question stringlengths 15 7.47k | generations listlengths 2 2 | entropy listlengths 2 2 |
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P.I. Find the largest natural number from which it is impossible to obtain a number divisible by 11 by erasing digits.
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"Alright, so I have this problem where I need to find the largest natural number such that it's impossible to obtain a number divisible by 11 by erasing digits. Hmm, okay. Let me try to break this down.\n\nFirst, I need to understand what it means for a number to be divisible by 11. I remember that a number is divi... | [
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"G1.3 A six-digit number 1234xy is divisible by both 8 and 9 . Given that $x+y=c$, find the value of(...TRUNCATED) | ["First, I'll analyze the number 1234xy, which is a six-digit number where x and y are unknown digit(...TRUNCATED) | [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) |
"8. Find $\\sqrt{\\frac{x}{63}-32} \\times \\sqrt{\\frac{y}{63}-32}$, given that $\\frac{1}{x}+\\fra(...TRUNCATED) | ["Okay, so I need to find the value of √(x/63 - 32) multiplied by √(y/63 - 32), given that 1/x +(...TRUNCATED) | [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) |
"10. It is required to fence a rectangular area adjacent to a wall. The fence should have a length o(...TRUNCATED) | ["First, I need to visualize the problem. There's a rectangular area adjacent to a wall, so one side(...TRUNCATED) | [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) |
"4. Median. In a set of 100 numbers. If one number is removed, the median of the remaining numbers i(...TRUNCATED) | ["Okay, so I need to figure out the median of a set of 100 numbers. The problem says that if one num(...TRUNCATED) | [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) |
"31. Given that $\\alpha$ is an acute angle satisfying\n$$\n\\sqrt{369-360 \\cos \\alpha}+\\sqrt{544(...TRUNCATED) | ["Alright, so I have this problem here where I need to find the value of 40 tan α, given that α is(...TRUNCATED) | [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) |
"## Task 7 - V00607 = V00503\n\nTo an imagined number, 16 is added, then multiplied by 7, followed b(...TRUNCATED) | ["First, I'll represent the imagined number as \\( x \\).\n\nWhen 16 is added to \\( x \\), the expr(...TRUNCATED) | [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) |
"IMO 1974 Problem A1 Three players play the following game. There are three cards each with a differ(...TRUNCATED) | ["Alright, so I’ve got this problem from IMO 1974, Problem A1. It involves three players who each (...TRUNCATED) | [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) |
9.1. Solve the equation:
$$
\left(x^{2}-20\right)^{2}+\left(x^{2}-19\right)^{2}=2019
$$ | ["Okay, so I've got this equation to solve: \\((x^2 - 20)^2 + (x^2 - 19)^2 = 2019\\). Hmm, let me tr(...TRUNCATED) | [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) |
"7. Encode the letters $a \\sim z$ as $(\\mathbf{a}=1, \\mathbf{b}=2, \\ldots, \\mathbf{z}=26)$, so (...TRUNCATED) | ["Okay, so I need to figure out the smallest three-digit \"zhonghuan number.\" From the problem stat(...TRUNCATED) | [[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.(...TRUNCATED) |
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