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?
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Submitted by Old Original Oskar!
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Rating: 3.0000 (15 votes)
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Solution:
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If you can only pick finite games, it would seem the game is finite. But then, the first player could pick "Metagame" as his game... and then the second, having to make the first move in this game, could also pick "Metagame"... and we'd have an infinite loop. So, if the game is finite, it can be picked, and that makes it infinite? However, if it really is infinite, then the first player couldn't pick it... thus making it finite. A paradox!
It could be argued that this game isn't well defined (since you cannot tell whether it is finite or infinite) and thus couldn't be picked by the second player... but this instantly makes the game finite, well defined, and we are back where we began, since the 2nd player could pick it. |
