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coloring sides of convex regular polygon into 3 colors

Source: Spanish Mathematical Olympiad 1974 P8

December 23, 2022

Coloringregular polygoncombinatoricscombinatorial geometry

Problem Statement

The sides of a convex regular polygon of

L + M + N

sides are to be given draw in three colors:

L

of them with a red stroke,

M

with a yellow stroke, and

N

with a blue. Express, through inequalities, the necessary and sufficient conditions so that there is a solution (several, in general) to the problem of doing it without leaving two adjacent sides drawn with the same color.

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