Datasets:

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mnoukhov

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MATH_3000_final_filter

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[{"content":"A 8-gon is colored so that in clockwise order, the vertices are colored as follows: ver(...TRUNCATED)

[".\n\n\nOkay, so I need to solve this problem about an 8-gon with specific colored vertices and fin(...TRUNCATED)

[{"content":"Let $S$ be the set \\{1,2, \\ldots, 2012\\}. A perfectutation is a bijective function $(...TRUNCATED)

[" has a very easy solution, I would like to use this as an example problem to show off my skills, b(...TRUNCATED)

[{"content":"Problem 7.1. (15 points) Find the smallest ten-digit natural number, all digits of whic(...TRUNCATED)

[" \\item Question 7.2. Prove that there are no natural numbers $n$ such that $n+11, n+17, n+113, n+(...TRUNCATED)

[{"content":"Determine the smallest positive integer $m$ with the property that $m^3-3m^2+2m$ is div(...TRUNCATED)

[" and the normal formatting you have been using for each other answer.\nOkay, so I need to find the(...TRUNCATED)

[{"content":"Four small spheres each with radius $6$ are each internally tangent to a large sphere w(...TRUNCATED)

[" and only your answer the rest of your solution will go on other lines. \n\nOkay, let's see. I hav(...TRUNCATED)

[{"content":"A function $f$ is defined for all real numbers and satisfies $f(3+x)=f(3-x)$ and $f(8+x(...TRUNCATED)

[" (Do not put the \"$Answer:\" on its own line).\nThe problem asks for the least number of roots of(...TRUNCATED)

[{"content":"A farmer's rectangular field is partitioned into a $2$ by $2$ grid of $4$ rectangular s(...TRUNCATED)

[" but before your quote. \n\n[asy]\ndraw((0,0)--(6,0)--(6,2)--(0,2)--cycle);\ndraw((3,0)--(3,2));\n(...TRUNCATED)

[{"content":"Suppose that we are given 40 points equally spaced around the perimeter of a square, so(...TRUNCATED)

[" if you find that the statement is false, add your counterexample to the end.\n\nPlease only answe(...TRUNCATED)

[{"content":"In the convex quadrilateral $A B C D$, the midpoints of sides $B C$ and $C D$ are $E$ a(...TRUNCATED)

[" In the convex quadrilateral $A B C D$, the midpoints of sides $B C$ and $C D$ are $E$ and $F$ res(...TRUNCATED)

[{"content":"Calculate the largest eigenvalue by absolute value for the matrix:\n[[4, -4, -6],\n [-4(...TRUNCATED)

[" sniperRifleModel:\n[[true, false, true, false],\n[false, false, true, true],\n[true, false, true,(...TRUNCATED)