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values | problem_prompt listlengths 1 1 | problem_with_hint_prompt listlengths 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | <|im_start|>user
The thousands digit of a five-digit number which is divisible by $37$ and $173$ is $3$. What is the hundreds digit of this number?
\[
\textbf{a)}\ 0 \quad \textbf{b)}\ 2 \quad \textbf{c)}\ 4 \quad \textbf{d)}\ 6 \quad \textbf{e)}\ 8
\]<|im_end|>
<|im_start|>assistant
| <think>
Okay, so I need to solve this number theory problem. The problem states that there is a five-digit number, let's call it N. This number N is divisible by both 37 and 173. I'm also told that its thousands digit is 3. The question asks for the hundreds digit of this number N. The options are given as a) 0, b) 2, ... | {
"content": "Okay, so I need to solve this number theory problem. The problem states that there is a five-digit number, let's call it N. This number N is divisible by both 37 and 173. I'm also told that its thousands digit is 3. The question asks for the hundreds digit of this number N.",
"location": 0
} | <think>
Okay, let's try to figure out this problem. So, we have a five-digit number. The thousands digit is 3, and the number is divisible by both 37 and 173. We need to find the hundreds digit of this number. The options are 0, 2, 4, 6, or 8.
First, I should recall that if a number is divisible by two numbers, it mu... | <think>
Okay, so I need to find a five-digit number that's divisible by both 37 and 173. The thousands digit is 3, and I need to figure out what the hundreds digit is. The options are 0, 2, 4, 6, or 8. Let me start by understanding the problem step by step.
First, since the number is divisible by both 37 and 173, it m... | <think>
Okay, so I need to find a five-digit number that's divisible by both 37 and 173. The thousands digit is 3, and I need to figure out what the hundreds digit is. The options are 0, 2, 4, 6, or 8. Let me start by understanding the problem step by step.
First, the number is five digits. Let me denote it as ABCDE, ... | <think>
Okay, so I need to find a five-digit number that's divisible by both 37 and 173. The thousands digit is 3, and I need to figure out what the hundreds digit is. The options are 0, 2, 4, 6, or 8. Let me start by understanding the problem step by step.
First, since the number is divisible by both 37 and 173, it m... | The thousands digit of a five-digit number which is divisible by $37$ and $173$ is $3$. What is the hundreds digit of this number?
\[
\textbf{a)}\ 0 \quad \textbf{b)}\ 2 \quad \textbf{c)}\ 4 \quad \textbf{d)}\ 6 \quad \textbf{e)}\ 8
\] | 2 | dapo | [
{
"content": "The thousands digit of a five-digit number which is divisible by $37$ and $173$ is $3$. What is the hundreds digit of this number?\n\n\\[\n\\textbf{a)}\\ 0 \\quad \\textbf{b)}\\ 2 \\quad \\textbf{c)}\\ 4 \\quad \\textbf{d)}\\ 6 \\quad \\textbf{e)}\\ 8\n\\]",
"role": "user"
}
] | [
{
"content": "The thousands digit of a five-digit number which is divisible by $37$ and $173$ is $3$. What is the hundreds digit of this number?\n\n\\[\n\\textbf{a)}\\ 0 \\quad \\textbf{b)}\\ 2 \\quad \\textbf{c)}\\ 4 \\quad \\textbf{d)}\\ 6 \\quad \\textbf{e)}\\ 8\n\\]\n\nOkay, so I need to solve this number t... |
36 | 4 | "<|im_start|>user\nTim is participating in the following three math contests. On each contest, his s(...TRUNCATED) | "<think>\nOkay, so I need to solve this problem about the expected value of Tim's scores. Let me par(...TRUNCATED) | {"content":"Okay, so I need to solve this problem about the expected value of Tim's scores. Let me p(...TRUNCATED) | "<think>\nOkay, so Tim is taking three different math contests, each with different numbers of probl(...TRUNCATED) | "<think>\nOkay, so Tim is taking three different math contests: Local Area Inspirational Math Exam ((...TRUNCATED) | "<think>\nOkay, so Tim is taking three math contests: Local Area Inspirational Math Exam (LAIME) wit(...TRUNCATED) | "<think>\nOkay, so Tim is taking three different math contests, each with a different number of prob(...TRUNCATED) | "Tim is participating in the following three math contests. On each contest, his score is the number(...TRUNCATED) | 50 | dapo | [{"content":"Tim is participating in the following three math contests. On each contest, his score i(...TRUNCATED) | [{"content":"Tim is participating in the following three math contests. On each contest, his score i(...TRUNCATED) |
255 | 4 | "<|im_start|>user\nThe letters $AAABBCC$ are arranged in random order. The probability no two adjace(...TRUNCATED) | "<think>\nOkay, so I need to solve this probability problem. The problem asks for the probability th(...TRUNCATED) | {"content":"Okay, so I need to solve this probability problem. The problem asks for the probability (...TRUNCATED) | "<think>\nOkay, so I need to find the probability that when I arrange the letters AAABBCC in a rando(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that when I arrange the letters AAABBCC in a rando(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that when I arrange the letters AAABBCC randomly, (...TRUNCATED) | "<think>\nOkay, so I need to find the probability that when I arrange the letters AAABBCC in a rando(...TRUNCATED) | "The letters $AAABBCC$ are arranged in random order. The probability no two adjacent letters will be(...TRUNCATED) | 124 | dapo | [{"content":"The letters $AAABBCC$ are arranged in random order. The probability no two adjacent let(...TRUNCATED) | [{"content":"The letters $AAABBCC$ are arranged in random order. The probability no two adjacent let(...TRUNCATED) |
47 | 0 | "<|im_start|>user\nThe real numbers $a_0, a_1, \\dots, a_{2013}$ and $b_0, b_1, \\dots, b_{2013}$ sa(...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem. It seems to be about sequences and recurrence rela(...TRUNCATED) | {"content":"Okay, let's try to tackle this problem. It seems to be about sequences and recurrence re(...TRUNCATED) | "<think>\nOkay, so I need to compute this sum: the sum from k=1 to 2013 of (a_k b_{k-1} - a_{k-1} b_(...TRUNCATED) | "<think>\nOkay, let me try to figure out this problem. So, we have two sequences, a_n and b_n, defin(...TRUNCATED) | "<think>\nOkay, so I need to compute this sum: the sum from k=1 to 2013 of (a_k b_{k-1} - a_{k-1} b_(...TRUNCATED) | "<think>\nOkay, so I need to compute this sum: the sum from k=1 to 2013 of (a_k b_{k-1} - a_{k-1} b_(...TRUNCATED) | "The real numbers $a_0, a_1, \\dots, a_{2013}$ and $b_0, b_1, \\dots, b_{2013}$ satisfy the recurren(...TRUNCATED) | 671 | dapo | [{"content":"The real numbers $a_0, a_1, \\dots, a_{2013}$ and $b_0, b_1, \\dots, b_{2013}$ satisfy (...TRUNCATED) | [{"content":"The real numbers $a_0, a_1, \\dots, a_{2013}$ and $b_0, b_1, \\dots, b_{2013}$ satisfy (...TRUNCATED) |
30 | 8 | "<|im_start|>user\nIn circle $\\theta_1$ with radius $1$, circles $\\phi_1, \\phi_2, \\dots, \\phi_8(...TRUNCATED) | "<think>\nOkay, let's try to tackle this geometry problem step by step. First, let me make sure I un(...TRUNCATED) | {"content":"Okay, let's try to tackle this geometry problem step by step. First, let me make sure I (...TRUNCATED) | "<think>\nOkay, so I need to find the radius of circle ω₂ that is tangent to all eight circles φ(...TRUNCATED) | "<think>\nOkay, so I need to find the radius of this circle ω₂ that is tangent to all eight circl(...TRUNCATED) | "<think>\nOkay, so I need to solve this geometry problem involving circles. Let me try to visualize (...TRUNCATED) | "<think>\nOkay, so I need to solve this geometry problem. Let me try to visualize it first. There's (...TRUNCATED) | "In circle $\\theta_1$ with radius $1$, circles $\\phi_1, \\phi_2, \\dots, \\phi_8$, with equal radi(...TRUNCATED) | 31 | dapo | [{"content":"In circle $\\theta_1$ with radius $1$, circles $\\phi_1, \\phi_2, \\dots, \\phi_8$, wit(...TRUNCATED) | [{"content":"In circle $\\theta_1$ with radius $1$, circles $\\phi_1, \\phi_2, \\dots, \\phi_8$, wit(...TRUNCATED) |
15 | 0 | "<|im_start|>user\nCompute the smallest positive integer $M$ such that there exists a positive integ(...TRUNCATED) | "<think>\nOkay, let's try to tackle this problem. It seems a bit complex, but I'll take it step by s(...TRUNCATED) | {"content":"Okay, let's try to tackle this problem. It seems a bit complex, but I'll take it step by(...TRUNCATED) | "<think>\nOkay, so I need to find the smallest positive integer M such that there exists a positive (...TRUNCATED) | "<think>\nOkay, so I need to find the smallest positive integer M such that there's a positive integ(...TRUNCATED) | "<think>\nOkay, so I need to find the smallest positive integer M such that there exists a positive (...TRUNCATED) | "<think>\nOkay, so I need to find the smallest positive integer M such that there's a positive integ(...TRUNCATED) | "Compute the smallest positive integer $M$ such that there exists a positive integer $n$ for which:\(...TRUNCATED) | 4250 | dapo | [{"content":"Compute the smallest positive integer $M$ such that there exists a positive integer $n$(...TRUNCATED) | [{"content":"Compute the smallest positive integer $M$ such that there exists a positive integer $n$(...TRUNCATED) |
107 | 4 | "<|im_start|>user\nHow many real numbers $x$ satisfy the equation $\\frac{1}{5}\\log_2 x = \\sin (5\(...TRUNCATED) | "<think>\nOkay, so I need to find the number of real solutions to the equation `(1/5)log₂(x) = sin(...TRUNCATED) | {"content":"Okay, so I need to find the number of real solutions to the equation `(1/5)log₂(x) = s(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many real numbers x satisfy the equation (1/5) log₂x =(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many real numbers x satisfy the equation (1/5) log₂x =(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many real numbers x satisfy the equation (1/5) log₂x =(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many real numbers x satisfy the equation (1/5) log₂x =(...TRUNCATED) | How many real numbers $x$ satisfy the equation $\frac{1}{5}\log_2 x = \sin (5\pi x)$ ? | 159 | dapo | [{"content":"How many real numbers $x$ satisfy the equation $\\frac{1}{5}\\log_2 x = \\sin (5\\pi x)(...TRUNCATED) | [{"content":"How many real numbers $x$ satisfy the equation $\\frac{1}{5}\\log_2 x = \\sin (5\\pi x)(...TRUNCATED) |
29 | 1 | "<|im_start|>user\nA $3 \\times 3 \\times 3$ cube composed of $27$ unit cubes rests on a horizontal (...TRUNCATED) | "<think>\nOkay, so I need to solve this geometry problem. Let's break it down. The problem is about (...TRUNCATED) | {"content":"Okay, so I need to solve this geometry problem. Let's break it down. The problem is abou(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many ways there are to select two distinct unit cubes fr(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many ways there are to select two distinct unit cubes fr(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many ways there are to select two distinct unit cubes fr(...TRUNCATED) | "<think>\nOkay, so I need to figure out how many ways there are to select two distinct unit cubes fr(...TRUNCATED) | "A $3 \\times 3 \\times 3$ cube composed of $27$ unit cubes rests on a horizontal plane. Determine t(...TRUNCATED) | 60 | dapo | [{"content":"A $3 \\times 3 \\times 3$ cube composed of $27$ unit cubes rests on a horizontal plane.(...TRUNCATED) | [{"content":"A $3 \\times 3 \\times 3$ cube composed of $27$ unit cubes rests on a horizontal plane.(...TRUNCATED) |
86 | 4 | "<|im_start|>user\nThere are $256$ players in a tennis tournament ranked from $1$ to $256$, where $1(...TRUNCATED) | "<think>\nOkay, so I need to solve this problem about a tennis tournament. It asks for an expected v(...TRUNCATED) | {"content":"Okay, so I need to solve this problem about a tennis tournament. It asks for an expected(...TRUNCATED) | "<think>\nOkay, so there's this tennis tournament with 256 players, ranked from 1 to 256. The goal i(...TRUNCATED) | "<think>\nOkay, so I need to figure out the expected value of the rank of the winner in this tennis (...TRUNCATED) | "<think>\nOkay, so I need to figure out the expected value of the rank of the winner in this tennis (...TRUNCATED) | "<think>\nOkay, so I need to figure out the expected value of the rank of the winner in this tennis (...TRUNCATED) | "There are $256$ players in a tennis tournament ranked from $1$ to $256$, where $1$ is the highest r(...TRUNCATED) | 103 | dapo | [{"content":"There are $256$ players in a tennis tournament ranked from $1$ to $256$, where $1$ is t(...TRUNCATED) | [{"content":"There are $256$ players in a tennis tournament ranked from $1$ to $256$, where $1$ is t(...TRUNCATED) |
17 | 9 | "<|im_start|>user\nA sequence $\\{a_n\\}$ is defined such that $a_i = i$ for $i = 1, 2, 3, \\ldots, (...TRUNCATED) | "<think>\nOkay, so I need to solve this problem about a sequence. Let me start by understanding the (...TRUNCATED) | {"content":"Okay, so I need to solve this problem about a sequence. Let me start by understanding th(...TRUNCATED) | "<think>\nOkay, so I need to figure out the limit of the sequence {a_n} as n approaches infinity, an(...TRUNCATED) | "<think>\nOkay, so I need to figure out the limit of the sequence {a_n} as n approaches infinity, an(...TRUNCATED) | "<think>\nOkay, so I need to figure out the limit of the sequence {a_n} as n approaches infinity, an(...TRUNCATED) | "<think>\nOkay, so I need to figure out the limit of the sequence {a_n} as n approaches infinity, an(...TRUNCATED) | "A sequence $\\{a_n\\}$ is defined such that $a_i = i$ for $i = 1, 2, 3, \\ldots, 2020$ and for $i >(...TRUNCATED) | 1347 | dapo | [{"content":"A sequence $\\{a_n\\}$ is defined such that $a_i = i$ for $i = 1, 2, 3, \\ldots, 2020$ (...TRUNCATED) | [{"content":"A sequence $\\{a_n\\}$ is defined such that $a_i = i$ for $i = 1, 2, 3, \\ldots, 2020$ (...TRUNCATED) |
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