olymmath

HMMT November 2016 U24

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Consider an infinite grid of equilateral triangles. Each edge (that is, each side of a small triangle) is colored one of NN colors. The coloring is done in such a way that any path between any two nonadjecent vertices consists of edges with at least two different colors. What is the smallest possible value of NN ?

Dataset text NuminaMath olympiads. Quoted with source.

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