MathDB
moving stones

Source: Russia 1994

October 6, 2008
combinatorics unsolvedcombinatorics

Problem Statement

On the vertices of a convex n n-gon are put m m stones, m>n m > n. In each move we can choose two stones standing at the same vertex and move them to the two distinct adjacent vertices. After N N moves the number of stones at each vertex was the same as at the beginning. Prove that N N is divisible by n n.