17 Dec
2003
17 Dec
'03
11:17 p.m.
From: Eli Brandt <ebrandt@jarthur.cs.hmc.edu> There are a finite number of legal positions in chess. If any shows up a third time, the game is over. Thus we have a bound on the length of a legal chess game. Hence the number of games is finite, and we don't have to quibble about whether it's countably or uncountably infinite.
Since this is the second time this has shown up here, I must clarify it by saying that it is only a draw when the pieces are in the same position with the same person to move for the third time. It is possible to repeat the position but change the opposition, which constitutes a different situation. tw