$n+1$ containers arranged in a circle
Source: 32-th Vietnamese Mathematical Olympiad 1994
February 24, 2007
invariantcombinatorics unsolvedcombinatorics
Problem Statement
There are containers arranged in a circle. One container has stones, the others are empty. A move is to choose two containers and , take a stone from and put it in one of the containers adjacent to , and to take a stone from and put it in one of the containers adjacent to . We can take . For which is it possible by series of moves to end up with one stone in each container except that which originally held stones.