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(041) O4

Part of 1983 Tournament Of Towns

Problems(1)

TOT 041 1983 Spring S-O4 K boys around a circle with sweets

Source:

8/18/2019
There are KK boys placed around a circle. Each of them has an even number of sweets. At a command each boy gives half of his sweets to the boy on his right. If, after that, any boy has an odd number of sweets, someone outside the circle gives him one more sweet to make the number even. This procedure can be repeated indefinitely. Prove that there will be a time at which all boys will have the same number of sweets.
(A Andjans, Riga)
combinatoricsEven