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?
There is no strategy in this game, as the parity of the number of crosses never changes. You win whenever the number of crosses is even.
Solution
