{"id": "L1-020-surface_rewrite", "original_id": "L1-020", "level": "L1", "source": "Math23K", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "一件外套，原价120元，现价是原价的(2/3)，现价多少元．", "answer": "80", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["arithmetic", "chinese", "word-problem"]}
{"id": "L1-020-add_noise", "original_id": "L1-020", "level": "L1", "source": "Math23K", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（注意：题目中所有涉及的物体数量均为正整数。）。一件衣服，原价120元，现价是原价的(2/3)，现价多少元．。", "answer": "80", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["arithmetic", "chinese", "word-problem"]}
{"id": "L1-015-surface_rewrite", "original_id": "L1-015", "level": "L1", "source": "GSM8K", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "Taylor, Dakota and Skyler decided to have lunch together at a nearby café.  Taylor orders $10 worth of food, Dakota orders $20 worth of food, and Skyler orders $30 worth of food.  How much should each pay in tips if they want to split a 20% tip for the whole meal evenly?", "answer": "4", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["arithmetic", "word-problem"]}
{"id": "L1-015-add_noise", "original_id": "L1-015", "level": "L1", "source": "GSM8K", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（请只根据题目给出的条件作答，不要引入额外假设。）。Julie, Letitia and Anton decided to have dinner together at a nearby restaurant.  Julie orders $10 worth of food, Letitia orders $20 worth of food, and Anton orders $30 worth of food.  How much should each pay in tips if they want to split a 20% tip for the whole meal evenly?。", "answer": "4", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["arithmetic", "word-problem"]}
{"id": "L1-011-surface_rewrite", "original_id": "L1-011", "level": "L1", "source": "GSM8K", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "Kai has five shopping bags that weigh the same amount as Owen’s two shopping bags. One of Owen’s shopping bags weighs three pounds and the other weighs seven. Kai’s shopping bags all weigh the same amount. How many pounds does one of Kai’s bags weigh?", "answer": "2", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["arithmetic", "word-problem"]}
{"id": "L1-011-add_noise", "original_id": "L1-011", "level": "L1", "source": "GSM8K", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（请只根据题目给出的条件作答，不要引入额外假设。）。Trace has five shopping bags that weigh the same amount as Gordon’s two shopping bags. One of Gordon’s shopping bags weighs three pounds and the other weighs seven. Trace’s shopping bags all weigh the same amount. How many pounds does one of Trace’s bags weigh?。", "answer": "2", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["arithmetic", "word-problem"]}
{"id": "L1-027-surface_rewrite", "original_id": "L1-027", "level": "L1", "source": "Math23K", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "一本书第一天看了(1/3)，第二天看的比第一天多3页，还剩5页没看，这本书总共有多少页？", "answer": "24", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["arithmetic", "chinese", "word-problem"]}
{"id": "L1-027-add_noise", "original_id": "L1-027", "level": "L1", "source": "Math23K", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（值得一提的是，这些数字的单位都是统一的，不需要额外换算。）。一本书第一天看了(1/3)，第二天看的比第一天多3页，还剩5页没看，这本书共有多少页？。", "answer": "24", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["arithmetic", "chinese", "word-problem"]}
{"id": "L2-024-surface_rewrite", "original_id": "L2-024", "level": "L2", "source": "AGIEval", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "Q: A special cereal mixture contains rice, wheat and corn in the ratio of 2:3:5. If a bag of the mixture contains 3 pounds of rice, how much corn does it contain? Answer Choices: (A)6.5 (B)7.5 (C)7 (D)6 (E)None of the above\nA: From A to E, the answer is", "answer": "(A)6.5", "answer_type": "choice", "verification": {"method": "choice_match"}, "tags": ["algebra", "choice", "standardized-test"]}
{"id": "L2-024-add_noise", "original_id": "L2-024", "level": "L2", "source": "AGIEval", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（该问题发生在一个理想化的数学环境中，不考虑空气阻力等因素。）。Q: A special cereal mixture contains rice, wheat and corn in the ratio of 2:3:5. If a bag of the mixture contains 3 pounds of rice, how much corn does it contain? Answer Choices: (A)6.5 (B)7.5 (C)7 (D)6 (E)None of the above\nA: Among A through E, the answer is。", "answer": "(A)6.5", "answer_type": "choice", "verification": {"method": "choice_match"}, "tags": ["algebra", "choice", "standardized-test"]}
{"id": "L2-026-surface_rewrite", "original_id": "L2-026", "level": "L2", "source": "AGIEval", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "Q: Determine the maximum distance you can travel with $8.50 on a cab which charges $3.50 for the first quarter-mile and 10 cents for each additional quarter mile. Answer Choices: (A)11.75 miles (B)12.75 miles (C)17.75 miles (D)14.75 miles (E)10.75 miles\nA: From A to E, the answer is", "answer": "(A)11.75 miles", "answer_type": "choice", "verification": {"method": "choice_match"}, "tags": ["algebra", "choice", "standardized-test"]}
{"id": "L2-026-add_noise", "original_id": "L2-026", "level": "L2", "source": "AGIEval", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（该问题发生在一个理想化的数学环境中，不考虑空气阻力等因素。）。Q: Calculate the maximum distance you can travel with $8.50 on a cab which charges $3.50 for the first quarter-mile and 10 cents for each additional quarter mile. Answer Choices: (A)11.75 miles (B)12.75 miles (C)17.75 miles (D)14.75 miles (E)10.75 miles\nA: Among A through E, the answer is。", "answer": "(A)11.75 miles", "answer_type": "choice", "verification": {"method": "choice_match"}, "tags": ["algebra", "choice", "standardized-test"]}
{"id": "L2-008-surface_rewrite", "original_id": "L2-008", "level": "L2", "source": "MATH", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "The number $$\\sqrt{104\\sqrt6+468\\sqrt{10}+144\\sqrt{15}+2006}$$can be written as $a\\sqrt2+b\\sqrt3+c\\sqrt5$, where $a$, $b$, and $c$ are positive integers.  Determine $a\\cdot b\\cdot c.$", "answer": "936", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["algebra", "competition", "geometry", "number-theory"]}
{"id": "L2-008-add_noise", "original_id": "L2-008", "level": "L2", "source": "MATH", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（小华在旁边看到了整个过程，但他没有参与计算。）。The number $$\\sqrt{104\\sqrt6+468\\sqrt{10}+144\\sqrt{15}+2006}$$can be written as $a\\sqrt2+b\\sqrt3+c\\sqrt5$, where $a$, $b$, and $c$ are positive integers.  Find $a\\cdot b\\cdot c.$。", "answer": "936", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["algebra", "competition", "geometry", "number-theory"]}
{"id": "L2-023-surface_rewrite", "original_id": "L2-023", "level": "L2", "source": "AGIEval", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "Q: Determine the total no. of distinct bike no.'s that can beformed using 2 letters followed by 2 no.'s. How many letters need to be distinct? Answer Choices: (A)74453 (B)64543 (C)74325 (D)65000 (E)97656\nA: From A to E, the answer is", "answer": "(C)74325", "answer_type": "choice", "verification": {"method": "choice_match"}, "tags": ["algebra", "choice", "standardized-test"]}
{"id": "L2-023-add_noise", "original_id": "L2-023", "level": "L2", "source": "AGIEval", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（题干中提到的所有价格都已经包含了税费，无需再计算附加费用。）。Q: Find the total no. of distinct bike no.'s that can beformed using 2 letters followed by 2 no.'s. How many letters need to be distinct? Answer Choices: (A)74453 (B)64543 (C)74325 (D)65000 (E)97656\nA: Among A through E, the answer is。", "answer": "(C)74325", "answer_type": "choice", "verification": {"method": "choice_match"}, "tags": ["algebra", "choice", "standardized-test"]}
{"id": "L3-012-surface_rewrite", "original_id": "L3-012", "level": "L3", "source": "MATH", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "Quinn has four brass house number digits: 2, 3, 5 and 7, and only has one of each number. How many distinct numbers can she form using one or more of the digits?", "answer": "64", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["algebra", "competition", "geometry"]}
{"id": "L3-012-add_noise", "original_id": "L3-012", "level": "L3", "source": "MATH", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（题干中提到的所有价格都已经包含了税费，无需再计算附加费用。）。Bekah has four brass house number digits: 2, 3, 5 and 7, and only has one of each number. How many distinct numbers can she form using one or more of the digits?。", "answer": "64", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["algebra", "competition", "geometry"]}
{"id": "L3-001-surface_rewrite", "original_id": "L3-001", "level": "L3", "source": "MATH", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "Determine the equation of the plane passing through the point $(0,7,-7)$ and containing the line\n\\[\\frac{x + 1}{-3} = \\frac{y - 3}{2} = \\frac{z + 2}{1}.\\]Enter your answer in the form\n\\[Ax + By + Cz + D = 0,\\]where $A,$ $B,$ $C,$ $D$ are integers such that $A > 0$ and $\\gcd(|A|,|B|,|C|,|D|) = 1.$", "answer": "x + y + z = 0", "answer_type": "expression", "verification": {"method": "symbolic_equivalence"}, "tags": ["algebra", "competition", "geometry", "number-theory"]}
{"id": "L3-001-add_noise", "original_id": "L3-001", "level": "L3", "source": "MATH", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（值得一提的是，这些数字的单位都是统一的，不需要额外换算。）。Find the equation of the plane passing through the point $(0,7,-7)$ and containing the line\n\\[\\frac{x + 1}{-3} = \\frac{y - 3}{2} = \\frac{z + 2}{1}.\\]Enter your answer in the form\n\\[Ax + By + Cz + D = 0,\\]where $A,$ $B,$ $C,$ $D$ are integers such that $A > 0$ and $\\gcd(|A|,|B|,|C|,|D|) = 1.$。", "answer": "x + y + z = 0", "answer_type": "expression", "verification": {"method": "symbolic_equivalence"}, "tags": ["algebra", "competition", "geometry", "number-theory"]}
{"id": "L3-046-surface_rewrite", "original_id": "L3-046", "level": "L3", "source": "AMC12", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "请解答下面的问题：一个圆心在 (r,r)、半径为整数 r 的圆。14 条不同线段连接 (0,aᵢ) 到 (bᵢ, 0)，长度 cᵢ 均为正整数，且都与圆相切，c₁ ≤ c₂ ≤ ... ≤ c₁₄。求最小可能的 r 对应的 c₁₄/c₁。", "answer": "17", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["amc", "competition", "geometry", "number-theory"]}
{"id": "L3-046-add_noise", "original_id": "L3-046", "level": "L3", "source": "AMC12", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "一个圆心在 (r,r)、半径为整数 r 的圆。14 条不同线段连接 (0,aᵢ) 到 (bᵢ, 0)，长度 cᵢ 均为正整数，且都与圆相切，c₁ ≤ c₂ ≤ ... ≤ c₁₄。（小华在旁边看到了整个过程，但他没有参与计算。）。求最小可能的 r 对应的 c₁₄/c₁。", "answer": "17", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["amc", "competition", "geometry", "number-theory"]}
{"id": "L3-044-surface_rewrite", "original_id": "L3-044", "level": "L3", "source": "AMC12", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "请解答下面的问题：存在唯一的整数序列 a₁, a₂, ..., a₂₀₂₃ 使得 tan(2023x) = (a₁tanx + a₃tan³x + ... + a₂₀₂₃tan²⁰²³x) / (1 + a₂tan²x + a₄tan⁴x + ... + a₂₀₂₂tan²⁰²²x)。求 a₂₀₂₃。", "answer": "-1", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["amc", "competition", "geometry", "number-theory"]}
{"id": "L3-044-add_noise", "original_id": "L3-044", "level": "L3", "source": "AMC12", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "存在唯一的整数序列 a₁, a₂, ..., a₂₀₂₃ 使得 tan(2023x) = (a₁tanx + a₃tan³x + ... + a₂₀₂₃tan²⁰²³x) / (1 + a₂tan²x + a₄tan⁴x + ... + a₂₀₂₂tan²⁰²²x)。（已知所有参与者的年龄都是整数岁。）。求 a₂₀₂₃。", "answer": "-1", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["amc", "competition", "geometry", "number-theory"]}
{"id": "L4-023-surface_rewrite", "original_id": "L4-023", "level": "L4", "source": "AIME", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "Let S be the set of all ordered triples of integers (a₁, a₂, a₃) with 1 ≤ a₁, a₂, a₃ ≤ 10. Each ordered triple in S generates a sequence according to the rule aₙ = aₙ₋₁ · |aₙ₋₂ - aₙ₋₃| for all n ≥ 4. Determine the number of such sequences for which aₙ = 0 for some n.", "answer": "494", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["aime", "combinatorics", "competition", "number-theory"]}
{"id": "L4-023-add_noise", "original_id": "L4-023", "level": "L4", "source": "AIME", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（值得一提的是，这些数字的单位都是统一的，不需要额外换算。）。Let S be the set of all ordered triples of integers (a₁, a₂, a₃) with 1 ≤ a₁, a₂, a₃ ≤ 10. Each ordered triple in S generates a sequence according to the rule aₙ = aₙ₋₁ · |aₙ₋₂ - aₙ₋₃| for all n ≥ 4. Find the number of such sequences for which aₙ = 0 for some n.。", "answer": "494", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["aime", "combinatorics", "competition", "number-theory"]}
{"id": "L4-019-surface_rewrite", "original_id": "L4-019", "level": "L4", "source": "AIME", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "Please solve the following problem. Let AB be a chord of a circle ω, and let P be a point on the chord AB. Circle ω₁ passes through A and P and is internally tangent to ω. Circle ω₂ passes through B and P and is internally tangent to ω. If ω₁ and ω₂ meet at P and Q, and if AB = 42 and PQ = 35, find the radius of ω.", "answer": "42", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["aime", "combinatorics", "competition", "geometry", "number-theory"]}
{"id": "L4-019-add_noise", "original_id": "L4-019", "level": "L4", "source": "AIME", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（注意：题目中所有涉及的物体数量均为正整数。）。Let AB be a chord of a circle ω, and let P be a point on the chord AB. Circle ω₁ passes through A and P and is internally tangent to ω. Circle ω₂ passes through B and P and is internally tangent to ω. If ω₁ and ω₂ meet at P and Q, and if AB = 42 and PQ = 35, find the radius of ω.。", "answer": "42", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["aime", "combinatorics", "competition", "geometry", "number-theory"]}
{"id": "L4-011-surface_rewrite", "original_id": "L4-011", "level": "L4", "source": "AIME", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "The following analog clock has two hands that can move independently of each other. Initially, both hands point to the number 12. The clock performs a sequence of hand movements so that on each movement, one of the two hands moves clockwise to the next number on the clock face while the other hand does not move. Let N be the number of sequences of 144 hand movements such that during the sequence, every possible positioning of the hands appears exactly once, and at the end of the 144 movements, the hands have returned to their initial position. Determine the remainder when N is divided by 1000.", "answer": "144", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["aime", "combinatorics", "competition", "number-theory"]}
{"id": "L4-011-add_noise", "original_id": "L4-011", "level": "L4", "source": "AIME", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（小华在旁边看到了整个过程，但他没有参与计算。）。The following analog clock has two hands that can move independently of each other. Initially, both hands point to the number 12. The clock performs a sequence of hand movements so that on each movement, one of the two hands moves clockwise to the next number on the clock face while the other hand does not move. Let N be the number of sequences of 144 hand movements such that during the sequence, every possible positioning of the hands appears exactly once, and at the end of the 144 movements, the hands have returned to their initial position. Find the remainder when N is divided by 1000.。", "answer": "144", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["aime", "combinatorics", "competition", "number-theory"]}
{"id": "L4-015-surface_rewrite", "original_id": "L4-015", "level": "L4", "source": "AIME", "contamination_risk": "low", "perturbation_type": "surface_rewrite", "perturbation_note": "规则化表面改写：人名、地名、常见物品、句式微调，数学条件与答案保持不变", "problem": "Let x, y, and z be positive real numbers satisfying: x + y + z = 1, x² + y² + z² = 1/2, and x³ + y³ + z³ = 1/3. Compute the value of 1/x + 1/y + 1/z.", "answer": "9", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["aime", "combinatorics", "competition", "number-theory"]}
{"id": "L4-015-add_noise", "original_id": "L4-015", "level": "L4", "source": "AIME", "contamination_risk": "low", "perturbation_type": "add_noise", "perturbation_note": "插入无关子句（GSM-NoOp 风格），答案保持不变", "problem": "（已知所有参与者的年龄都是整数岁。）。Let x, y, and z be positive real numbers satisfying: x + y + z = 1, x² + y² + z² = 1/2, and x³ + y³ + z³ = 1/3. Find the value of 1/x + 1/y + 1/z.。", "answer": "9", "answer_type": "integer", "verification": {"method": "exact_match"}, "tags": ["aime", "combinatorics", "competition", "number-theory"]}