Most two person games are finite; for example, chess has rules that don't allow an infinite game, and tic-tac-toe obviously ends after at most 9 plays.

Let's define a new two person game: the "Metagame". The first player first picks any two person finite game (e.g., chess or tic-tac-toe). Then, the second player sets up the board (or whatever is needed) and makes the first move in that game, and the Metagame winner will be whoever wins that game.

The question: is Metagame finite or infinite?

If we define a finite game as any game which can be shown to have an end and an infinite game as any game which cannot be shown to have an end, then the "Metagame", as it was described in the puzzle, is infinite because there are no rules in place which require it to have an end.

Posted by Erik O. on 2005-04-14 15:17:05