MathDB

2

Part of 2022 Taiwan Mathematics Olympiad

Problems(1)

2022 black/white balls and 1011 black/white boxes

Source: 2022 Taiwan Mathematics Olympiad

10/28/2022
There are 20222022 black balls numbered 11 to 20222022 and 20222022 white balls numbered 11 to 20222022 as well. There are also 10111011 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 20222022 balls we chose have all the numbers from 11 to 20222022.
combinatorics