VMO 1990 Problem 6

Some children are sitting in a circle. Each has an even number of tokens (possibly zero). A child gives half his tokens to the child on his right. Then the child on his right does the same and so on. If a child about to give tokens has an odd number, then the teacher gives him an extra token. Show that after several steps, all the children will have the same number of tokens, except one who has twice the number.