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Consider the following game.
Initially, there are two tokens in a row; the left one is blue and the right one is red. You can change the configuration by performing a number of moves. In each move, you can either insert two successive tokens of the same color (red or blue) or remove two successive tokens of the same color.
Is it possible to produce a configuration where there are exactly two tokens, the left token being red, and the right one being blue?