n children are sitting around a circular table. Each child starts out with an integer number of candies. The following step is repeated:
Every child who has an odd number of candies is given another piece of candy by the teacher. Each child now has an even number. Now every child passes half of his/her candy to the child on his/her left.
Prove that eventually all the children will have the same amount of candy.
Source: Puzzle Toad, CMU
Update (30/12/09): Solution: PDF Document from CMU Site