MathDB

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

Q_{1}, \ldots, Q_{24}

whose corners are vertices of the 100-gon, so that
[*] the quadrilaterals

Q_{1}, \ldots, Q_{24}

are pairwise disjoint, and [*] every quadrilateral

Q_{i}

has three corners of one color and one corner of the other color.

Problem Statement