Vietnam NMO 1990_6
Source:
October 26, 2008
combinatorics unsolvedcombinatorics
Problem Statement
The children sitting around a circle are playing the game as follows. At first the teacher gives each child an even number of candies (bigger than , may be equal, maybe different). A certain child gives half of his candies to his neighbor on the right. Then the child who has just received candies does the same if he has an even number of candies, otherwise he gets one candy from the teacher and then does the job; and so on. Prove that after several steps there will be a child who will be able, giving the teacher half of his candies, to make the numbers of candies of all the children equal.