MathDB

A rich knight has a chest and a lot of coins, so every day he puts into the chest some quantity of coins - among the numbers

1, 2, \ldots, 100

. If there exist two days on which he added equal quantities of coins (say,

k

coins) and he has added in total at most

100k

coins on the days between these two days, he stops putting coins into the chest. Prove that this will necessarily happen eventually.

Problem Statement