Problem

Source:

Tags: combinatorics



A group of children is sitting around a round table . At first, each child has an even number of candies. Each turn, each child gives half of his candies to the child sitting at his right. If, after a turn, a child has an odd number of candies, the teacher gives him\her an extra candy. Show that after a finite number of rounds all children will have the same number of candies.