Another Cousin of Nim

  1. 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?
  2. Fifty checkers on the table and you begin. What is your best strategy ?
[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]

Source: Le Monde 22/09/98 - Elisabeth Busser and Gilles Cohen. Submitted by Philippe Fondanaiche.

Solution
Mail to Ken