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Coloring of polygon

Source: Romania TST 1995 Test 1 P3

February 21, 2014
geometrygeometric transformationrotationcombinatorics proposedcombinatorics

Problem Statement

Let n≥6n \geq 6 and 3≤p<n−p3 \leq p < n - p be two integers. The vertices of a regular nn-gon are colored so that pp vertices are red and the others are black. Prove that there exist two congruent polygons with at least [p/2]+1[p/2] + 1 vertices, one with all the vertices red and the other with all the vertices black.
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