MOG 2014 3

3

We can replace all the '-' with '-1' and the '+' with '1' and rather than deleting and replacing signs we can just multiply them together. This still obeys all the rules of the game.

Multiplication is commutative meaning that the order in which you multiply numbers has no effect on the final answer.

\therefore after multiplying all the \pm1 we will be left with 1^{2014}\times(-1)^{2015}=-1 And so we can conclude that the final sign left on the board is a '-'

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