There are N egg baskets and the number of eggs in each basket is a known quantity. Two players take turns to remove these eggs from the baskets. On each turn, a player must remove at least one egg, and may remove any number of eggs provided they all belong to the same basket. The player picking the last egg(s) wins the game. If you are allowed to decide who is going to start first, what mathematical function would you use to decide so that you end up on the winning side?
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