"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."

Why?

(Tic Tac Toe = Noughts and Crosses)

One thing that I fail to see is how this is an 8 way symmetry rather than a 4 way symmetry.

Given the board:

1 2 3
4 5 6
7 8 9
For example the sequence "1-5-9" has the equivalents
3-5-7
9-5-2 and
7-5-3
This seems to hold true for any sequence of turns.

Where do you get twice as many equivalents from?

Posted by levik on 2002-09-29 05:56:14