Another Cousin of Nim
[And of course the inevitable extension - what is the best strategy for
starting with N checkers on the table? What are the losing positions? -KD]
Two players have twenty checkers on the table. Each has his turn and
removes one, two or three checkers but is forbidden to take the same
number of checkers previously removed by his opponent. The player who takes
the last checker or prevents his opponent from playing is the winner.
Your opponent begins by removing 3 checkers. Who will be the winner?
Fifty checkers on the table and you begin. What is your best strategy ?
Source: Le Monde 22/09/98 - Elisabeth Busser and Gilles Cohen.
Submitted by Philippe Fondanaiche.
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