Question 10
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.
- 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.