choices listlengths 0 0 | example stringlengths 444 1.27k | full_prompt stringlengths 551 1.38k | gold listlengths 1 1 | gold_index listlengths 0 0 | instruction stringclasses 1
value | metrics dict | num_asked_few_shots int64 0 0 | num_effective_few_shots int64 0 0 | padded listlengths 1 1 | pred_logits listlengths 0 0 | prediction_logits listlengths 0 0 | predictions listlengths 1 1 | specifics dict | truncated listlengths 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"321"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I have this problem here: Let Ο β 1 be a 13th root of unity. Find the remainder when the product β_{k=0}^{12}(2 - 2Ο^k + Ο^{2k}) is divided by 1000. Hmm, okay. Let me try to figure this out step by step.\n\nFirst, I know that Ο is a primitive 13th root of unity, so Ο^13 = 1, and the minimal polyn... | {
"extracted_golds": [
"321",
"321"
],
"extracted_predictions": [
"321",
"321"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"480"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I have this problem here about a hyperbola and a rhombus whose diagonals intersect at the origin. I need to find the greatest real number that is less than BDΒ² for all such rhombi. Hmm, let me break this down step by step.\n\nFirst, the hyperbola is given by the equation xΒ²/20 - yΒ²/24 = 1. So, th... | {
"extracted_golds": [
"480",
"480"
],
"extracted_predictions": [
"480",
"480"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"104"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this geometry problem. So, we have two rectangles, ABCD and EFGH. The points D, E, C, F are collinear, meaning they all lie on a straight line. Also, the points A, D, H, G lie on a circle. Weβre given some lengths: BC is 16, AB is 107, FG is 17, and EF is 184. We need to fin... | {
"extracted_golds": [
"104",
"104"
],
"extracted_predictions": [
"107",
"107"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"055"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this problem step by step. So, the problem is about Alice choosing a set A of positive integers, and then Bob lists all finite nonempty sets B of positive integers where the maximum element of B is in A. The total number of such sets B is 2024, and we need to find the sum of... | {
"extracted_golds": [
"55",
"55"
],
"extracted_predictions": [
"58",
"58"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"236"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let's try to solve this problem step by step. The problem is about finding the sum of the squares of all items in a list of positive integers with certain conditions. Let me parse the given information first.\n\nFirst, the sum of the items in the list is 30. So, if I denote the list as \\( a_1, a_2,... | {
"extracted_golds": [
"236",
"236"
],
"extracted_predictions": [
"236",
"236"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"721"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let's try to tackle this problem step by step. The problem is about finding the radius squared of the smallest sphere that can contain any rectangular box with a surface area of 54 and volume 23. Then, we need to express this radius squared as a fraction p/q where p and q are coprime, and find p + q... | {
"extracted_golds": [
"721",
"721"
],
"extracted_predictions": [
"27",
"27"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"104"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I have this problem about a tetrahedron ABCD with specific edge lengths. The question is asking for the distance from a point I inside the tetrahedron to each of its faces, given that all these distances are equal. This distance is supposed to be in the form mβn/p, and then I need to find m + n +... | {
"extracted_golds": [
"104",
"104"
],
"extracted_predictions": [
"1",
"1"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"540"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I need to find the largest possible real part of the expression \\((75 + 117i)z + \\frac{96 + 144i}{z}\\) where \\(z\\) is a complex number with \\(|z| = 4\\). Hmm, let's start by recalling that if \\(z\\) is a complex number with magnitude 4, then we can write \\(z\\) in polar form as \\(z = 4e^... | {
"extracted_golds": [
"540",
"540"
],
"extracted_predictions": [
"540",
"540"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"294"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I need to find the number of paths of length 16 on an 8x8 grid that start at the lower left corner and go to the upper right corner. The key thing is that these paths change direction exactly four times. Hmm, let's break this down step by step.\n\nFirst, let me visualize the grid. An 8x8 grid mea... | {
"extracted_golds": [
"294",
"294"
],
"extracted_predictions": [
"294",
"294"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"073"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this problem step by step. So, we have 900 residents in Aimeville. Each of them owns a bag of candy hearts, which is mentioned, but I don't think that affects the answer because all residents own it. The other items are a diamond ring, a set of golf clubs, and a garden spade... | {
"extracted_golds": [
"73",
"73"
],
"extracted_predictions": [
"34",
"34"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"116"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this probability problem. So, Jen is playing a lottery where she picks 4 distinct numbers from the set S = {1,2,3,...,10}. Then, 4 numbers are randomly chosen from S. She wins a prize if at least two of her numbers are among the chosen ones, and the grand prize if all four o... | {
"extracted_golds": [
"116",
"116"
],
"extracted_predictions": [
"116",
"116"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"080"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I have this problem about a convex equilateral hexagon ABCDEF where all pairs of opposite sides are parallel. The triangle formed by extending the sides AB, CD, and EF has side lengths 200, 240, and 300. I need to find the side length of the hexagon. Hmm, let's break this down step by step.\n\nFi... | {
"extracted_golds": [
"80",
"80"
],
"extracted_predictions": [
"120",
"120"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"902"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this problem step by step. So, we have a 5x5 grid, and we need to place some chips (either white or black) in the cells. The rules are:\n\n1. Each cell can have at most one chip.\n2. All chips in the same row and all chips in the same column must have the same color.\n3. If ... | {
"extracted_golds": [
"902",
"902"
],
"extracted_predictions": [
"227",
"227"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"315"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I need to find the number of rectangles that can be formed inside a regular dodecagon (12-sided polygon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon. Hmm, let me try to visualize this. The problem mentions that each side of the rectangle is on a side or a... | {
"extracted_golds": [
"315",
"315"
],
"extracted_predictions": [
"3",
"3"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"468"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I have this geometry problem here. Let me read it again to make sure I get all the details. It says: In triangle ABC, the circumcenter is O and the incenter is I. The line IA is perpendicular to the line OI. The circumradius is 13, and the inradius is 6. We need to find the product AB times AC. A... | {
"extracted_golds": [
"468",
"468"
],
"extracted_predictions": [
"156 + 624*sqrt(30)",
"156 + 624\\sqrt{30}"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"699"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let's try to tackle this problem step by step. The problem is asking for the greatest four-digit number N such that if any one of its digits is changed to 1, the resulting number is divisible by 7. Then, we need to find Q + R where Q is the quotient and R is the remainder when N is divided by 1000. ... | {
"extracted_golds": [
"699",
"699"
],
"extracted_predictions": [
"629",
"629"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"113"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I have this geometry problem here. Let me read it again and make sure I understand all the parts.\n\nWe have triangle ABC inscribed in a circle Ο. The tangents to Ο at B and C meet at point D. Then, the line AD intersects Ο again at point P. The sides of the triangle are given: AB = 5, BC = 9, an... | {
"extracted_golds": [
"113",
"113"
],
"extracted_predictions": [
"47",
"47"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"197"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this problem step by step. So, we have triangle ABC with two circles of radius 34 tangent to sides AB and BC respectively, and eight circles of radius 34 arranged sequentially tangent to each other and to the sides of the triangle. Then, replacing the eight circles with 2024... | {
"extracted_golds": [
"197",
"197"
],
"extracted_predictions": [
"20",
"20"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"023"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this problem step by step. So, we have points O at (0,0), A at (1/2, 0), and B at (0, sqrt(3)/2). The family F consists of all unit-length segments PQ in the first quadrant where P is on the x-axis and Q is on the y-axis. We need to find a point C on segment AB (other than A... | {
"extracted_golds": [
"23",
"23"
],
"extracted_predictions": [
"19",
"19"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"371"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I have this problem here about a regular octagon where each vertex is colored either red or blue randomly, each with a 50% chance. Then we need to find the probability that the octagon can be rotated such that all blue vertices end up in positions that were originally red. Hmm, that sounds a bit ... | {
"extracted_golds": [
"371",
"371"
],
"extracted_predictions": [
"529",
"529"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"601"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I need to find the number of triples of nonnegative integers (a, b, c) such that a + b + c = 300 and the sum aΒ²b + aΒ²c + bΒ²a + bΒ²c + cΒ²a + cΒ²b equals 6,000,000. Hmm, this seems a bit complicated, but let's break it down step by step.\n\nFirst, let me note that the problem involves both a linear e... | {
"extracted_golds": [
"601",
"601"
],
"extracted_predictions": [
"7",
"7"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"127"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this problem step by step. So, we have a torus T that's created by revolving a circle of radius 3 around an axis that's 6 units away from the center of the circle. That makes sense, like a donut shape. The sphere S has a radius of 11. When the torus rests on the outside of t... | {
"extracted_golds": [
"127",
"127"
],
"extracted_predictions": [
"20",
"20"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"110"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so I need to find the least prime number p such that there exists a positive integer n where nβ΄ + 1 is divisible by pΒ². Then, using that p, I have to find the smallest positive integer m where mβ΄ + 1 is divisible by pΒ². Hmm, let's start with the first part.\n\nFirst, I remember that for primes p, if... | {
"extracted_golds": [
"110",
"110"
],
"extracted_predictions": [
"2898",
"2898"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"033"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to solve this problem step by step. So, we have three equations involving logarithms with base 2, and we need to find the value of |logβ(xβ΄yΒ³zΒ²)|, which will be expressed as a fraction m/n where m and n are coprime, and then find m + n. Alright, let's start by understanding the given equa... | {
"extracted_golds": [
"33",
"33"
],
"extracted_predictions": [
"33",
"33"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"025"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to solve this problem step by step. So, the problem says there are real numbers x and y, both greater than 1, such that log base x of y^x equals 10, and log base y of x^(4y) also equals 10. We need to find the product xy. Hmm, logarithms can sometimes be tricky, but let me break it down.\... | {
"extracted_golds": [
"25",
"25"
],
"extracted_predictions": [
"25",
"25"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"809"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, so Alice and Bob are playing this game where there's a stack of n tokens. They take turns, with Alice going first. Each turn, a player can remove either 1 or 4 tokens. Whoever takes the last token wins. We need to find how many positive integers n β€ 2024 make it so that Bob can guarantee a win, no m... | {
"extracted_golds": [
"809",
"809"
],
"extracted_predictions": [
"809",
"809"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"045"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this problem step by step. So, we have a 2x3 grid, and we need to place digits in each cell such that two conditions are satisfied:\n\n1. The sum of the two numbers formed by reading left to right (i.e., each row) is 999.\n2. The sum of the three numbers formed by reading to... | {
"extracted_golds": [
"45",
"45"
],
"extracted_predictions": [
"45",
"45"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"204"
] | [] | {
"extractive_match": 1
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this problem step by step. So, Aya walks 9 kilometers every morning, right? And she stops at a coffee shop afterwards. The problem gives two different scenarios where she walks at different speeds and tells us how long each walk takes, including the time spent in the coffee ... | {
"extracted_golds": [
"204",
"204"
],
"extracted_predictions": [
"204",
"204"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"385"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out how to solve this problem. The problem is asking for the number of intersections between two graphs: y = 4g(f(sin(2Οx))) and x = 4g(f(cos(3Οy))). Hmm, that seems a bit complicated, but maybe if I break it down step by step, it will make more sense.\n\nFirst, let me understan... | {
"extracted_golds": [
"385",
"385"
],
"extracted_predictions": [
"48",
"48"
]
} | [
0
] | |
[] | Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final number or expression that solves the problem. Think step by step before an... | <|im_start|>system
You are a helpful assistant<|im_end|>
<|im_start|>user
Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\boxed{ANSWER}$. I hope it is correct' (without quotes) where ANSWER is just the final ... | [
"211"
] | [] | {
"extractive_match": 0
} | 0 | 0 | [
0
] | [] | [] | [
"<think>\nOkay, let me try to figure out this problem step by step. The problem is about finding the smallest integer base \\( b \\geq 2 \\) such that there are more than ten \\( b \\)-beautiful numbers. A \\( b \\)-beautiful number \\( n \\) is a positive integer that has exactly two digits in base \\( b \\), and ... | {
"extracted_golds": [
"211",
"211"
],
"extracted_predictions": [
"16",
"16"
]
} | [
0
] |
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