Andrew and Betty play a game in which they lay out a row of three coins, heads up. They take turns, begining with Andrew, turning over one of the coins at a time. They must not produce a pattern of heads and tails which has already occurred earlier in the game. The first person who cannot make a move is the loser.

1. If they each play as well as possible, who is the winner?

2. If the game were played with four coins instead of three, who would be the winner?

3. If the game is played with three coins but the player who cannot make a move is declared the winner, who wins now?

...if there is a simple winning strategy for the second version of the puzzle (player who does not have a valid move anymore wins) and n number of coins? The cases n=1,2,3 are easily verified as being in favor of player 2, but I suppose there must be a simple strategy for general n, along the lines of the one I gave in my earlier post. Ideas?

Posted by JLo on 2006-09-17 16:45:41