boxes of stones
Source: All-Russian olympiad 1995, Grade 9, Second Day, Problem 7
October 21, 2013
functioninvariantcombinatorics proposedcombinatorics
Problem Statement
There are three boxes of stones. Sisyphus moves stones one by one between the boxes. Whenever he moves a stone, Zeus gives him the number of coins that is equal to the difference between the number of stones in the box the stone was put in, and that in the box the stone was taken from (the moved stone does not count). If this difference is negative, then Sisyphus returns the corresponding amount to Zeus (if Sisyphus cannot pay, generous Zeus allows him to make the move and pay later).
After some time all the stones lie in their initial boxes. What is the greatest possible earning of Sisyphus at that moment?
I. Izmest’ev