This game starts with some noughts and some crosses. You and your opponent take turns removing two shapes, and adding a new one according to this rule: if the shapes are identical, add a nought; otherwise, add a cross. When only one shape remains, you win if it's a nought, and lose if it's a cross.
Is there a winning strategy for any of the players? How should you play?
No matter what strategy is used, the "cross" player will win if there is an odd number of crosses at the beginning, and lose otherwise.
After each possible move, the parity of the number of crosses won't change (it can stay the same or go down by 2) so if there was an odd number of them, it will eventually go down to 1, while if there was an even number, it will go down to 0.
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