MathDB
Balls and buckets

Source: BdMO 2023 Secondary National P4

February 12, 2023
combinatorics

Problem Statement

20232023 balls are divided into several buckets such that no bucket contains more than 9999 balls. We can remove balls from any bucket or remove an entire bucket, as many times as we want. Prove that we can remove them in such a way that each of the remaining buckets will have an equal number of balls and the total number of remaining balls will be at least 100100.