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2008 PUMaC Individual Finals B2

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October 4, 2019
combinatorics

Problem Statement

Let PP be a convex polygon, and let n≥3n \ge 3 be a positive integer. On each side of PP, erect a regular nn-gon that shares that side of PP, and is outside PP. If none of the interiors of these regular n-gons overlap, we call P nn-good. (a) Find the largest value of nn such that every convex polygon is nn-good. (b) Find the smallest value of nn such that no convex polygon is nn-good.
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