Coloring the edges between 67 vertices
Source: Spanish Mathematical Olympiad, National Stage, 2011
August 9, 2011
combinatorics unsolvedcombinatorics
Problem Statement
Each pair of vertices of a regular -gon is joined by a line segment. Suppose of these segments are selected, and each of them is painted one of ten available colors. Find the minimum possible value of for which, regardless of which segments were selected and how they were painted, there will always be a vertex of the polygon that belongs to seven segments of the same color.