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It is infinite if it isn't? (Posted on 2005-04-12) Difficulty: 3 of 5
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
SolutionNo SubjectDej Mar2013-03-11 12:58:10
SolutionSolutionMath Man2013-03-11 09:54:50
SolutionNo Subjectdaniel2006-11-13 10:41:04
solutionRachael2006-05-23 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 eitherHugo2006-04-18 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 eithermatthew walker2006-04-18 11:11:10
SolutionSolutionEric2006-01-09 03:38:21
wtfDiana2006-01-08 12:45:57
CommentChris, Phd2005-11-27 22:29:16
Sounds like a fun gamehookedonphonics2005-10-09 20:05:21
re: hmmm..alex2005-09-20 17:14:48
hmmm..jeffrey2005-08-13 04:34:36
But...Paddy2005-07-06 12:50:07
Some Thoughtshaha ^^Amon2005-04-30 01:21:51
re: SolutionKen Haley2005-04-29 04:09:36
No Subjectgary wallravin2005-04-17 21:43:48
Some ThoughtsNo SubjectStephen Ticsay2005-04-15 01:43:31
SolutionNo SubjectBryan2005-04-14 19:36:00
SolutionSolution needs definitions...Erik O.2005-04-14 15:17:05
A Decent ReferenceRichard2005-04-14 01:08:33
re: No paradoxJer2005-04-13 17:12:08
re: No paradoxBryan2005-04-13 17:09:38
No paradoxDavid Shin2005-04-13 15:56:49
Some ThoughtsAnother soluitionErik O.2005-04-13 15:24:40
SolutionSolutionAvin2005-04-13 13:37:34
I bet player 1armando2005-04-13 07:57:17
infinite varietyLarry2005-04-13 05:28:18
Definitions are tricky!Richard2005-04-12 23:28:06
Some ThoughtsFurther thoughtsFederico Kereki2005-04-12 22:36:22
No SubjectHugo2005-04-12 22:14:16
re(2): Possible paradoxGamer2005-04-12 21:17:16
re: Possible paradoxDavid Shin2005-04-12 21:06:55
re: Possible paradoxCharlie2005-04-12 20:51:18
QuestionI'm not getting this.Charlie2005-04-12 20:49:38
Some ThoughtsPossible paradoxFederico Kereki2005-04-12 20:47:31
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