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4

Part of 2010 Philippine MO

Problems(1)

2010 Philippines MO P4

Source:

11/16/2015
There are 20082008 blue, 20092009 red and 20102010 yellow chips on a table. At each step, one chooses two chips of different colors, and recolor both of them using the third color. Can all the chips be of the same color after some steps? Prove your answer.
combinatorics2010PMO