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 It is infinite if it isn't? (Posted on 2005-04-12)
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?

 Submitted by Old Original Oskar! Rating: 2.9286 (14 votes) Solution: (Hide) 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.

Comments: ( You must be logged in to post comments.)
 Subject Author Date No Subject Dej Mar 2013-03-11 12:58:10 Solution Math Man 2013-03-11 09:54:50 No Subject daniel 2006-11-13 10:41:04 solution Rachael 2006-05-23 02:12:00 re: the answer is yes in that any game will be either finite of infinite and no in that metagame itself can not be classified as either Hugo 2006-04-18 12:40:17 the answer is yes in that any game will be either finite of infinite and no in that metagame itself can not be classified as either matthew walker 2006-04-18 11:11:10 Solution Eric 2006-01-09 03:38:21 wtf Diana 2006-01-08 12:45:57 Comment Chris, Phd 2005-11-27 22:29:16 Sounds like a fun game hookedonphonics 2005-10-09 20:05:21 re: hmmm.. alex 2005-09-20 17:14:48 hmmm.. jeffrey 2005-08-13 04:34:36 But... Paddy 2005-07-06 12:50:07 haha ^^ Amon 2005-04-30 01:21:51 re: Solution Ken Haley 2005-04-29 04:09:36 No Subject gary wallravin 2005-04-17 21:43:48 No Subject Stephen Ticsay 2005-04-15 01:43:31 No Subject Bryan 2005-04-14 19:36:00 Solution needs definitions... Erik O. 2005-04-14 15:17:05 A Decent Reference Richard 2005-04-14 01:08:33 re: No paradox Jer 2005-04-13 17:12:08 re: No paradox Bryan 2005-04-13 17:09:38 No paradox David Shin 2005-04-13 15:56:49 Another soluition Erik O. 2005-04-13 15:24:40 Solution Avin 2005-04-13 13:37:34 I bet player 1 armando 2005-04-13 07:57:17 infinite variety Larry 2005-04-13 05:28:18 Definitions are tricky! Richard 2005-04-12 23:28:06 Further thoughts Federico Kereki 2005-04-12 22:36:22 No Subject Hugo 2005-04-12 22:14:16 re(2): Possible paradox Gamer 2005-04-12 21:17:16 re: Possible paradox David Shin 2005-04-12 21:06:55 re: Possible paradox Charlie 2005-04-12 20:51:18 I'm not getting this. Charlie 2005-04-12 20:49:38 Possible paradox Federico Kereki 2005-04-12 20:47:31

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