2022 black/white balls and 1011 black/white boxes
Source: 2022 Taiwan Mathematics Olympiad
October 28, 2022
combinatorics
Problem Statement
There are black balls numbered to and white balls numbered to as well. There are also black boxes and white boxes each. In each box we put two balls that are the same color as the the box. Prove that no matter how the balls are distributed, we can always pick one ball from each box such that the balls we chose have all the numbers from to .