instruction_seed stringlengths 15 7.54k | response_seed stringlengths 15 7.54k | reasoning stringlengths 0 107k | deepseek_solution stringlengths 0 4.03k | __original_row_idx int64 0 40k | source stringclasses 1
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You are going to distribute a certain number of silver coins equally among your 8 closest relatives. However, if you divide the coins into 8 equal piles, you notice that 3 relatives would receive an extra silver coin. You have fewer than 50 silver coins. What is the largest number of silver coins you could have to caus... | You are going to distribute a certain number of silver coins equally among your 8 closest relatives. However, if you divide the coins into 8 equal piles, you notice that 3 relatives would receive an extra silver coin. You have fewer than 50 silver coins. What is the largest number of silver coins you could have to caus... | Okay, let me try to figure out this problem. So, the task is to distribute a certain number of silver coins equally among 8 closest relatives. But when you divide the coins into 8 equal piles, 3 relatives end up getting an extra coin. And we know the total number of coins is fewer than 50. We need to find the largest p... | To solve the problem of distributing silver coins among 8 relatives such that 3 relatives receive an extra coin, we need to find the largest number of coins less than 50 that satisfies this condition.
1. When dividing the coins into 8 equal piles, there is a remainder of 3. This means the number of coins can be expre... | 892 | ai2-adapt-dev/openmath-2-math | <think>
Okay, let me try to figure out this problem. So, the task is to distribute a certain number of silver coins equally among 8 closest relatives. But when you divide the coins into 8 equal piles, 3 relatives end up getting an extra coin. And we know the total number of coins is fewer than 50. We need to find the l... | [
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"value": "You are going to distribute a certain number of silver coins equally among your 8 closest relatives. However, if you divide the coins into 8 equal piles, you notice that 3 relatives would receive an extra silver coin. You have fewer than 50 silver coins. What is the largest numb... |
A drawer in a darkened room contains $100$ red socks, $80$ green socks, $60$ blue socks and $40$ black socks. A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn. What is the smallest number of socks that must be selected to guarantee that the selection contains at ... | A drawer in a darkened room contains $100$ red socks, $80$ green socks, $60$ blue socks and $40$ black socks. A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn. What is the smallest number of socks that must be selected to guarantee that the selection contains at ... | Okay, so I need to figure out the smallest number of socks someone has to pick from this drawer in the dark to guarantee at least 10 pairs. The drawer has 100 red, 80 green, 60 blue, and 40 black socks. A pair is two of the same color, and socks can't be counted in more than one pair. The answer choices are 21, 23, 24,... | To determine the smallest number of socks needed to guarantee at least 10 pairs, we consider the worst-case scenario using the Pigeonhole Principle. The drawer contains 100 red, 80 green, 60 blue, and 40 black socks. A pair is two socks of the same color, and no sock can be counted in more than one pair.
1. **Worst-ca... | 33,118 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to figure out the smallest number of socks someone has to pick from this drawer in the dark to guarantee at least 10 pairs. The drawer has 100 red, 80 green, 60 blue, and 40 black socks. A pair is two of the same color, and socks can't be counted in more than one pair. The answer choices are 21,... | [
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"from": "human",
"value": "A drawer in a darkened room contains $100$ red socks, $80$ green socks, $60$ blue socks and $40$ black socks. A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn. What is the smallest number of socks that must be selected to ... |
"In a circular ring of radius $R$, there is a quadrilateral $ABCD$ whose vertices all lie on the cir(...TRUNCATED) | "In a circular ring of radius $R$, there is a quadrilateral $ABCD$ whose vertices all lie on the cir(...TRUNCATED) | "Okay, so I need to find the length of side AD in a quadrilateral ABCD inscribed in a circle of radi(...TRUNCATED) | "Given a quadrilateral \\(ABCD\\) inscribed in a circle of radius \\(R\\) with sides \\(AB\\) and \\(...TRUNCATED) | 14,910 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the length of side AD in a quadrilateral ABCD inscribed in a circl(...TRUNCATED) | [{"from":"human","value":"In a circular ring of radius $R$, there is a quadrilateral $ABCD$ whose ve(...TRUNCATED) |
"Compute \\[ \\left\\lfloor \\dfrac {2005^3}{2003 \\cdot 2004} - \\dfrac {2003^3}{2004 \\cdot 2005} (...TRUNCATED) | "Compute \\[ \\left\\lfloor \\dfrac {2005^3}{2003 \\cdot 2004} - \\dfrac {2003^3}{2004 \\cdot 2005} (...TRUNCATED) | "Okay, so I need to compute the floor of this expression: (2005³)/(2003·2004) minus (2003³)/(2004(...TRUNCATED) | "To compute the floor of the expression \\(\\left\\lfloor \\dfrac{2005^3}{2003 \\cdot 2004} - \\dfra(...TRUNCATED) | 2,731 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to compute the floor of this expression: (2005³)/(2003·2004) minus (2003(...TRUNCATED) | [{"from":"human","value":"Compute \\[ \\left\\lfloor \\dfrac {2005^3}{2003 \\cdot 2004} - \\dfrac {2(...TRUNCATED) |
"Samantha and Sophia live 2.5 kilometers apart. It takes Samantha 8 minutes to walk directly to Soph(...TRUNCATED) | "Samantha and Sophia live 2.5 kilometers apart. It takes Samantha 8 minutes to walk directly to Soph(...TRUNCATED) | "Okay, so Samantha and Sophia live 2.5 kilometers apart, and it takes Samantha 8 minutes to walk tha(...TRUNCATED) | "Samantha's walking speed can be calculated using the given distance and time. She walks 2.5 kilomet(...TRUNCATED) | 16,872 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so Samantha and Sophia live 2.5 kilometers apart, and it takes Samantha 8 minutes to(...TRUNCATED) | [{"from":"human","value":"Samantha and Sophia live 2.5 kilometers apart. It takes Samantha 8 minutes(...TRUNCATED) |
"Billy and his two friends shared some candy in the ratio of $3:5:7$. After sharing the candy, Billy(...TRUNCATED) | "Billy and his two friends shared some candy in the ratio of $3:5:7$. After sharing the candy, Billy(...TRUNCATED) | "Okay, let me try to figure this problem out step by step. So, Billy and his two friends shared some(...TRUNCATED) | "Billy and his two friends shared some candy in the ratio \\(3:5:7\\). After sharing, Billy had 36 p(...TRUNCATED) | 30,899 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, let me try to figure this problem out step by step. So, Billy and his two friends sh(...TRUNCATED) | [{"from":"human","value":"Billy and his two friends shared some candy in the ratio of $3:5:7$. After(...TRUNCATED) |
"What is the greatest positive integer that must divide the sum of the first ten terms of any arithm(...TRUNCATED) | "What is the greatest positive integer that must divide the sum of the first ten terms of any arithm(...TRUNCATED) | "Okay, so I need to find the greatest positive integer that must divide the sum of the first ten ter(...TRUNCATED) | "To find the greatest positive integer that must divide the sum of the first ten terms of any arithm(...TRUNCATED) | 19,624 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find the greatest positive integer that must divide the sum of the firs(...TRUNCATED) | [{"from":"human","value":"What is the greatest positive integer that must divide the sum of the firs(...TRUNCATED) |
Find a nonzero $p$ such that $px^2-12x+4=0$ has only one solution. | Find a nonzero $p$ such that $px^2-12x+4=0$ has only one solution. | "Okay, so I need to find a nonzero value of p such that the quadratic equation px² - 12x + 4 = 0 ha(...TRUNCATED) | "To find a nonzero \\( p \\) such that the quadratic equation \\( px^2 - 12x + 4 = 0 \\) has only on(...TRUNCATED) | 25,572 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to find a nonzero value of p such that the quadratic equation px² - 12x +(...TRUNCATED) | [{"from":"human","value":"Find a nonzero $p$ such that $px^2-12x+4=0$ has only one solution."},{"fro(...TRUNCATED) |
"A spaceship travels along a circular orbit around a planet. The spaceship's instruments detect a ch(...TRUNCATED) | "A spaceship travels along a circular orbit around a planet. The spaceship's instruments detect a ch(...TRUNCATED) | "Okay, so there's a spaceship moving in a circular orbit around a planet. The problem says that the (...TRUNCATED) | "The spaceship's velocity vector changes direction by 1020 degrees as it travels around a circular o(...TRUNCATED) | 8,914 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so there's a spaceship moving in a circular orbit around a planet. The problem says (...TRUNCATED) | [{"from":"human","value":"A spaceship travels along a circular orbit around a planet. The spaceship'(...TRUNCATED) |
"Consider the following functions and their domains:\n\nA. $a(x) = \\sqrt{1 - \\sin(x)},$ $x \\in [0(...TRUNCATED) | "Consider the following functions and their domains:\n\nA. $a(x) = \\sqrt{1 - \\sin(x)},$ $x \\in [0(...TRUNCATED) | "Okay, so I need to figure out which of these functions have inverses. Hmm, inverses... Right, a fun(...TRUNCATED) | "To determine which functions have inverses, we need to check if they are bijective (both injective (...TRUNCATED) | 14,171 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to figure out which of these functions have inverses. Hmm, inverses... Rig(...TRUNCATED) | [{"from":"human","value":"Consider the following functions and their domains:\n\nA. $a(x) = \\sqrt{1(...TRUNCATED) |
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