Pisa Nim
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In this two-player game, players take turns removing a number of pebbles from a pile. The first player can remove any number, but must leave some pebbles. Thereafter, each player can remove up to two times the number of pebbles removed by the previous player. For example, if Player 1 removes 2 pebbles on the first move, Player 2 can remove 1, 2, 3, or 4 pebbles. Then if Player 2 decides to remove 3, Player 1 can remove up to 6 pebbles. However, if Player 2 removes only one pebble, Player one can only remove 1 or 2 on the next move.