Empty a pile of stones
Source: Own. IMO 2021 Malaysian Training Camp 1
December 31, 2020
combinatorics
Problem Statement
There are piles of stones with stones in each pile. Amber can choose any two non-empty piles of stones, and Barbara can take one stone from one of the two chosen piles and puts it into the other pile. Amber wins if she can eventually make an empty pile. What is the least such that Amber can always win?