E$ lies on line $AB$, 20 units from $A$. Find the area of triangle $BEC$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 1000 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Tom's algebra notebook consists of 50 pages, 25 sheets of paper. Specifically, page 1 and page 2 are the front and back of the first sheet of paper, page 3 and page 4 are the front and back of the second sheet of paper, and so on. One day, Tom left the notebook on the table while he went out, and ... | math | true | {
"ground_truth": "13",
"style": "rule"
} | {
"index": 12031,
"original_question": "Tom's algebra notebook consists of 50 pages, 25 sheets of paper. Specifically, page 1 and page 2 are the front and back of the first sheet of paper, page 3 and page 4 are the front and back of the second sheet of paper, and so on. One day, Tom left the notebook on the table w... | true | 0.0625 | 0.375 | [
{
"content": "Tom's algebra notebook consists of 50 pages, 25 sheets of paper. Specifically, page 1 and page 2 are the front and back of the first sheet of paper, page 3 and page 4 are the front and back of the second sheet of paper, and so on. One day, Tom left the notebook on the table while he went out, and ... | 13 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Thirty girls - 13 in red dresses and 17 in blue dresses - were dancing around a Christmas tree. Afterwards, each was asked if the girl to her right was in a blue dress. It turned out that only those who stood between two girls in dresses of the same color answered correctly. How many girls could h... | math | true | {
"ground_truth": "17",
"style": "rule"
} | {
"index": 8203,
"original_question": "Thirty girls - 13 in red dresses and 17 in blue dresses - were dancing around a Christmas tree. Afterwards, each was asked if the girl to her right was in a blue dress. It turned out that only those who stood between two girls in dresses of the same color answered correctly. H... | true | 0 | 0.625 | [
{
"content": "Thirty girls - 13 in red dresses and 17 in blue dresses - were dancing around a Christmas tree. Afterwards, each was asked if the girl to her right was in a blue dress. It turned out that only those who stood between two girls in dresses of the same color answered correctly. How many girls could h... | 17 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given that the right focus of the ellipse $\\frac{{x}^{2}}{{a}^{2}}+\\frac{{y}^{2}}{{b}^{2}}=1(a>b>0)$ is $F(\\sqrt{6},0)$, a line $l$ passing through $F$ intersects the ellipse at points $A$ and $B$. If the midpoint of chord $AB$ has coordinates $(\\frac{\\sqrt{6}}{3},-1)$, calculate the area of ... | math | true | {
"ground_truth": "12\\sqrt{3}\\pi",
"style": "rule"
} | {
"index": 8527,
"original_question": "Given that the right focus of the ellipse $\\frac{{x}^{2}}{{a}^{2}}+\\frac{{y}^{2}}{{b}^{2}}=1(a>b>0)$ is $F(\\sqrt{6},0)$, a line $l$ passing through $F$ intersects the ellipse at points $A$ and $B$. If the midpoint of chord $AB$ has coordinates $(\\frac{\\sqrt{6}}{3},-1)$, c... | true | 0 | 1 | [
{
"content": "Given that the right focus of the ellipse $\\frac{{x}^{2}}{{a}^{2}}+\\frac{{y}^{2}}{{b}^{2}}=1(a>b>0)$ is $F(\\sqrt{6},0)$, a line $l$ passing through $F$ intersects the ellipse at points $A$ and $B$. If the midpoint of chord $AB$ has coordinates $(\\frac{\\sqrt{6}}{3},-1)$, calculate the area of ... | 12\sqrt{3}\pi | |
null | null | null | math__deepscaler_preview | [
{
"content": "In a convex $n$-gon, a diagonal is selected. The selected diagonal is intersected by exactly 14 other diagonals of the $n$-gon. Find the sum of all possible values of $n$. A vertex of the $n$-gon is not considered an intersection. Please output the final answer within \\boxed{}.",
"role": "use... | math | true | {
"ground_truth": "28",
"style": "rule"
} | {
"index": 12353,
"original_question": "In a convex $n$-gon, a diagonal is selected. The selected diagonal is intersected by exactly 14 other diagonals of the $n$-gon. Find the sum of all possible values of $n$. A vertex of the $n$-gon is not considered an intersection.",
"reward_metric": null,
"split": "train"... | true | 0.25 | 1 | [
{
"content": "In a convex $n$-gon, a diagonal is selected. The selected diagonal is intersected by exactly 14 other diagonals of the $n$-gon. Find the sum of all possible values of $n$. A vertex of the $n$-gon is not considered an intersection. Please output the final answer within \\boxed{}.",
"role": "use... | 28 | |
null | null | null | math__deepscaler_preview | [
{
"content": "A line passing through the left focus $F_1$ of a hyperbola at an inclination of 30° intersects with the right branch of the hyperbola at point $P$. If the circle with the diameter $PF_1$ just passes through the right focus of the hyperbola, determine the eccentricity of the hyperbola. Please outpu... | math | true | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"index": 9761,
"original_question": "A line passing through the left focus $F_1$ of a hyperbola at an inclination of 30° intersects with the right branch of the hyperbola at point $P$. If the circle with the diameter $PF_1$ just passes through the right focus of the hyperbola, determine the eccentricity of the hy... | true | 0.3125 | 1 | [
{
"content": "A line passing through the left focus $F_1$ of a hyperbola at an inclination of 30° intersects with the right branch of the hyperbola at point $P$. If the circle with the diameter $PF_1$ just passes through the right focus of the hyperbola, determine the eccentricity of the hyperbola. Please outpu... | \sqrt{3} | |
null | null | null | math__deepscaler_preview | [
{
"content": "A store arranges a decorative tower of balls where the top level has 2 balls and each lower level has 3 more balls than the level above. The display uses 225 balls. What is the number of levels in the tower? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 8249,
"original_question": "A store arranges a decorative tower of balls where the top level has 2 balls and each lower level has 3 more balls than the level above. The display uses 225 balls. What is the number of levels in the tower?",
"reward_metric": null,
"split": "train"
} | true | 0.875 | 1 | [
{
"content": "A store arranges a decorative tower of balls where the top level has 2 balls and each lower level has 3 more balls than the level above. The display uses 225 balls. What is the number of levels in the tower? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 12 | |
null | null | null | math__deepscaler_preview | [
{
"content": "A set consists of 120 distinct blocks. Each block is one of 3 materials (plastic, wood, metal), 3 sizes (small, medium, large), 4 colors (blue, green, red, yellow), and 5 shapes (circle, hexagon, square, triangle, rectangle). How many blocks in the set differ from the 'wood small blue hexagon' in ... | math | true | {
"ground_truth": "44",
"style": "rule"
} | {
"index": 9539,
"original_question": "A set consists of 120 distinct blocks. Each block is one of 3 materials (plastic, wood, metal), 3 sizes (small, medium, large), 4 colors (blue, green, red, yellow), and 5 shapes (circle, hexagon, square, triangle, rectangle). How many blocks in the set differ from the 'wood sm... | true | 0.875 | 1 | [
{
"content": "A set consists of 120 distinct blocks. Each block is one of 3 materials (plastic, wood, metal), 3 sizes (small, medium, large), 4 colors (blue, green, red, yellow), and 5 shapes (circle, hexagon, square, triangle, rectangle). How many blocks in the set differ from the 'wood small blue hexagon' in ... | 44 | |
null | null | null | math__deepscaler_preview | [
{
"content": "At HappyTails Training Center, cats can learn to do three tricks: jump, fetch, and spin. Of the cats at the center:\n- 40 cats can jump\n- 25 cats can fetch\n- 30 cats can spin\n- 15 cats can jump and fetch\n- 10 cats can fetch and spin\n- 12 cats can jump and spin\n- 5 cats can do all three\n- 7 ... | math | true | {
"ground_truth": "70",
"style": "rule"
} | {
"index": 9633,
"original_question": "At HappyTails Training Center, cats can learn to do three tricks: jump, fetch, and spin. Of the cats at the center:\n- 40 cats can jump\n- 25 cats can fetch\n- 30 cats can spin\n- 15 cats can jump and fetch\n- 10 cats can fetch and spin\n- 12 cats can jump and spin\n- 5 cats c... | true | 1 | 1 | [
{
"content": "At HappyTails Training Center, cats can learn to do three tricks: jump, fetch, and spin. Of the cats at the center:\n- 40 cats can jump\n- 25 cats can fetch\n- 30 cats can spin\n- 15 cats can jump and fetch\n- 10 cats can fetch and spin\n- 12 cats can jump and spin\n- 5 cats can do all three\n- 7 ... | 70 | |
null | null | null | math__deepscaler_preview | [
{
"content": "What is the maximum value that the expression \\(\\frac{1}{a+\\frac{2010}{b+\\frac{1}{c}}}\\) can take, where \\(a, b, c\\) are distinct non-zero digits? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "1/203",
"style": "rule"
} | {
"index": 13117,
"original_question": "What is the maximum value that the expression \\(\\frac{1}{a+\\frac{2010}{b+\\frac{1}{c}}}\\) can take, where \\(a, b, c\\) are distinct non-zero digits?",
"reward_metric": null,
"split": "train"
} | true | 0.0625 | 1 | [
{
"content": "What is the maximum value that the expression \\(\\frac{1}{a+\\frac{2010}{b+\\frac{1}{c}}}\\) can take, where \\(a, b, c\\) are distinct non-zero digits? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 1/203 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Square $IJKL$ is contained within square $WXYZ$ such that each side of $IJKL$ can be extended to pass through a vertex of $WXYZ$. The side length of square $WXYZ$ is $\\sqrt{98}$, and $WI = 2$. What is the area of the inner square $IJKL$?\nA) $62$\nB) $98 - 4\\sqrt{94}$\nC) $94 - 4\\sqrt{94}$\nD) ... | math | true | {
"ground_truth": "98 - 4\\sqrt{94}",
"style": "rule"
} | {
"index": 13118,
"original_question": "Square $IJKL$ is contained within square $WXYZ$ such that each side of $IJKL$ can be extended to pass through a vertex of $WXYZ$. The side length of square $WXYZ$ is $\\sqrt{98}$, and $WI = 2$. What is the area of the inner square $IJKL$?\nA) $62$\nB) $98 - 4\\sqrt{94}$\nC) $... | true | 0.25 | 0 | [
{
"content": "Square $IJKL$ is contained within square $WXYZ$ such that each side of $IJKL$ can be extended to pass through a vertex of $WXYZ$. The side length of square $WXYZ$ is $\\sqrt{98}$, and $WI = 2$. What is the area of the inner square $IJKL$?\nA) $62$\nB) $98 - 4\\sqrt{94}$\nC) $94 - 4\\sqrt{94}$\nD) ... | 98 - 4\sqrt{94} | |
null | null | null | math__deepscaler_preview | [
{
"content": "The jury, when preparing versions of the district math olympiad problems for grades $7, 8, 9, 10, 11$, aims to ensure that each version for each grade contains exactly 7 problems, of which exactly 4 do not appear in any other version. What is the maximum number of problems that can be included in ... | math | true | {
"ground_truth": "27",
"style": "rule"
} | {
"index": 13120,
"original_question": "The jury, when preparing versions of the district math olympiad problems for grades $7, 8, 9, 10, 11$, aims to ensure that each version for each grade contains exactly 7 problems, of which exactly 4 do not appear in any other version. What is the maximum number of problems th... | true | 0.0625 | 1 | [
{
"content": "The jury, when preparing versions of the district math olympiad problems for grades $7, 8, 9, 10, 11$, aims to ensure that each version for each grade contains exactly 7 problems, of which exactly 4 do not appear in any other version. What is the maximum number of problems that can be included in ... | 27 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Find the largest positive integer \\( n \\) for which we can find a set of distinct positive integers such that each integer is at most 2002 and if \\( a \\) and \\( b \\) are in the set, then \\( a^2 \\) and \\( ab \\) are not in the set. Please output the final answer within \\boxed{}.",
"ro... | math | true | {
"ground_truth": "1958",
"style": "rule"
} | {
"index": 13121,
"original_question": "Find the largest positive integer \\( n \\) for which we can find a set of distinct positive integers such that each integer is at most 2002 and if \\( a \\) and \\( b \\) are in the set, then \\( a^2 \\) and \\( ab \\) are not in the set.",
"reward_metric": null,
"split"... | true | 0.0625 | 1 | [
{
"content": "Find the largest positive integer \\( n \\) for which we can find a set of distinct positive integers such that each integer is at most 2002 and if \\( a \\) and \\( b \\) are in the set, then \\( a^2 \\) and \\( ab \\) are not in the set. Please output the final answer within \\boxed{}.",
"ro... | 1958 | |
null | null | null | math__deepscaler_preview | [
{
"content": "What is the maximum number of kings that can be placed on a chessboard such that no two of them attack each other? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "16",
"style": "rule"
} | {
"index": 13123,
"original_question": "What is the maximum number of kings that can be placed on a chessboard such that no two of them attack each other?",
"reward_metric": null,
"split": "train"
} | true | 0 | 1 | [
{
"content": "What is the maximum number of kings that can be placed on a chessboard such that no two of them attack each other? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 16 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Adam, Bendeguz, Cathy, and Dennis all see a positive integer $n$ . Adam says, \" $n$ leaves a remainder of $2$ when divided by $3$ .\" Bendeguz says, \"For some $k$ , $n$ is the sum of the first $k$ positive integers.\" Cathy says, \"Let $s$ be the largest perfect square that is less t... | math | true | {
"ground_truth": "210",
"style": "rule"
} | {
"index": 13128,
"original_question": "Adam, Bendeguz, Cathy, and Dennis all see a positive integer $n$ . Adam says, \" $n$ leaves a remainder of $2$ when divided by $3$ .\" Bendeguz says, \"For some $k$ , $n$ is the sum of the first $k$ positive integers.\" Cathy says, \"Let $s$ be the largest perfect... | true | 0 | 1 | [
{
"content": "Adam, Bendeguz, Cathy, and Dennis all see a positive integer $n$ . Adam says, \" $n$ leaves a remainder of $2$ when divided by $3$ .\" Bendeguz says, \"For some $k$ , $n$ is the sum of the first $k$ positive integers.\" Cathy says, \"Let $s$ be the largest perfect square that is less t... | 210 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given the function \\( y = \\sqrt{a x^2 + b x + c} \\) (where \\(a, b, c \\in \\mathbb{R}\\) and \\(a < 0\\)), the domain is \\( D \\). If the points \\( (s, f(t)) \\) (where \\( s, t \\in D \\)) form a square, then the real number \\( a \\) equals ______. Please output the final answer within \\b... | math | true | {
"ground_truth": "-4",
"style": "rule"
} | {
"index": 13130,
"original_question": "Given the function \\( y = \\sqrt{a x^2 + b x + c} \\) (where \\(a, b, c \\in \\mathbb{R}\\) and \\(a < 0\\)), the domain is \\( D \\). If the points \\( (s, f(t)) \\) (where \\( s, t \\in D \\)) form a square, then the real number \\( a \\) equals ______.",
"reward_metric"... | true | 0.25 | 1 | [
{
"content": "Given the function \\( y = \\sqrt{a x^2 + b x + c} \\) (where \\(a, b, c \\in \\mathbb{R}\\) and \\(a < 0\\)), the domain is \\( D \\). If the points \\( (s, f(t)) \\) (where \\( s, t \\in D \\)) form a square, then the real number \\( a \\) equals ______. Please output the final answer within \\b... | -4 | |
null | null | null | math__deepscaler_preview | [
{
"content": "How many numbers, divisible by 4 and less than 1000, do not contain any of the digits 6, 7, 8, 9, or 0? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "31",
"style": "rule"
} | {
"index": 13131,
"original_question": "How many numbers, divisible by 4 and less than 1000, do not contain any of the digits 6, 7, 8, 9, or 0?",
"reward_metric": null,
"split": "train"
} | true | 0.0625 | 1 | [
{
"content": "How many numbers, divisible by 4 and less than 1000, do not contain any of the digits 6, 7, 8, 9, or 0? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 31 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Solve the system\n\n$$\n\\left\\{\\begin{array}{l}\nx^{3}+3 y^{3}=11 \\\\\nx^{2} y+x y^{2}=6\n\\end{array}\\right.\n$$\n\nCalculate the values of the expression $\\frac{x_{k}}{y_{k}}$ for each solution $\\left(x_{k}, y_{k}\\right)$ of the system and find the smallest among them. If necessary, roun... | math | true | {
"ground_truth": "-1.31",
"style": "rule"
} | {
"index": 13135,
"original_question": "Solve the system\n\n$$\n\\left\\{\\begin{array}{l}\nx^{3}+3 y^{3}=11 \\\\\nx^{2} y+x y^{2}=6\n\\end{array}\\right.\n$$\n\nCalculate the values of the expression $\\frac{x_{k}}{y_{k}}$ for each solution $\\left(x_{k}, y_{k}\\right)$ of the system and find the smallest among th... | true | 0 | 1 | [
{
"content": "Solve the system\n\n$$\n\\left\\{\\begin{array}{l}\nx^{3}+3 y^{3}=11 \\\\\nx^{2} y+x y^{2}=6\n\\end{array}\\right.\n$$\n\nCalculate the values of the expression $\\frac{x_{k}}{y_{k}}$ for each solution $\\left(x_{k}, y_{k}\\right)$ of the system and find the smallest among them. If necessary, roun... | -1.31 | |
null | null | null | math__deepscaler_preview | [
{
"content": "What is the sum of the first 1234 terms of the sequence where the number of 2s between consecutive 1s increases by 1 each time? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "2419",
"style": "rule"
} | {
"index": 13137,
"original_question": "What is the sum of the first 1234 terms of the sequence where the number of 2s between consecutive 1s increases by 1 each time?",
"reward_metric": null,
"split": "train"
} | true | 0.375 | 0.9375 | [
{
"content": "What is the sum of the first 1234 terms of the sequence where the number of 2s between consecutive 1s increases by 1 each time? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 2419 | |
null | null | null | math__deepscaler_preview | [
{
"content": "A gives 24 apples to B and C, and each of the three people has at least two apples. How many different ways are there to distribute the apples? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "190",
"style": "rule"
} | {
"index": 13138,
"original_question": "A gives 24 apples to B and C, and each of the three people has at least two apples. How many different ways are there to distribute the apples?",
"reward_metric": null,
"split": "train"
} | true | 1 | 1 | [
{
"content": "A gives 24 apples to B and C, and each of the three people has at least two apples. How many different ways are there to distribute the apples? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 190 | |
null | null | null | math__deepscaler_preview | [
{
"content": "In the diagram, a rectangular ceiling \\( P Q R S \\) measures \\( 6 \\mathrm{~m} \\) by \\( 4 \\mathrm{~m} \\) and is to be completely covered using 12 rectangular tiles, each measuring \\( 1 \\mathrm{~m} \\) by \\( 2 \\mathrm{~m} \\). If there is a beam, \\( T U \\), that is positioned so that \... | math | true | {
"ground_truth": "180",
"style": "rule"
} | {
"index": 13140,
"original_question": "In the diagram, a rectangular ceiling \\( P Q R S \\) measures \\( 6 \\mathrm{~m} \\) by \\( 4 \\mathrm{~m} \\) and is to be completely covered using 12 rectangular tiles, each measuring \\( 1 \\mathrm{~m} \\) by \\( 2 \\mathrm{~m} \\). If there is a beam, \\( T U \\), that i... | true | 0 | 0.9375 | [
{
"content": "In the diagram, a rectangular ceiling \\( P Q R S \\) measures \\( 6 \\mathrm{~m} \\) by \\( 4 \\mathrm{~m} \\) and is to be completely covered using 12 rectangular tiles, each measuring \\( 1 \\mathrm{~m} \\) by \\( 2 \\mathrm{~m} \\). If there is a beam, \\( T U \\), that is positioned so that \... | 180 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Let \\( S = \\{1, 2, 3, \\ldots, 100\\} \\). Find the smallest positive integer \\( n \\) such that every \\( n \\)-element subset of \\( S \\) contains 4 pairwise coprime numbers. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "75",
"style": "rule"
} | {
"index": 13142,
"original_question": "Let \\( S = \\{1, 2, 3, \\ldots, 100\\} \\). Find the smallest positive integer \\( n \\) such that every \\( n \\)-element subset of \\( S \\) contains 4 pairwise coprime numbers.",
"reward_metric": null,
"split": "train"
} | true | 0.0625 | 0.9375 | [
{
"content": "Let \\( S = \\{1, 2, 3, \\ldots, 100\\} \\). Find the smallest positive integer \\( n \\) such that every \\( n \\)-element subset of \\( S \\) contains 4 pairwise coprime numbers. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 75 | |
null | null | null | math__deepscaler_preview | [
{
"content": "In a tetrahedron \\(ABCD\\), \\(\\angle ADB = \\angle BDC = \\angle CDA = 60^\\circ\\). The areas of \\(\\triangle ADB\\), \\(\\triangle BDC\\), and \\(\\triangle CDA\\) are \\(\\frac{\\sqrt{3}}{2}\\), \\(2\\), and \\(1\\) respectively. What is the volume of the tetrahedron? Please output the fina... | math | true | {
"ground_truth": "\\frac{2\\sqrt{6}}{9}",
"style": "rule"
} | {
"index": 13145,
"original_question": "In a tetrahedron \\(ABCD\\), \\(\\angle ADB = \\angle BDC = \\angle CDA = 60^\\circ\\). The areas of \\(\\triangle ADB\\), \\(\\triangle BDC\\), and \\(\\triangle CDA\\) are \\(\\frac{\\sqrt{3}}{2}\\), \\(2\\), and \\(1\\) respectively. What is the volume of the tetrahedron?"... | true | 0 | 1 | [
{
"content": "In a tetrahedron \\(ABCD\\), \\(\\angle ADB = \\angle BDC = \\angle CDA = 60^\\circ\\). The areas of \\(\\triangle ADB\\), \\(\\triangle BDC\\), and \\(\\triangle CDA\\) are \\(\\frac{\\sqrt{3}}{2}\\), \\(2\\), and \\(1\\) respectively. What is the volume of the tetrahedron? Please output the fina... | \frac{2\sqrt{6}}{9} | |
null | null | null | math__deepscaler_preview | [
{
"content": "The Hangzhou Asian Games are underway, and table tennis, known as China's \"national sport,\" is receiving a lot of attention. In table tennis matches, each game is played to 11 points, with one point awarded for each winning shot. In a game, one side serves two balls first, followed by the other ... | math | true | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"index": 13146,
"original_question": "The Hangzhou Asian Games are underway, and table tennis, known as China's \"national sport,\" is receiving a lot of attention. In table tennis matches, each game is played to 11 points, with one point awarded for each winning shot. In a game, one side serves two balls first, ... | true | 0.0625 | 0.9375 | [
{
"content": "The Hangzhou Asian Games are underway, and table tennis, known as China's \"national sport,\" is receiving a lot of attention. In table tennis matches, each game is played to 11 points, with one point awarded for each winning shot. In a game, one side serves two balls first, followed by the other ... | \frac{3}{4} | |
null | null | null | math__deepscaler_preview | [
{
"content": "Square $ABCD$ is constructed along diameter $AB$ of a semicircle, where both the square and semicircle are coplanar. Line segment $AB$ has a length of 8 centimeters. If point $M$ is the midpoint of arc $AB$, what is the length of segment $MD$? Please output the final answer within \\boxed{}.",
... | math | true | {
"ground_truth": "4\\sqrt{10}",
"style": "rule"
} | {
"index": 13148,
"original_question": "Square $ABCD$ is constructed along diameter $AB$ of a semicircle, where both the square and semicircle are coplanar. Line segment $AB$ has a length of 8 centimeters. If point $M$ is the midpoint of arc $AB$, what is the length of segment $MD$?",
"reward_metric": null,
"sp... | true | 0 | 0 | [
{
"content": "Square $ABCD$ is constructed along diameter $AB$ of a semicircle, where both the square and semicircle are coplanar. Line segment $AB$ has a length of 8 centimeters. If point $M$ is the midpoint of arc $AB$, what is the length of segment $MD$? Please output the final answer within \\boxed{}.",
... | 4\sqrt{10} | |
null | null | null | math__deepscaler_preview | [
{
"content": "Find the number of solutions in natural numbers for the equation \\(\\left\\lfloor \\frac{x}{10} \\right\\rfloor = \\left\\lfloor \\frac{x}{11} \\right\\rfloor + 1\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "110",
"style": "rule"
} | {
"index": 13149,
"original_question": "Find the number of solutions in natural numbers for the equation \\(\\left\\lfloor \\frac{x}{10} \\right\\rfloor = \\left\\lfloor \\frac{x}{11} \\right\\rfloor + 1\\).",
"reward_metric": null,
"split": "train"
} | true | 0.125 | 1 | [
{
"content": "Find the number of solutions in natural numbers for the equation \\(\\left\\lfloor \\frac{x}{10} \\right\\rfloor = \\left\\lfloor \\frac{x}{11} \\right\\rfloor + 1\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 110 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given the set $I=\\{1,2,3,4,5\\}$. Choose two non-empty subsets $A$ and $B$ from $I$ such that the smallest number in $B$ is greater than the largest number in $A$. The number of different ways to choose such subsets $A$ and $B$ is ______. Please output the final answer within \\boxed{}.",
"ro... | math | true | {
"ground_truth": "49",
"style": "rule"
} | {
"index": 13150,
"original_question": "Given the set $I=\\{1,2,3,4,5\\}$. Choose two non-empty subsets $A$ and $B$ from $I$ such that the smallest number in $B$ is greater than the largest number in $A$. The number of different ways to choose such subsets $A$ and $B$ is ______.",
"reward_metric": null,
"split"... | true | 0.0625 | 1 | [
{
"content": "Given the set $I=\\{1,2,3,4,5\\}$. Choose two non-empty subsets $A$ and $B$ from $I$ such that the smallest number in $B$ is greater than the largest number in $A$. The number of different ways to choose such subsets $A$ and $B$ is ______. Please output the final answer within \\boxed{}.",
"ro... | 49 | |
null | null | null | math__deepscaler_preview | [
{
"content": "A tetrahedron \\( P-ABC \\) has edge lengths \\( PA = BC = \\sqrt{6} \\), \\( PB = AC = \\sqrt{8} \\), and \\( PC = AB = \\sqrt{10} \\). Find the radius of the circumsphere of this tetrahedron. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"index": 13153,
"original_question": "A tetrahedron \\( P-ABC \\) has edge lengths \\( PA = BC = \\sqrt{6} \\), \\( PB = AC = \\sqrt{8} \\), and \\( PC = AB = \\sqrt{10} \\). Find the radius of the circumsphere of this tetrahedron.",
"reward_metric": null,
"split": "train"
} | true | 0.125 | 1 | [
{
"content": "A tetrahedron \\( P-ABC \\) has edge lengths \\( PA = BC = \\sqrt{6} \\), \\( PB = AC = \\sqrt{8} \\), and \\( PC = AB = \\sqrt{10} \\). Find the radius of the circumsphere of this tetrahedron. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | \sqrt{3} | |
null | null | null | math__deepscaler_preview | [
{
"content": "Recall that the sum of the angles of a triangle is 180 degrees. In triangle $ABC$, angle $A$ is a right angle. Let $BM$ be the median of the triangle and $D$ be the midpoint of $BM$. It turns out that $\\angle ABD = \\angle ACD$. What are the measures of these angles? Please output the final answe... | math | true | {
"ground_truth": "30",
"style": "rule"
} | {
"index": 13154,
"original_question": "Recall that the sum of the angles of a triangle is 180 degrees. In triangle $ABC$, angle $A$ is a right angle. Let $BM$ be the median of the triangle and $D$ be the midpoint of $BM$. It turns out that $\\angle ABD = \\angle ACD$. What are the measures of these angles?",
"re... | true | 0.125 | 1 | [
{
"content": "Recall that the sum of the angles of a triangle is 180 degrees. In triangle $ABC$, angle $A$ is a right angle. Let $BM$ be the median of the triangle and $D$ be the midpoint of $BM$. It turns out that $\\angle ABD = \\angle ACD$. What are the measures of these angles? Please output the final answe... | 30 | |
null | null | null | math__deepscaler_preview | [
{
"content": "In a bag, there are $5$ balls of the same size, including $3$ red balls and $2$ white balls.<br/>$(1)$ If one ball is drawn with replacement each time, and this process is repeated $3$ times, with the number of times a red ball is drawn denoted as $X$, find the probability distribution and expecta... | math | true | {
"ground_truth": "\\frac{108}{625}",
"style": "rule"
} | {
"index": 13155,
"original_question": "In a bag, there are $5$ balls of the same size, including $3$ red balls and $2$ white balls.<br/>$(1)$ If one ball is drawn with replacement each time, and this process is repeated $3$ times, with the number of times a red ball is drawn denoted as $X$, find the probability di... | true | 0.125 | 0.125 | [
{
"content": "In a bag, there are $5$ balls of the same size, including $3$ red balls and $2$ white balls.<br/>$(1)$ If one ball is drawn with replacement each time, and this process is repeated $3$ times, with the number of times a red ball is drawn denoted as $X$, find the probability distribution and expecta... | \frac{108}{625} | |
null | null | null | math__deepscaler_preview | [
{
"content": "A point is randomly thrown onto the segment $[11, 18]$ and let $k$ be the resulting value. Find the probability that the roots of the equation $\\left(k^{2}+2k-99\\right)x^{2}+(3k-7)x+2=0$ satisfy the condition $x_{1} \\leq 2x_{2}$. Please output the final answer within \\boxed{}.",
"role": "u... | math | true | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"index": 13159,
"original_question": "A point is randomly thrown onto the segment $[11, 18]$ and let $k$ be the resulting value. Find the probability that the roots of the equation $\\left(k^{2}+2k-99\\right)x^{2}+(3k-7)x+2=0$ satisfy the condition $x_{1} \\leq 2x_{2}$.",
"reward_metric": null,
"split": "trai... | true | 0.5625 | 1 | [
{
"content": "A point is randomly thrown onto the segment $[11, 18]$ and let $k$ be the resulting value. Find the probability that the roots of the equation $\\left(k^{2}+2k-99\\right)x^{2}+(3k-7)x+2=0$ satisfy the condition $x_{1} \\leq 2x_{2}$. Please output the final answer within \\boxed{}.",
"role": "u... | \frac{2}{3} | |
null | null | null | math__deepscaler_preview | [
{
"content": "What are the last three digits of \\(2003^N\\), where \\(N = 2002^{2001}\\)? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "241",
"style": "rule"
} | {
"index": 13165,
"original_question": "What are the last three digits of \\(2003^N\\), where \\(N = 2002^{2001}\\)?",
"reward_metric": null,
"split": "train"
} | true | 0.0625 | 1 | [
{
"content": "What are the last three digits of \\(2003^N\\), where \\(N = 2002^{2001}\\)? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 241 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Let $A(2,0)$ be a fixed point in the plane, and let $P\\left(\\sin \\left(2 t-60^{\\circ}\\right), \\cos \\left(2 t-60^{\\circ}\\right)\\right)$ be a moving point. Find the area swept by the line segment $AP$ as $t$ changes from $15^{\\circ}$ to $45^{\\circ}$. Please output the final answer within... | math | true | {
"ground_truth": "\\frac{\\pi}{6}",
"style": "rule"
} | {
"index": 13167,
"original_question": "Let $A(2,0)$ be a fixed point in the plane, and let $P\\left(\\sin \\left(2 t-60^{\\circ}\\right), \\cos \\left(2 t-60^{\\circ}\\right)\\right)$ be a moving point. Find the area swept by the line segment $AP$ as $t$ changes from $15^{\\circ}$ to $45^{\\circ}$.",
"reward_met... | true | 0.4375 | 1 | [
{
"content": "Let $A(2,0)$ be a fixed point in the plane, and let $P\\left(\\sin \\left(2 t-60^{\\circ}\\right), \\cos \\left(2 t-60^{\\circ}\\right)\\right)$ be a moving point. Find the area swept by the line segment $AP$ as $t$ changes from $15^{\\circ}$ to $45^{\\circ}$. Please output the final answer within... | \frac{\pi}{6} | |
null | null | null | math__deepscaler_preview | [
{
"content": "On a \\(10 \\times 10\\) grid, there are 11 horizontal grid lines and 11 vertical grid lines. The line segments connecting adjacent nodes on the same line are called \"links.\" What is the minimum number of links that must be removed so that at each node, there are at most 3 remaining links? Pleas... | math | true | {
"ground_truth": "41",
"style": "rule"
} | {
"index": 13170,
"original_question": "On a \\(10 \\times 10\\) grid, there are 11 horizontal grid lines and 11 vertical grid lines. The line segments connecting adjacent nodes on the same line are called \"links.\" What is the minimum number of links that must be removed so that at each node, there are at most 3 ... | true | 0 | 1 | [
{
"content": "On a \\(10 \\times 10\\) grid, there are 11 horizontal grid lines and 11 vertical grid lines. The line segments connecting adjacent nodes on the same line are called \"links.\" What is the minimum number of links that must be removed so that at each node, there are at most 3 remaining links? Pleas... | 41 | |
null | null | null | math__deepscaler_preview | [
{
"content": "\\( \\mathrm{n} \\) is a positive integer not greater than 100 and not less than 10, and \\( \\mathrm{n} \\) is a multiple of the sum of its digits. How many such \\( \\mathrm{n} \\) are there? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "24",
"style": "rule"
} | {
"index": 13172,
"original_question": "\\( \\mathrm{n} \\) is a positive integer not greater than 100 and not less than 10, and \\( \\mathrm{n} \\) is a multiple of the sum of its digits. How many such \\( \\mathrm{n} \\) are there?",
"reward_metric": null,
"split": "train"
} | true | 0.125 | 1 | [
{
"content": "\\( \\mathrm{n} \\) is a positive integer not greater than 100 and not less than 10, and \\( \\mathrm{n} \\) is a multiple of the sum of its digits. How many such \\( \\mathrm{n} \\) are there? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 24 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Each cell of a $100 \\times 100$ board is painted in either blue or white. We call a cell balanced if it has an equal number of blue and white neighboring cells. What is the maximum number of balanced cells that can be found on the board? (Cells are considered neighbors if they share a side.) Plea... | math | true | {
"ground_truth": "9608",
"style": "rule"
} | {
"index": 13175,
"original_question": "Each cell of a $100 \\times 100$ board is painted in either blue or white. We call a cell balanced if it has an equal number of blue and white neighboring cells. What is the maximum number of balanced cells that can be found on the board? (Cells are considered neighbors if th... | true | 0 | 0.9375 | [
{
"content": "Each cell of a $100 \\times 100$ board is painted in either blue or white. We call a cell balanced if it has an equal number of blue and white neighboring cells. What is the maximum number of balanced cells that can be found on the board? (Cells are considered neighbors if they share a side.) Plea... | 9608 | |
null | null | null | math__deepscaler_preview | [
{
"content": "The distance from \\(A\\) to \\(B\\) is 999 km. Along the road, there are kilometer markers indicating the distances to \\(A\\) and \\(B\\): 0।999, 1।998, \\(\\ldots, 999।0. How many of these markers have only two different digits? Please output the final answer within \\boxed{}.",
"role": "us... | math | true | {
"ground_truth": "40",
"style": "rule"
} | {
"index": 13177,
"original_question": "The distance from \\(A\\) to \\(B\\) is 999 km. Along the road, there are kilometer markers indicating the distances to \\(A\\) and \\(B\\): 0।999, 1।998, \\(\\ldots, 999।0. How many of these markers have only two different digits?",
"reward_metric": null,
"split": "train... | true | 0 | 1 | [
{
"content": "The distance from \\(A\\) to \\(B\\) is 999 km. Along the road, there are kilometer markers indicating the distances to \\(A\\) and \\(B\\): 0।999, 1।998, \\(\\ldots, 999।0. How many of these markers have only two different digits? Please output the final answer within \\boxed{}.",
"role": "us... | 40 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Let \\(ABCD\\) be a square of side length 1. \\(P\\) and \\(Q\\) are two points on the plane such that \\(Q\\) is the circumcentre of \\(\\triangle BPC\\) and \\(D\\) is the circumcentre of \\(\\triangle PQA\\). Find the largest possible value of \\(PQ^2\\). Express the answer in the form \\(a + \... | math | true | {
"ground_truth": "2 + \\sqrt{3}",
"style": "rule"
} | {
"index": 13178,
"original_question": "Let \\(ABCD\\) be a square of side length 1. \\(P\\) and \\(Q\\) are two points on the plane such that \\(Q\\) is the circumcentre of \\(\\triangle BPC\\) and \\(D\\) is the circumcentre of \\(\\triangle PQA\\). Find the largest possible value of \\(PQ^2\\). Express the answe... | true | 0.25 | 1 | [
{
"content": "Let \\(ABCD\\) be a square of side length 1. \\(P\\) and \\(Q\\) are two points on the plane such that \\(Q\\) is the circumcentre of \\(\\triangle BPC\\) and \\(D\\) is the circumcentre of \\(\\triangle PQA\\). Find the largest possible value of \\(PQ^2\\). Express the answer in the form \\(a + \... | 2 + \sqrt{3} | |
null | null | null | math__deepscaler_preview | [
{
"content": "Find the sum of all divisors \\(d=2^a \\cdot 3^b\\) (where \\(a, b > 0\\)) of \\(N=19^{88}-1\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "744",
"style": "rule"
} | {
"index": 13183,
"original_question": "Find the sum of all divisors \\(d=2^a \\cdot 3^b\\) (where \\(a, b > 0\\)) of \\(N=19^{88}-1\\).",
"reward_metric": null,
"split": "train"
} | true | 0 | 1 | [
{
"content": "Find the sum of all divisors \\(d=2^a \\cdot 3^b\\) (where \\(a, b > 0\\)) of \\(N=19^{88}-1\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 744 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given $w$ and $z$ are complex numbers such that $|w+z|=2$ and $|w^2+z^2|=18,$ find the smallest possible value of $|w^3+z^3|.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "50",
"style": "rule"
} | {
"index": 13185,
"original_question": "Given $w$ and $z$ are complex numbers such that $|w+z|=2$ and $|w^2+z^2|=18,$ find the smallest possible value of $|w^3+z^3|.$",
"reward_metric": null,
"split": "train"
} | true | 0.75 | 1 | [
{
"content": "Given $w$ and $z$ are complex numbers such that $|w+z|=2$ and $|w^2+z^2|=18,$ find the smallest possible value of $|w^3+z^3|.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 50 | |
null | null | null | math__deepscaler_preview | [
{
"content": "The sum of one hundred natural numbers $x, x+1, x+2, \\cdots, x+99$ is denoted as $a$. If the sum of the digits of $a$ is 50, then what is the smallest value of $x$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "99950",
"style": "rule"
} | {
"index": 13186,
"original_question": "The sum of one hundred natural numbers $x, x+1, x+2, \\cdots, x+99$ is denoted as $a$. If the sum of the digits of $a$ is 50, then what is the smallest value of $x$?",
"reward_metric": null,
"split": "train"
} | true | 0 | 0.9375 | [
{
"content": "The sum of one hundred natural numbers $x, x+1, x+2, \\cdots, x+99$ is denoted as $a$. If the sum of the digits of $a$ is 50, then what is the smallest value of $x$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 99950 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Two cars, A and B, start from points A and B respectively and travel towards each other at the same time. They meet at point C after 6 hours. If car A maintains its speed and car B increases its speed by 5 km/h, they will meet 12 km away from point C. If car B maintains its speed and car A increas... | math | true | {
"ground_truth": "30",
"style": "rule"
} | {
"index": 13190,
"original_question": "Two cars, A and B, start from points A and B respectively and travel towards each other at the same time. They meet at point C after 6 hours. If car A maintains its speed and car B increases its speed by 5 km/h, they will meet 12 km away from point C. If car B maintains its s... | true | 0.125 | 1 | [
{
"content": "Two cars, A and B, start from points A and B respectively and travel towards each other at the same time. They meet at point C after 6 hours. If car A maintains its speed and car B increases its speed by 5 km/h, they will meet 12 km away from point C. If car B maintains its speed and car A increas... | 30 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Let \\( f(x) \\) be a function defined on \\( \\mathbf{R} \\) such that for any real number \\( x \\), \\( f(x+3) f(x-4) = -1 \\). When \\( 0 \\leq x < 7 \\), \\( f(x) = \\log_{2}(9-x) \\). Find the value of \\( f(-100) \\). Please output the final answer within \\boxed{}.",
"role": "user"
}... | math | true | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"index": 13192,
"original_question": "Let \\( f(x) \\) be a function defined on \\( \\mathbf{R} \\) such that for any real number \\( x \\), \\( f(x+3) f(x-4) = -1 \\). When \\( 0 \\leq x < 7 \\), \\( f(x) = \\log_{2}(9-x) \\). Find the value of \\( f(-100) \\).",
"reward_metric": null,
"split": "train"
} | true | 0.1875 | 1 | [
{
"content": "Let \\( f(x) \\) be a function defined on \\( \\mathbf{R} \\) such that for any real number \\( x \\), \\( f(x+3) f(x-4) = -1 \\). When \\( 0 \\leq x < 7 \\), \\( f(x) = \\log_{2}(9-x) \\). Find the value of \\( f(-100) \\). Please output the final answer within \\boxed{}.",
"role": "user"
}... | -\frac{1}{2} | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given that the function $y=f(x)$ is an odd function defined on $\\mathbb{R}$ and satisfies $f(x-1)=f(x+1)$ for all $x \\in \\mathbb{R}$. When $x \\in (0,1]$ and $x_1 \\neq x_2$, we have $\\frac{f(x_2) - f(x_1)}{x_2 - x_1} < 0$. Determine the correct statement(s) among the following:\n\n(1) $f(1)=0... | math | true | {
"ground_truth": "(1) (2) (3)",
"style": "rule"
} | {
"index": 13196,
"original_question": "Given that the function $y=f(x)$ is an odd function defined on $\\mathbb{R}$ and satisfies $f(x-1)=f(x+1)$ for all $x \\in \\mathbb{R}$. When $x \\in (0,1]$ and $x_1 \\neq x_2$, we have $\\frac{f(x_2) - f(x_1)}{x_2 - x_1} < 0$. Determine the correct statement(s) among the fol... | true | 0.0625 | 0 | [
{
"content": "Given that the function $y=f(x)$ is an odd function defined on $\\mathbb{R}$ and satisfies $f(x-1)=f(x+1)$ for all $x \\in \\mathbb{R}$. When $x \\in (0,1]$ and $x_1 \\neq x_2$, we have $\\frac{f(x_2) - f(x_1)}{x_2 - x_1} < 0$. Determine the correct statement(s) among the following:\n\n(1) $f(1)=0... | (1) (2) (3) | |
null | null | null | math__deepscaler_preview | [
{
"content": "8 distinct nonzero natural numbers are arranged in increasing order. The average of the first 3 numbers is 9, the average of all 8 numbers is 19, and the average of the last 3 numbers is 29. What is the maximum possible difference between the second largest number and the second smallest number? P... | math | true | {
"ground_truth": "26",
"style": "rule"
} | {
"index": 13197,
"original_question": "8 distinct nonzero natural numbers are arranged in increasing order. The average of the first 3 numbers is 9, the average of all 8 numbers is 19, and the average of the last 3 numbers is 29. What is the maximum possible difference between the second largest number and the sec... | true | 0.0625 | 1 | [
{
"content": "8 distinct nonzero natural numbers are arranged in increasing order. The average of the first 3 numbers is 9, the average of all 8 numbers is 19, and the average of the last 3 numbers is 29. What is the maximum possible difference between the second largest number and the second smallest number? P... | 26 | |
null | null | null | math__deepscaler_preview | [
{
"content": "There are 700 cards in a box, in six colors: red, orange, yellow, green, blue, and white. The ratio of the number of red, orange, and yellow cards is $1: 3: 4$, and the ratio of the number of green, blue, and white cards is $3:1:6$. Given that there are 50 more yellow cards than blue cards, determ... | math | true | {
"ground_truth": "312",
"style": "rule"
} | {
"index": 13200,
"original_question": "There are 700 cards in a box, in six colors: red, orange, yellow, green, blue, and white. The ratio of the number of red, orange, and yellow cards is $1: 3: 4$, and the ratio of the number of green, blue, and white cards is $3:1:6$. Given that there are 50 more yellow cards t... | true | 0 | 1 | [
{
"content": "There are 700 cards in a box, in six colors: red, orange, yellow, green, blue, and white. The ratio of the number of red, orange, and yellow cards is $1: 3: 4$, and the ratio of the number of green, blue, and white cards is $3:1:6$. Given that there are 50 more yellow cards than blue cards, determ... | 312 | |
null | null | null | math__deepscaler_preview | [
{
"content": "\\( 427 \\div 2.68 \\times 16 \\times 26.8 \\div 42.7 \\times 16 \\) Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "25600",
"style": "rule"
} | {
"index": 13203,
"original_question": "\\( 427 \\div 2.68 \\times 16 \\times 26.8 \\div 42.7 \\times 16 \\)",
"reward_metric": null,
"split": "train"
} | true | 0.0625 | 1 | [
{
"content": "\\( 427 \\div 2.68 \\times 16 \\times 26.8 \\div 42.7 \\times 16 \\) Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 25600 | |
null | null | null | math__deepscaler_preview | [
{
"content": "A novel is recorded onto compact discs, taking a total of 505 minutes to read aloud. Each disc can hold up to 53 minutes of reading. Assuming the smallest possible number of discs is used and each disc contains the same length of reading, calculate the number of minutes of reading each disc will c... | math | true | {
"ground_truth": "50.5",
"style": "rule"
} | {
"index": 13204,
"original_question": "A novel is recorded onto compact discs, taking a total of 505 minutes to read aloud. Each disc can hold up to 53 minutes of reading. Assuming the smallest possible number of discs is used and each disc contains the same length of reading, calculate the number of minutes of re... | true | 0.875 | 1 | [
{
"content": "A novel is recorded onto compact discs, taking a total of 505 minutes to read aloud. Each disc can hold up to 53 minutes of reading. Assuming the smallest possible number of discs is used and each disc contains the same length of reading, calculate the number of minutes of reading each disc will c... | 50.5 | |
null | null | null | math__deepscaler_preview | [
{
"content": "The percentage of seventh-grade students participating in the gymnastics section is between 2.9% and 3.1%. Determine the smallest possible number of students in this class. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "33",
"style": "rule"
} | {
"index": 13207,
"original_question": "The percentage of seventh-grade students participating in the gymnastics section is between 2.9% and 3.1%. Determine the smallest possible number of students in this class.",
"reward_metric": null,
"split": "train"
} | true | 0.0625 | 1 | [
{
"content": "The percentage of seventh-grade students participating in the gymnastics section is between 2.9% and 3.1%. Determine the smallest possible number of students in this class. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 33 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Twenty points are equally spaced around the circumference of a circle. Kevin draws all the possible chords that connect pairs of these points. How many of these chords are longer than the radius of the circle but shorter than its diameter? Please output the final answer within \\boxed{}.",
"ro... | math | true | {
"ground_truth": "120",
"style": "rule"
} | {
"index": 13210,
"original_question": "Twenty points are equally spaced around the circumference of a circle. Kevin draws all the possible chords that connect pairs of these points. How many of these chords are longer than the radius of the circle but shorter than its diameter?",
"reward_metric": null,
"split"... | true | 0 | 1 | [
{
"content": "Twenty points are equally spaced around the circumference of a circle. Kevin draws all the possible chords that connect pairs of these points. How many of these chords are longer than the radius of the circle but shorter than its diameter? Please output the final answer within \\boxed{}.",
"ro... | 120 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Find the maximum positive integer $r$ that satisfies the following condition: For any five 500-element subsets of the set $\\{1,2, \\cdots, 1000\\}$, there exist two subsets that have at least $r$ common elements. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "200",
"style": "rule"
} | {
"index": 13211,
"original_question": "Find the maximum positive integer $r$ that satisfies the following condition: For any five 500-element subsets of the set $\\{1,2, \\cdots, 1000\\}$, there exist two subsets that have at least $r$ common elements.",
"reward_metric": null,
"split": "train"
} | true | 0.1875 | 0.9375 | [
{
"content": "Find the maximum positive integer $r$ that satisfies the following condition: For any five 500-element subsets of the set $\\{1,2, \\cdots, 1000\\}$, there exist two subsets that have at least $r$ common elements. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 200 | |
null | null | null | math__deepscaler_preview | [
{
"content": "In trapezoid \\(ABCD\\), the angles \\(A\\) and \\(D\\) at the base \\(AD\\) are \\(60^{\\circ}\\) and \\(30^{\\circ}\\) respectively. Point \\(N\\) lies on the base \\(BC\\) such that \\(BN : NC = 2\\). Point \\(M\\) lies on the base \\(AD\\), the line \\(MN\\) is perpendicular to the bases of th... | math | true | {
"ground_truth": "3:4",
"style": "rule"
} | {
"index": 13212,
"original_question": "In trapezoid \\(ABCD\\), the angles \\(A\\) and \\(D\\) at the base \\(AD\\) are \\(60^{\\circ}\\) and \\(30^{\\circ}\\) respectively. Point \\(N\\) lies on the base \\(BC\\) such that \\(BN : NC = 2\\). Point \\(M\\) lies on the base \\(AD\\), the line \\(MN\\) is perpendicu... | true | 0 | 0.4375 | [
{
"content": "In trapezoid \\(ABCD\\), the angles \\(A\\) and \\(D\\) at the base \\(AD\\) are \\(60^{\\circ}\\) and \\(30^{\\circ}\\) respectively. Point \\(N\\) lies on the base \\(BC\\) such that \\(BN : NC = 2\\). Point \\(M\\) lies on the base \\(AD\\), the line \\(MN\\) is perpendicular to the bases of th... | 3:4 | |
null | null | null | math__deepscaler_preview | [
{
"content": "In each square of an $11\\times 11$ board, we are to write one of the numbers $-1$ , $0$ , or $1$ in such a way that the sum of the numbers in each column is nonnegative and the sum of the numbers in each row is nonpositive. What is the smallest number of zeros that can be written on the boa... | math | true | {
"ground_truth": "11",
"style": "rule"
} | {
"index": 13214,
"original_question": "In each square of an $11\\times 11$ board, we are to write one of the numbers $-1$ , $0$ , or $1$ in such a way that the sum of the numbers in each column is nonnegative and the sum of the numbers in each row is nonpositive. What is the smallest number of zeros that can... | true | 0.4375 | 1 | [
{
"content": "In each square of an $11\\times 11$ board, we are to write one of the numbers $-1$ , $0$ , or $1$ in such a way that the sum of the numbers in each column is nonnegative and the sum of the numbers in each row is nonpositive. What is the smallest number of zeros that can be written on the boa... | 11 | |
null | null | null | math__deepscaler_preview | [
{
"content": "The last three digits of \\( 1978^n \\) and \\( 1978^m \\) are the same. Find the positive integers \\( m \\) and \\( n \\) such that \\( m+n \\) is minimized (here \\( n > m \\geq 1 \\)). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "106",
"style": "rule"
} | {
"index": 13218,
"original_question": "The last three digits of \\( 1978^n \\) and \\( 1978^m \\) are the same. Find the positive integers \\( m \\) and \\( n \\) such that \\( m+n \\) is minimized (here \\( n > m \\geq 1 \\)).",
"reward_metric": null,
"split": "train"
} | true | 0 | 1 | [
{
"content": "The last three digits of \\( 1978^n \\) and \\( 1978^m \\) are the same. Find the positive integers \\( m \\) and \\( n \\) such that \\( m+n \\) is minimized (here \\( n > m \\geq 1 \\)). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 106 | |
null | null | null | math__deepscaler_preview | [
{
"content": "The villages Arkadino, Borisovo, and Vadimovo are connected by straight roads in pairs. Adjacent to the road between Arkadino and Borisovo is a square field, one side of which completely coincides with this road. Adjacent to the road between Borisovo and Vadimovo is a rectangular field, one side o... | math | true | {
"ground_truth": "135",
"style": "rule"
} | {
"index": 13221,
"original_question": "The villages Arkadino, Borisovo, and Vadimovo are connected by straight roads in pairs. Adjacent to the road between Arkadino and Borisovo is a square field, one side of which completely coincides with this road. Adjacent to the road between Borisovo and Vadimovo is a rectang... | true | 0.125 | 0.875 | [
{
"content": "The villages Arkadino, Borisovo, and Vadimovo are connected by straight roads in pairs. Adjacent to the road between Arkadino and Borisovo is a square field, one side of which completely coincides with this road. Adjacent to the road between Borisovo and Vadimovo is a rectangular field, one side o... | 135 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Let \\( f(x) = x^2 + px + q \\). It is known that the inequality \\( |f(x)| > \\frac{1}{2} \\) has no solutions on the interval \\([2, 4]\\). Find \\( \\underbrace{f(f(\\ldots f}_{2017}\\left(\\frac{5-\\sqrt{11}}{2}\\right)) \\ldots) \\). Round your answer to the nearest hundredth if necessary. Pl... | math | true | {
"ground_truth": "4.16",
"style": "rule"
} | {
"index": 13222,
"original_question": "Let \\( f(x) = x^2 + px + q \\). It is known that the inequality \\( |f(x)| > \\frac{1}{2} \\) has no solutions on the interval \\([2, 4]\\). Find \\( \\underbrace{f(f(\\ldots f}_{2017}\\left(\\frac{5-\\sqrt{11}}{2}\\right)) \\ldots) \\). Round your answer to the nearest hund... | true | 0 | 1 | [
{
"content": "Let \\( f(x) = x^2 + px + q \\). It is known that the inequality \\( |f(x)| > \\frac{1}{2} \\) has no solutions on the interval \\([2, 4]\\). Find \\( \\underbrace{f(f(\\ldots f}_{2017}\\left(\\frac{5-\\sqrt{11}}{2}\\right)) \\ldots) \\). Round your answer to the nearest hundredth if necessary. Pl... | 4.16 | |
null | null | null | math__deepscaler_preview | [
{
"content": "In the following diagram, \\(ABCD\\) is a square, and \\(E\\) is the center of the square \\(ABCD\\). \\(P\\) is a point on a semi-circle with diameter \\(AB\\). \\(Q\\) is a point on a semi-circle with diameter \\(AD\\). Moreover, \\(Q, A,\\) and \\(P\\) are collinear (that is, they are on the sa... | math | true | {
"ground_truth": "34",
"style": "rule"
} | {
"index": 13223,
"original_question": "In the following diagram, \\(ABCD\\) is a square, and \\(E\\) is the center of the square \\(ABCD\\). \\(P\\) is a point on a semi-circle with diameter \\(AB\\). \\(Q\\) is a point on a semi-circle with diameter \\(AD\\). Moreover, \\(Q, A,\\) and \\(P\\) are collinear (that ... | true | 0.0625 | 1 | [
{
"content": "In the following diagram, \\(ABCD\\) is a square, and \\(E\\) is the center of the square \\(ABCD\\). \\(P\\) is a point on a semi-circle with diameter \\(AB\\). \\(Q\\) is a point on a semi-circle with diameter \\(AD\\). Moreover, \\(Q, A,\\) and \\(P\\) are collinear (that is, they are on the sa... | 34 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Let $\\mathbf{a},$ $\\mathbf{b},$ $\\mathbf{c},$ $\\mathbf{d}$ be four distinct unit vectors in space such that \n\\[\\mathbf{a} \\cdot \\mathbf{b} = \\mathbf{a} \\cdot \\mathbf{c} = \\mathbf{b} \\cdot \\mathbf{c} = \\mathbf{b} \\cdot \\mathbf{d} = \\mathbf{c} \\cdot \\mathbf{d} = -\\frac{1}{7}.\\... | math | true | {
"ground_truth": "-\\frac{19}{21}",
"style": "rule"
} | {
"index": 13224,
"original_question": "Let $\\mathbf{a},$ $\\mathbf{b},$ $\\mathbf{c},$ $\\mathbf{d}$ be four distinct unit vectors in space such that \n\\[\\mathbf{a} \\cdot \\mathbf{b} = \\mathbf{a} \\cdot \\mathbf{c} = \\mathbf{b} \\cdot \\mathbf{c} = \\mathbf{b} \\cdot \\mathbf{d} = \\mathbf{c} \\cdot \\mathbf... | true | 0 | 1 | [
{
"content": "Let $\\mathbf{a},$ $\\mathbf{b},$ $\\mathbf{c},$ $\\mathbf{d}$ be four distinct unit vectors in space such that \n\\[\\mathbf{a} \\cdot \\mathbf{b} = \\mathbf{a} \\cdot \\mathbf{c} = \\mathbf{b} \\cdot \\mathbf{c} = \\mathbf{b} \\cdot \\mathbf{d} = \\mathbf{c} \\cdot \\mathbf{d} = -\\frac{1}{7}.\\... | -\frac{19}{21} | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given the function $f(x) = e^x \\cos x - x$.\n\n(I) Find the equation of the tangent line to the curve $y = f(x)$ at the point $(0, f(0))$;\n\n(II) Find the maximum and minimum values of the function $f(x)$ on the interval $[0, \\frac{\\pi}{2}]$. Please output the final answer within \\boxed{}.",
... | math | true | {
"ground_truth": "-\\frac{\\pi}{2}",
"style": "rule"
} | {
"index": 13225,
"original_question": "Given the function $f(x) = e^x \\cos x - x$.\n\n(I) Find the equation of the tangent line to the curve $y = f(x)$ at the point $(0, f(0))$;\n\n(II) Find the maximum and minimum values of the function $f(x)$ on the interval $[0, \\frac{\\pi}{2}]$.",
"reward_metric": null,
... | true | 0.0625 | 1 | [
{
"content": "Given the function $f(x) = e^x \\cos x - x$.\n\n(I) Find the equation of the tangent line to the curve $y = f(x)$ at the point $(0, f(0))$;\n\n(II) Find the maximum and minimum values of the function $f(x)$ on the interval $[0, \\frac{\\pi}{2}]$. Please output the final answer within \\boxed{}.",
... | -\frac{\pi}{2} | |
null | null | null | math__deepscaler_preview | [
{
"content": "Points \\( M \\) and \\( N \\) are the midpoints of sides \\( BC \\) and \\( AD \\) of quadrilateral \\( ABCD \\). It is known that \\(\\angle B = 150^\\circ\\), \\(\\angle C = 90^\\circ\\), and \\(AB = CD\\). Find the angle between the lines \\(MN\\) and \\(BC\\). Please output the final answer w... | math | true | {
"ground_truth": "60",
"style": "rule"
} | {
"index": 13230,
"original_question": "Points \\( M \\) and \\( N \\) are the midpoints of sides \\( BC \\) and \\( AD \\) of quadrilateral \\( ABCD \\). It is known that \\(\\angle B = 150^\\circ\\), \\(\\angle C = 90^\\circ\\), and \\(AB = CD\\). Find the angle between the lines \\(MN\\) and \\(BC\\).",
"rewar... | true | 0.125 | 1 | [
{
"content": "Points \\( M \\) and \\( N \\) are the midpoints of sides \\( BC \\) and \\( AD \\) of quadrilateral \\( ABCD \\). It is known that \\(\\angle B = 150^\\circ\\), \\(\\angle C = 90^\\circ\\), and \\(AB = CD\\). Find the angle between the lines \\(MN\\) and \\(BC\\). Please output the final answer w... | 60 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Triangle $DEF$ has vertices $D(0,10)$, $E(4,0)$, $F(10,0)$. A vertical line intersects $DF$ at $P$ and $\\overline{EF}$ at $Q$, forming triangle $PQF$. If the area of $\\triangle PQF$ is 16, determine the positive difference of the $x$ and $y$ coordinates of point $P$. Please output the final answ... | math | true | {
"ground_truth": "8\\sqrt{2}-10",
"style": "rule"
} | {
"index": 13238,
"original_question": "Triangle $DEF$ has vertices $D(0,10)$, $E(4,0)$, $F(10,0)$. A vertical line intersects $DF$ at $P$ and $\\overline{EF}$ at $Q$, forming triangle $PQF$. If the area of $\\triangle PQF$ is 16, determine the positive difference of the $x$ and $y$ coordinates of point $P$.",
"r... | true | 0 | 1 | [
{
"content": "Triangle $DEF$ has vertices $D(0,10)$, $E(4,0)$, $F(10,0)$. A vertical line intersects $DF$ at $P$ and $\\overline{EF}$ at $Q$, forming triangle $PQF$. If the area of $\\triangle PQF$ is 16, determine the positive difference of the $x$ and $y$ coordinates of point $P$. Please output the final answ... | 8\sqrt{2}-10 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given a tetrahedron \\( A B C D \\) with side lengths \\( A B = 41 \\), \\( A C = 7 \\), \\( A D = 18 \\), \\( B C = 36 \\), \\( B D = 27 \\), and \\( C D = 13 \\), let \\( d \\) be the distance between the midpoints of edges \\( A B \\) and \\( C D \\). Find the value of \\( d^{2} \\). Please out... | math | true | {
"ground_truth": "137",
"style": "rule"
} | {
"index": 13240,
"original_question": "Given a tetrahedron \\( A B C D \\) with side lengths \\( A B = 41 \\), \\( A C = 7 \\), \\( A D = 18 \\), \\( B C = 36 \\), \\( B D = 27 \\), and \\( C D = 13 \\), let \\( d \\) be the distance between the midpoints of edges \\( A B \\) and \\( C D \\). Find the value of \\(... | true | 0 | 1 | [
{
"content": "Given a tetrahedron \\( A B C D \\) with side lengths \\( A B = 41 \\), \\( A C = 7 \\), \\( A D = 18 \\), \\( B C = 36 \\), \\( B D = 27 \\), and \\( C D = 13 \\), let \\( d \\) be the distance between the midpoints of edges \\( A B \\) and \\( C D \\). Find the value of \\( d^{2} \\). Please out... | 137 | |
null | null | null | math__deepscaler_preview | [
{
"content": "On a number line, there are three points A, B, and C which represent the numbers -24, -10, and 10, respectively. Two electronic ants, named Alpha and Beta, start moving towards each other from points A and C, respectively. Alpha moves at a speed of 4 units per second, while Beta moves at a speed o... | math | true | {
"ground_truth": "-44",
"style": "rule"
} | {
"index": 13241,
"original_question": "On a number line, there are three points A, B, and C which represent the numbers -24, -10, and 10, respectively. Two electronic ants, named Alpha and Beta, start moving towards each other from points A and C, respectively. Alpha moves at a speed of 4 units per second, while B... | true | 0 | 0.875 | [
{
"content": "On a number line, there are three points A, B, and C which represent the numbers -24, -10, and 10, respectively. Two electronic ants, named Alpha and Beta, start moving towards each other from points A and C, respectively. Alpha moves at a speed of 4 units per second, while Beta moves at a speed o... | -44 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Let \\( f(n) \\) be the number of 0's in the decimal representation of the positive integer \\( n \\). For example, \\( f(10001123) = 3 \\) and \\( f(1234567) = 0 \\). Find the value of\n\\[ f(1) + f(2) + f(3) + \\ldots + f(99999) \\] Please output the final answer within \\boxed{}.",
"role": ... | math | true | {
"ground_truth": "38889",
"style": "rule"
} | {
"index": 13242,
"original_question": "Let \\( f(n) \\) be the number of 0's in the decimal representation of the positive integer \\( n \\). For example, \\( f(10001123) = 3 \\) and \\( f(1234567) = 0 \\). Find the value of\n\\[ f(1) + f(2) + f(3) + \\ldots + f(99999) \\]",
"reward_metric": null,
"split": "tr... | true | 0 | 1 | [
{
"content": "Let \\( f(n) \\) be the number of 0's in the decimal representation of the positive integer \\( n \\). For example, \\( f(10001123) = 3 \\) and \\( f(1234567) = 0 \\). Find the value of\n\\[ f(1) + f(2) + f(3) + \\ldots + f(99999) \\] Please output the final answer within \\boxed{}.",
"role": ... | 38889 | |
null | null | null | math__deepscaler_preview | [
{
"content": "In the center of a circular field, there is a geologists' house. Six straight roads radiate from it, dividing the field into six equal sectors. Two geologists set out on a journey from their house at a speed of 5 km/h along randomly chosen roads. Determine the probability that the distance between... | math | true | {
"ground_truth": "0.5",
"style": "rule"
} | {
"index": 13243,
"original_question": "In the center of a circular field, there is a geologists' house. Six straight roads radiate from it, dividing the field into six equal sectors. Two geologists set out on a journey from their house at a speed of 5 km/h along randomly chosen roads. Determine the probability tha... | true | 0.0625 | 1 | [
{
"content": "In the center of a circular field, there is a geologists' house. Six straight roads radiate from it, dividing the field into six equal sectors. Two geologists set out on a journey from their house at a speed of 5 km/h along randomly chosen roads. Determine the probability that the distance between... | 0.5 | |
null | null | null | math__deepscaler_preview | [
{
"content": "In the triangular prism \\( P-ABC \\),\n\\[\n\\begin{array}{l}\n\\angle APB = \\angle BPC = \\angle CPA = 90^{\\circ}, \\\\\nPA = 4, \\, PB = PC = 3.\n\\end{array}\n\\]\n\nFind the minimum sum of the squares of the distances from any point on the base \\( ABC \\) to the three lateral faces. Please... | math | true | {
"ground_truth": "\\frac{144}{41}",
"style": "rule"
} | {
"index": 13247,
"original_question": "In the triangular prism \\( P-ABC \\),\n\\[\n\\begin{array}{l}\n\\angle APB = \\angle BPC = \\angle CPA = 90^{\\circ}, \\\\\nPA = 4, \\, PB = PC = 3.\n\\end{array}\n\\]\n\nFind the minimum sum of the squares of the distances from any point on the base \\( ABC \\) to the three... | true | 0.0625 | 1 | [
{
"content": "In the triangular prism \\( P-ABC \\),\n\\[\n\\begin{array}{l}\n\\angle APB = \\angle BPC = \\angle CPA = 90^{\\circ}, \\\\\nPA = 4, \\, PB = PC = 3.\n\\end{array}\n\\]\n\nFind the minimum sum of the squares of the distances from any point on the base \\( ABC \\) to the three lateral faces. Please... | \frac{144}{41} | |
null | null | null | math__deepscaler_preview | [
{
"content": "A 60-degree angle contains five circles, where each subsequent circle (starting from the second) touches the previous one. By how many times is the sum of the areas of all five circles greater than the area of the smallest circle? Please output the final answer within \\boxed{}.",
"role": "use... | math | true | {
"ground_truth": "7381",
"style": "rule"
} | {
"index": 13249,
"original_question": "A 60-degree angle contains five circles, where each subsequent circle (starting from the second) touches the previous one. By how many times is the sum of the areas of all five circles greater than the area of the smallest circle?",
"reward_metric": null,
"split": "train"... | true | 0 | 1 | [
{
"content": "A 60-degree angle contains five circles, where each subsequent circle (starting from the second) touches the previous one. By how many times is the sum of the areas of all five circles greater than the area of the smallest circle? Please output the final answer within \\boxed{}.",
"role": "use... | 7381 | |
null | null | null | math__deepscaler_preview | [
{
"content": "What is the minimum number of sides of a regular polygon that approximates the area of its circumscribed circle with an error of less than 1 per thousand (0.1%)? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "82",
"style": "rule"
} | {
"index": 13250,
"original_question": "What is the minimum number of sides of a regular polygon that approximates the area of its circumscribed circle with an error of less than 1 per thousand (0.1%)?",
"reward_metric": null,
"split": "train"
} | true | 0.0625 | 0.875 | [
{
"content": "What is the minimum number of sides of a regular polygon that approximates the area of its circumscribed circle with an error of less than 1 per thousand (0.1%)? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 82 | |
null | null | null | math__deepscaler_preview | [
{
"content": "A man, standing on a lawn, is wearing a circular sombrero of radius 3 feet. The hat blocks the sunlight, causing the grass directly under it to die instantly. If the man walks in a circle of radius 5 feet, what area of dead grass will result? Please output the final answer within \\boxed{}.",
... | math | true | {
"ground_truth": "60\\pi",
"style": "rule"
} | {
"index": 13251,
"original_question": "A man, standing on a lawn, is wearing a circular sombrero of radius 3 feet. The hat blocks the sunlight, causing the grass directly under it to die instantly. If the man walks in a circle of radius 5 feet, what area of dead grass will result?",
"reward_metric": null,
"spl... | true | 0 | 1 | [
{
"content": "A man, standing on a lawn, is wearing a circular sombrero of radius 3 feet. The hat blocks the sunlight, causing the grass directly under it to die instantly. If the man walks in a circle of radius 5 feet, what area of dead grass will result? Please output the final answer within \\boxed{}.",
... | 60\pi | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given the sequence $\\{a_n\\}$ satisfies $a_1=3$, and for any integer $n$, always has $(a_{n+1}-1)(1-a_n)=2a_n$, calculate the sum of the first 2018 terms of the sequence $\\{a_n\\}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "589",
"style": "rule"
} | {
"index": 13258,
"original_question": "Given the sequence $\\{a_n\\}$ satisfies $a_1=3$, and for any integer $n$, always has $(a_{n+1}-1)(1-a_n)=2a_n$, calculate the sum of the first 2018 terms of the sequence $\\{a_n\\}$.",
"reward_metric": null,
"split": "train"
} | true | 0.75 | 1 | [
{
"content": "Given the sequence $\\{a_n\\}$ satisfies $a_1=3$, and for any integer $n$, always has $(a_{n+1}-1)(1-a_n)=2a_n$, calculate the sum of the first 2018 terms of the sequence $\\{a_n\\}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 589 | |
null | null | null | math__deepscaler_preview | [
{
"content": "The circles $k_{1}$ and $k_{2}$, both with unit radius, touch each other at point $P$. One of their common tangents that does not pass through $P$ is the line $e$. For $i>2$, let $k_{i}$ be the circle different from $k_{i-2}$ that touches $k_{1}$, $k_{i-1}$, and $e$. Determine the radius of $k_{19... | math | true | {
"ground_truth": "\\frac{1}{1998^2}",
"style": "rule"
} | {
"index": 13259,
"original_question": "The circles $k_{1}$ and $k_{2}$, both with unit radius, touch each other at point $P$. One of their common tangents that does not pass through $P$ is the line $e$. For $i>2$, let $k_{i}$ be the circle different from $k_{i-2}$ that touches $k_{1}$, $k_{i-1}$, and $e$. Determin... | true | 0 | 1 | [
{
"content": "The circles $k_{1}$ and $k_{2}$, both with unit radius, touch each other at point $P$. One of their common tangents that does not pass through $P$ is the line $e$. For $i>2$, let $k_{i}$ be the circle different from $k_{i-2}$ that touches $k_{1}$, $k_{i-1}$, and $e$. Determine the radius of $k_{19... | \frac{1}{1998^2} | |
null | null | null | math__deepscaler_preview | [
{
"content": "In trapezoid $ABCD$ , the diagonals intersect at $E$ , the area of $\\triangle ABE$ is 72 and the area of $\\triangle CDE$ is 50. What is the area of trapezoid $ABCD$ ? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "242",
"style": "rule"
} | {
"index": 13263,
"original_question": "In trapezoid $ABCD$ , the diagonals intersect at $E$ , the area of $\\triangle ABE$ is 72 and the area of $\\triangle CDE$ is 50. What is the area of trapezoid $ABCD$ ?",
"reward_metric": null,
"split": "train"
} | true | 0.25 | 1 | [
{
"content": "In trapezoid $ABCD$ , the diagonals intersect at $E$ , the area of $\\triangle ABE$ is 72 and the area of $\\triangle CDE$ is 50. What is the area of trapezoid $ABCD$ ? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 242 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Calculate the definite integral:\n\n$$\n\\int_{\\pi / 2}^{2 \\pi} 2^{8} \\cdot \\cos ^{8} x \\, dx\n$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "105\\pi",
"style": "rule"
} | {
"index": 13267,
"original_question": "Calculate the definite integral:\n\n$$\n\\int_{\\pi / 2}^{2 \\pi} 2^{8} \\cdot \\cos ^{8} x \\, dx\n$$",
"reward_metric": null,
"split": "train"
} | true | 0 | 1 | [
{
"content": "Calculate the definite integral:\n\n$$\n\\int_{\\pi / 2}^{2 \\pi} 2^{8} \\cdot \\cos ^{8} x \\, dx\n$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 105\pi | |
null | null | null | math__deepscaler_preview | [
{
"content": "Find the smallest positive integer $n$ such that there exists a sequence of $n+1$ terms $a_{0}, a_{1}, \\cdots, a_{n}$ satisfying $a_{0}=0, a_{n}=2008$, and $\\left|a_{i}-a_{i-1}\\right|=i^{2}$ for $i=1,2, \\cdots, n$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "19",
"style": "rule"
} | {
"index": 13270,
"original_question": "Find the smallest positive integer $n$ such that there exists a sequence of $n+1$ terms $a_{0}, a_{1}, \\cdots, a_{n}$ satisfying $a_{0}=0, a_{n}=2008$, and $\\left|a_{i}-a_{i-1}\\right|=i^{2}$ for $i=1,2, \\cdots, n$.",
"reward_metric": null,
"split": "train"
} | true | 0.0625 | 1 | [
{
"content": "Find the smallest positive integer $n$ such that there exists a sequence of $n+1$ terms $a_{0}, a_{1}, \\cdots, a_{n}$ satisfying $a_{0}=0, a_{n}=2008$, and $\\left|a_{i}-a_{i-1}\\right|=i^{2}$ for $i=1,2, \\cdots, n$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 19 | |
null | null | null | math__deepscaler_preview | [
{
"content": "There are two positive integers, \\(A\\) and \\(B\\). The sum of the digits of \\(A\\) is \\(19\\), the sum of the digits of \\(B\\) is \\(20\\), and their addition results in carrying over twice. What is the sum of the digits of \\((\\mathbf{A} + B)\\)? Please output the final answer within \\box... | math | true | {
"ground_truth": "21",
"style": "rule"
} | {
"index": 13271,
"original_question": "There are two positive integers, \\(A\\) and \\(B\\). The sum of the digits of \\(A\\) is \\(19\\), the sum of the digits of \\(B\\) is \\(20\\), and their addition results in carrying over twice. What is the sum of the digits of \\((\\mathbf{A} + B)\\)?",
"reward_metric": ... | true | 0.75 | 0.875 | [
{
"content": "There are two positive integers, \\(A\\) and \\(B\\). The sum of the digits of \\(A\\) is \\(19\\), the sum of the digits of \\(B\\) is \\(20\\), and their addition results in carrying over twice. What is the sum of the digits of \\((\\mathbf{A} + B)\\)? Please output the final answer within \\box... | 21 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given set \\( S \\) such that \\( |S| = 10 \\). Let \\( A_1, A_2, \\cdots, A_k \\) be non-empty subsets of \\( S \\), and the intersection of any two subsets contains at most two elements. Find the maximum value of \\( k \\). Please output the final answer within \\boxed{}.",
"role": "user"
... | math | true | {
"ground_truth": "175",
"style": "rule"
} | {
"index": 13272,
"original_question": "Given set \\( S \\) such that \\( |S| = 10 \\). Let \\( A_1, A_2, \\cdots, A_k \\) be non-empty subsets of \\( S \\), and the intersection of any two subsets contains at most two elements. Find the maximum value of \\( k \\).",
"reward_metric": null,
"split": "train"
} | true | 0 | 1 | [
{
"content": "Given set \\( S \\) such that \\( |S| = 10 \\). Let \\( A_1, A_2, \\cdots, A_k \\) be non-empty subsets of \\( S \\), and the intersection of any two subsets contains at most two elements. Find the maximum value of \\( k \\). Please output the final answer within \\boxed{}.",
"role": "user"
... | 175 | |
null | null | null | math__deepscaler_preview | [
{
"content": "A number's cube is a five-digit number; the first digit is 4, and the fifth digit is 6. What is this number? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "36",
"style": "rule"
} | {
"index": 13273,
"original_question": "A number's cube is a five-digit number; the first digit is 4, and the fifth digit is 6. What is this number?",
"reward_metric": null,
"split": "train"
} | true | 0.875 | 1 | [
{
"content": "A number's cube is a five-digit number; the first digit is 4, and the fifth digit is 6. What is this number? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 36 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Arrange 6 volunteers for 3 different tasks, each task requires 2 people. Due to the work requirements, A and B must work on the same task, and C and D cannot work on the same task. How many different arrangements are there? Please output the final answer within \\boxed{}.",
"role": "user"
}
... | math | true | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 13279,
"original_question": "Arrange 6 volunteers for 3 different tasks, each task requires 2 people. Due to the work requirements, A and B must work on the same task, and C and D cannot work on the same task. How many different arrangements are there?",
"reward_metric": null,
"split": "train"
} | true | 0.4375 | 1 | [
{
"content": "Arrange 6 volunteers for 3 different tasks, each task requires 2 people. Due to the work requirements, A and B must work on the same task, and C and D cannot work on the same task. How many different arrangements are there? Please output the final answer within \\boxed{}.",
"role": "user"
}
... | 12 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Solve the equations:\n\n(1) 2x^2 - 5x + 1 = 0;\n\n(2) 3x(x - 2) = 2(2 - x). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "-\\frac{2}{3}",
"style": "rule"
} | {
"index": 13280,
"original_question": "Solve the equations:\n\n(1) 2x^2 - 5x + 1 = 0;\n\n(2) 3x(x - 2) = 2(2 - x).",
"reward_metric": null,
"split": "train"
} | true | 0 | 1 | [
{
"content": "Solve the equations:\n\n(1) 2x^2 - 5x + 1 = 0;\n\n(2) 3x(x - 2) = 2(2 - x). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | -\frac{2}{3} | |
null | null | null | math__deepscaler_preview | [
{
"content": "A five-digit number \\(abcde\\) satisfies:\n\\[ a < b, \\, b > c > d, \\, d < e, \\, \\text{and} \\, a > d, \\, b > e. \\]\n\nFor example, 34 201, 49 412. If the digit order's pattern follows a variation similar to the monotonicity of a sine function over one period, then the five-digit number is ... | math | true | {
"ground_truth": "2892",
"style": "rule"
} | {
"index": 13282,
"original_question": "A five-digit number \\(abcde\\) satisfies:\n\\[ a < b, \\, b > c > d, \\, d < e, \\, \\text{and} \\, a > d, \\, b > e. \\]\n\nFor example, 34 201, 49 412. If the digit order's pattern follows a variation similar to the monotonicity of a sine function over one period, then the... | true | 0 | 1 | [
{
"content": "A five-digit number \\(abcde\\) satisfies:\n\\[ a < b, \\, b > c > d, \\, d < e, \\, \\text{and} \\, a > d, \\, b > e. \\]\n\nFor example, 34 201, 49 412. If the digit order's pattern follows a variation similar to the monotonicity of a sine function over one period, then the five-digit number is ... | 2892 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Nine balls numbered $1, 2, \\cdots, 9$ are placed in a bag. These balls differ only in their numbers. Person A draws a ball from the bag, the number on the ball is $a$, and after returning it to the bag, person B draws another ball, the number on this ball is $b$. The probability that the inequali... | math | true | {
"ground_truth": "61/81",
"style": "rule"
} | {
"index": 13283,
"original_question": "Nine balls numbered $1, 2, \\cdots, 9$ are placed in a bag. These balls differ only in their numbers. Person A draws a ball from the bag, the number on the ball is $a$, and after returning it to the bag, person B draws another ball, the number on this ball is $b$. The probabi... | true | 0.0625 | 1 | [
{
"content": "Nine balls numbered $1, 2, \\cdots, 9$ are placed in a bag. These balls differ only in their numbers. Person A draws a ball from the bag, the number on the ball is $a$, and after returning it to the bag, person B draws another ball, the number on this ball is $b$. The probability that the inequali... | 61/81 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Find the total number of sets of positive integers \\((x, y, z)\\), where \\(x, y\\) and \\(z\\) are positive integers, with \\(x < y < z\\) such that\n$$\nx + y + z = 203.\n$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "3333",
"style": "rule"
} | {
"index": 13284,
"original_question": "Find the total number of sets of positive integers \\((x, y, z)\\), where \\(x, y\\) and \\(z\\) are positive integers, with \\(x < y < z\\) such that\n$$\nx + y + z = 203.\n$$",
"reward_metric": null,
"split": "train"
} | true | 0.0625 | 1 | [
{
"content": "Find the total number of sets of positive integers \\((x, y, z)\\), where \\(x, y\\) and \\(z\\) are positive integers, with \\(x < y < z\\) such that\n$$\nx + y + z = 203.\n$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 3333 | |
null | null | null | math__deepscaler_preview | [
{
"content": "How many triangles with integer sides have a perimeter equal to 27? (Triangles that differ only in the order of sides, such as 7, 10, 10 and 10, 10, 7, are considered the same triangle.) Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "19",
"style": "rule"
} | {
"index": 13285,
"original_question": "How many triangles with integer sides have a perimeter equal to 27? (Triangles that differ only in the order of sides, such as 7, 10, 10 and 10, 10, 7, are considered the same triangle.)",
"reward_metric": null,
"split": "train"
} | true | 0 | 1 | [
{
"content": "How many triangles with integer sides have a perimeter equal to 27? (Triangles that differ only in the order of sides, such as 7, 10, 10 and 10, 10, 7, are considered the same triangle.) Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 19 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Find the number of integers between 1 and 2013 with the property that the sum of its digits equals 9. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "101",
"style": "rule"
} | {
"index": 13288,
"original_question": "Find the number of integers between 1 and 2013 with the property that the sum of its digits equals 9.",
"reward_metric": null,
"split": "train"
} | true | 0 | 1 | [
{
"content": "Find the number of integers between 1 and 2013 with the property that the sum of its digits equals 9. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 101 | |
null | null | null | math__deepscaler_preview | [
{
"content": "In a geometric sequence $\\\\{a\\_n\\\\}$, $a\\_n > 0 (n \\in \\mathbb{N}^*)$, the common ratio $q \\in (0, 1)$, and $a\\_1a\\_5 + 2aa\\_5 + a\\_2a\\_8 = 25$, and the geometric mean of $a\\_3$ and $a\\_5$ is $2$.\n\n(1) Find the general term formula of the sequence $\\\\{a\\_n\\\\}$;\n\n(2) If $b\... | math | true | {
"ground_truth": "19",
"style": "rule"
} | {
"index": 13291,
"original_question": "In a geometric sequence $\\\\{a\\_n\\\\}$, $a\\_n > 0 (n \\in \\mathbb{N}^*)$, the common ratio $q \\in (0, 1)$, and $a\\_1a\\_5 + 2aa\\_5 + a\\_2a\\_8 = 25$, and the geometric mean of $a\\_3$ and $a\\_5$ is $2$.\n\n(1) Find the general term formula of the sequence $\\\\{a\\_... | true | 0.3125 | 1 | [
{
"content": "In a geometric sequence $\\\\{a\\_n\\\\}$, $a\\_n > 0 (n \\in \\mathbb{N}^*)$, the common ratio $q \\in (0, 1)$, and $a\\_1a\\_5 + 2aa\\_5 + a\\_2a\\_8 = 25$, and the geometric mean of $a\\_3$ and $a\\_5$ is $2$.\n\n(1) Find the general term formula of the sequence $\\\\{a\\_n\\\\}$;\n\n(2) If $b\... | 19 | |
null | null | null | math__deepscaler_preview | [
{
"content": "In the triangle \\(A B C\\), angle \\(C\\) is a right angle, and \\(AC: AB = 3: 5\\). A circle with its center on the extension of leg \\(AC\\) beyond point \\(C\\) is tangent to the extension of hypotenuse \\(AB\\) beyond point \\(B\\) and intersects leg \\(BC\\) at point \\(P\\), with \\(BP: PC ... | math | true | {
"ground_truth": "37/15",
"style": "rule"
} | {
"index": 13292,
"original_question": "In the triangle \\(A B C\\), angle \\(C\\) is a right angle, and \\(AC: AB = 3: 5\\). A circle with its center on the extension of leg \\(AC\\) beyond point \\(C\\) is tangent to the extension of hypotenuse \\(AB\\) beyond point \\(B\\) and intersects leg \\(BC\\) at point \\... | true | 0 | 1 | [
{
"content": "In the triangle \\(A B C\\), angle \\(C\\) is a right angle, and \\(AC: AB = 3: 5\\). A circle with its center on the extension of leg \\(AC\\) beyond point \\(C\\) is tangent to the extension of hypotenuse \\(AB\\) beyond point \\(B\\) and intersects leg \\(BC\\) at point \\(P\\), with \\(BP: PC ... | 37/15 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$, let $F_1$ and $F_2$ be the left and right foci, and let $P$ and $Q$ be two points on the right branch. If $\\overrightarrow{PF_2} = 2\\overrightarrow{F_2Q}$ and $\\overrightarrow{F_1Q} \\cdot \\overrightarrow{PQ} = 0$, determine the ec... | math | true | {
"ground_truth": "\\frac{\\sqrt{17}}{3}",
"style": "rule"
} | {
"index": 13294,
"original_question": "Given the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$, let $F_1$ and $F_2$ be the left and right foci, and let $P$ and $Q$ be two points on the right branch. If $\\overrightarrow{PF_2} = 2\\overrightarrow{F_2Q}$ and $\\overrightarrow{F_1Q} \\cdot \\overrightarrow{PQ} ... | true | 0 | 1 | [
{
"content": "Given the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$, let $F_1$ and $F_2$ be the left and right foci, and let $P$ and $Q$ be two points on the right branch. If $\\overrightarrow{PF_2} = 2\\overrightarrow{F_2Q}$ and $\\overrightarrow{F_1Q} \\cdot \\overrightarrow{PQ} = 0$, determine the ec... | \frac{\sqrt{17}}{3} | |
null | null | null | math__deepscaler_preview | [
{
"content": "A five-digit number is called irreducible if it cannot be expressed as a product of two three-digit numbers.\n\nWhat is the greatest number of consecutive irreducible five-digit numbers? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 13297,
"original_question": "A five-digit number is called irreducible if it cannot be expressed as a product of two three-digit numbers.\n\nWhat is the greatest number of consecutive irreducible five-digit numbers?",
"reward_metric": null,
"split": "train"
} | true | 0 | 0.5625 | [
{
"content": "A five-digit number is called irreducible if it cannot be expressed as a product of two three-digit numbers.\n\nWhat is the greatest number of consecutive irreducible five-digit numbers? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 99 | |
null | null | null | math__deepscaler_preview | [
{
"content": "\\(ABCD\\) is a convex quadrilateral where \\(AB = 7\\), \\(BC = 4\\), and \\(AD = DC\\). Also, \\(\\angle ABD = \\angle DBC\\). Point \\(E\\) is on segment \\(AB\\) such that \\(\\angle DEB = 90^\\circ\\). Find the length of segment \\(AE\\). Please output the final answer within \\boxed{}.",
... | math | true | {
"ground_truth": "1.5",
"style": "rule"
} | {
"index": 13301,
"original_question": "\\(ABCD\\) is a convex quadrilateral where \\(AB = 7\\), \\(BC = 4\\), and \\(AD = DC\\). Also, \\(\\angle ABD = \\angle DBC\\). Point \\(E\\) is on segment \\(AB\\) such that \\(\\angle DEB = 90^\\circ\\). Find the length of segment \\(AE\\).",
"reward_metric": null,
"sp... | true | 0.0625 | 1 | [
{
"content": "\\(ABCD\\) is a convex quadrilateral where \\(AB = 7\\), \\(BC = 4\\), and \\(AD = DC\\). Also, \\(\\angle ABD = \\angle DBC\\). Point \\(E\\) is on segment \\(AB\\) such that \\(\\angle DEB = 90^\\circ\\). Find the length of segment \\(AE\\). Please output the final answer within \\boxed{}.",
... | 1.5 | |
null | null | null | math__deepscaler_preview | [
{
"content": "\nWhat is the maximum area that a rectangle can have if the coordinates of its vertices satisfy the equation \\( |y-x| = (y+x+1)(5-x-y) \\), and its sides are parallel to the lines \\( y = x \\) and \\( y = -x \\)? Give the square of the value of the maximum area found as the answer. (12 points) P... | math | true | {
"ground_truth": "432",
"style": "rule"
} | {
"index": 13302,
"original_question": "\nWhat is the maximum area that a rectangle can have if the coordinates of its vertices satisfy the equation \\( |y-x| = (y+x+1)(5-x-y) \\), and its sides are parallel to the lines \\( y = x \\) and \\( y = -x \\)? Give the square of the value of the maximum area found as the... | true | 0.0625 | 1 | [
{
"content": "\nWhat is the maximum area that a rectangle can have if the coordinates of its vertices satisfy the equation \\( |y-x| = (y+x+1)(5-x-y) \\), and its sides are parallel to the lines \\( y = x \\) and \\( y = -x \\)? Give the square of the value of the maximum area found as the answer. (12 points) P... | 432 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Travis is hopping around on the vertices of a cube. Each minute he hops from the vertex he's currently on to the other vertex of an edge that he is next to. After four minutes, what is the probability that he is back where he started? Please output the final answer within \\boxed{}.",
"role": ... | math | true | {
"ground_truth": "7/27",
"style": "rule"
} | {
"index": 13303,
"original_question": "Travis is hopping around on the vertices of a cube. Each minute he hops from the vertex he's currently on to the other vertex of an edge that he is next to. After four minutes, what is the probability that he is back where he started?",
"reward_metric": null,
"split": "tr... | true | 0 | 1 | [
{
"content": "Travis is hopping around on the vertices of a cube. Each minute he hops from the vertex he's currently on to the other vertex of an edge that he is next to. After four minutes, what is the probability that he is back where he started? Please output the final answer within \\boxed{}.",
"role": ... | 7/27 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given a lawn with a rectangular shape of $120$ feet by $200$ feet, a mower with a $32$-inch swath width, and a $6$-inch overlap between each cut, and a walking speed of $4000$ feet per hour, calculate the time it will take John to mow the entire lawn. Please output the final answer within \\boxed{... | math | true | {
"ground_truth": "2.8",
"style": "rule"
} | {
"index": 13308,
"original_question": "Given a lawn with a rectangular shape of $120$ feet by $200$ feet, a mower with a $32$-inch swath width, and a $6$-inch overlap between each cut, and a walking speed of $4000$ feet per hour, calculate the time it will take John to mow the entire lawn.",
"reward_metric": nul... | true | 0.5625 | 0.5625 | [
{
"content": "Given a lawn with a rectangular shape of $120$ feet by $200$ feet, a mower with a $32$-inch swath width, and a $6$-inch overlap between each cut, and a walking speed of $4000$ feet per hour, calculate the time it will take John to mow the entire lawn. Please output the final answer within \\boxed{... | 2.8 | |
null | null | null | math__deepscaler_preview | [
{
"content": "How many five-character license plates consist of a consonant, followed by a vowel, followed by a consonant, a digit, and then a special character from the set {$, #, @}? (For this problem, consider Y as both a consonant and a vowel.) Please output the final answer within \\boxed{}.",
"role": ... | math | true | {
"ground_truth": "79,380",
"style": "rule"
} | {
"index": 13310,
"original_question": "How many five-character license plates consist of a consonant, followed by a vowel, followed by a consonant, a digit, and then a special character from the set {$, #, @}? (For this problem, consider Y as both a consonant and a vowel.)",
"reward_metric": null,
"split": "tr... | true | 0.1875 | 0.875 | [
{
"content": "How many five-character license plates consist of a consonant, followed by a vowel, followed by a consonant, a digit, and then a special character from the set {$, #, @}? (For this problem, consider Y as both a consonant and a vowel.) Please output the final answer within \\boxed{}.",
"role": ... | 79,380 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Find all \\( x \\in [1,2) \\) such that for any positive integer \\( n \\), the value of \\( \\left\\lfloor 2^n x \\right\\rfloor \\mod 4 \\) is either 1 or 2. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "4/3",
"style": "rule"
} | {
"index": 13312,
"original_question": "Find all \\( x \\in [1,2) \\) such that for any positive integer \\( n \\), the value of \\( \\left\\lfloor 2^n x \\right\\rfloor \\mod 4 \\) is either 1 or 2.",
"reward_metric": null,
"split": "train"
} | true | 0 | 0.9375 | [
{
"content": "Find all \\( x \\in [1,2) \\) such that for any positive integer \\( n \\), the value of \\( \\left\\lfloor 2^n x \\right\\rfloor \\mod 4 \\) is either 1 or 2. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 4/3 | |
null | null | null | math__deepscaler_preview | [
{
"content": "\nIn the 100th year of his reign, the Immortal Treasurer decided to start issuing new coins. This year, he issued an unlimited supply of coins with a denomination of \\(2^{100} - 1\\), next year with a denomination of \\(2^{101} - 1\\), and so on. As soon as the denomination of a new coin can be o... | math | true | {
"ground_truth": "200",
"style": "rule"
} | {
"index": 13313,
"original_question": "\nIn the 100th year of his reign, the Immortal Treasurer decided to start issuing new coins. This year, he issued an unlimited supply of coins with a denomination of \\(2^{100} - 1\\), next year with a denomination of \\(2^{101} - 1\\), and so on. As soon as the denomination ... | true | 0.1875 | 1 | [
{
"content": "\nIn the 100th year of his reign, the Immortal Treasurer decided to start issuing new coins. This year, he issued an unlimited supply of coins with a denomination of \\(2^{100} - 1\\), next year with a denomination of \\(2^{101} - 1\\), and so on. As soon as the denomination of a new coin can be o... | 200 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given the probability of failing on the first attempt and succeeding on the second attempt to guess the last digit of a phone number is requested, calculate the probability of this event. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "\\frac{1}{10}",
"style": "rule"
} | {
"index": 13314,
"original_question": "Given the probability of failing on the first attempt and succeeding on the second attempt to guess the last digit of a phone number is requested, calculate the probability of this event.",
"reward_metric": null,
"split": "train"
} | true | 0.375 | 0.625 | [
{
"content": "Given the probability of failing on the first attempt and succeeding on the second attempt to guess the last digit of a phone number is requested, calculate the probability of this event. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | \frac{1}{10} | |
null | null | null | math__deepscaler_preview | [
{
"content": "Determine the number of 0-1 binary sequences of ten 0's and ten 1's which do not contain three 0's together. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "24068",
"style": "rule"
} | {
"index": 13315,
"original_question": "Determine the number of 0-1 binary sequences of ten 0's and ten 1's which do not contain three 0's together.",
"reward_metric": null,
"split": "train"
} | true | 0 | 1 | [
{
"content": "Determine the number of 0-1 binary sequences of ten 0's and ten 1's which do not contain three 0's together. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 24068 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Given the vector $$\\overrightarrow {a_{k}} = (\\cos \\frac {k\\pi}{6}, \\sin \\frac {k\\pi}{6} + \\cos \\frac {k\\pi}{6})$$ for k=0, 1, 2, …, 12, find the value of $$\\sum\\limits_{k=0}^{11} (\\overrightarrow {a_{k}} \\cdot \\overrightarrow {a_{k+1}})$$. Please output the final answer within \\bo... | math | true | {
"ground_truth": "9\\sqrt{3}",
"style": "rule"
} | {
"index": 13316,
"original_question": "Given the vector $$\\overrightarrow {a_{k}} = (\\cos \\frac {k\\pi}{6}, \\sin \\frac {k\\pi}{6} + \\cos \\frac {k\\pi}{6})$$ for k=0, 1, 2, …, 12, find the value of $$\\sum\\limits_{k=0}^{11} (\\overrightarrow {a_{k}} \\cdot \\overrightarrow {a_{k+1}})$$.",
"reward_metric":... | true | 0 | 0.9375 | [
{
"content": "Given the vector $$\\overrightarrow {a_{k}} = (\\cos \\frac {k\\pi}{6}, \\sin \\frac {k\\pi}{6} + \\cos \\frac {k\\pi}{6})$$ for k=0, 1, 2, …, 12, find the value of $$\\sum\\limits_{k=0}^{11} (\\overrightarrow {a_{k}} \\cdot \\overrightarrow {a_{k+1}})$$. Please output the final answer within \\bo... | 9\sqrt{3} | |
null | null | null | math__deepscaler_preview | [
{
"content": "Compute the value of \\(1^{25}+2^{24}+3^{23}+\\ldots+24^{2}+25^{1}\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "66071772829247409",
"style": "rule"
} | {
"index": 13317,
"original_question": "Compute the value of \\(1^{25}+2^{24}+3^{23}+\\ldots+24^{2}+25^{1}\\).",
"reward_metric": null,
"split": "train"
} | true | 0 | 0.875 | [
{
"content": "Compute the value of \\(1^{25}+2^{24}+3^{23}+\\ldots+24^{2}+25^{1}\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 66071772829247409 | |
null | null | null | math__deepscaler_preview | [
{
"content": "Between 1000 and 9999, how many four-digit integers with all different digits have an absolute difference of 2 between the first and last digits? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | math | true | {
"ground_truth": "840",
"style": "rule"
} | {
"index": 13319,
"original_question": "Between 1000 and 9999, how many four-digit integers with all different digits have an absolute difference of 2 between the first and last digits?",
"reward_metric": null,
"split": "train"
} | true | 0.25 | 1 | [
{
"content": "Between 1000 and 9999, how many four-digit integers with all different digits have an absolute difference of 2 between the first and last digits? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | 840 |
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