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Tic Tac Toe (Posted on 2002-09-27) Difficulty: 3 of 5
A computer science teacher poses his students a problem.

"I want you write a computer program that plays tic-tac-toe legally and runs through ALL the possible combinations of the game, and finds out the total."

The students settle down to work..

An hour later, a student gets up and proclaims "I've got it! The number of possible combinations in a game is 344,242."

At which point another student quickly replies, "I haven't finished yet, but I'm sure Fred made a mistake in his program."


(Tic Tac Toe = Noughts and Crosses)

See The Solution Submitted by Cheradenine    
Rating: 3.5455 (11 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 4 of 12 |
If the problem refers to in-play configurations, at any point of play a square may have one of three values: X, O, blank. Having 9 squares, the number of board configurations is then 3^9 = 19683 possible arrangements.

The actual number is significantly less than that, since the problem requires the configurations to be valid; eg. a configuration with X's in all 9 squares is invalid. So the answer must be much less than 344,242.

If the problem refers to end-game configurations, then there are fewer than 2^9 = 512 configurations. And with respect to friedlinguini's comment, this solution doesn't even address symmetry, which further reduces the number of unique valid combinations.
  Posted by Jacob Fugal on 2002-09-28 08:21:43
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