Random Problem
Contents
Easy Problem
The sumcan be expressed as , where and are positive integers. What is ?
Solution
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Medium Problem
Show that there exist no finite decimals such that when its digits are rearranged to a different decimal , .
Solution
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Hardish Problem
A cylinder is inscribed in a circular cone with base radius of and height of . What is the maximum possible volume of this cylinder is ?
Solution
???
Hard Problem
A regular -gon is inscribed in a circle with radius . Let be the set of distances (not necessarily distinct) from the center of the circle to each side of the -gon, and be the set of distances (not necessarily distinct) from the center of the circle to each diagonal of the -gon. Let be the union of and . What is the sum of the squares of all of the elements in ?
Solution
?? ?