Ten boxes in a circle
Source: Canadian Repêchage 2009: Problem 10
April 25, 2014
functioncombinatorics proposedcombinatorics
Problem Statement
Ten boxes are arranged in a circle. Each box initially contains a positive number of golf balls. A move consists of taking all of the golf balls from one of the boxes and placing them into the boxes that follow it in a counterclockwise direction, putting one ball into each box. Prove that if the next move always starts with the box where the last ball of the previous move was placed, then after some number of moves, we get back to the initial distribution of golf balls in the boxes.