2020 IMO Shortlist C2

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. (Austria)

在正则 100 边形中，41 个顶点为黑色，其余 59 个顶点为白色。证明存在 24 个凸四边形 $Q_{1}, \ldots, Q_{24}$，其角点是 100 边形的顶点，因此 - 四边形 $Q_{1}, \ldots, Q_{24}$ 成对不相交，并且 - 每个四边形 $Q_{i}$ 都有一个颜色的三个角和另一个颜色的一个角。 (奥地利)