olymmath

IMO 1992 Problem 3

  • Day 1

Consider 99 points in space, no four of which are coplanar. Each pair of points is joined by an edge (that is, a line segment) and each edge is either colored blue or red or left uncolored. Find the smallest value of n n\, such that whenever exactly n n\, edges are colored, the set of colored edges necessarily contains a triangle all of whose edges have the same color.

Dataset text AI-MO AoPS. Quoted with source.

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