IMO 2020 Shortlist C2
In a regular 100-gon, 41 vertices are colored black and the remaining 59 vertices are colored white. Prove that there ex...
Category: Combinatorics
Problem
In a regular 100-gon, 41 vertices are colored black and the remaining 59 vertices are colored white. Prove that there exist 24 convex quadrilaterals Q1, ..., Q24 whose corners are vertices of the 100-gon, so that • the quadrilaterals Q1, ..., Q24 are pairwise disjoint, and • every quadrilateral Qi has three corners of one color and one corner of the other color. (Austria)