# Tic-tac-toe on Mobius strip has something counter-intuitive. Please help!

*From*: Bhushit Joshipura <joshipura@xxxxxxxxx>*Date*: Tue, 19 Aug 2008 02:28:33 -0700 (PDT)

Hello,

I am not a mathematician.

I am trying to define tic-tac-toe on Mobius strip. (http://

surfaces.sourceforge.net)

I came across a problem while defining the diagonals. I need help.

Here is how I defined a Mobius strip board: (hopefully the picture

looks good)

+----------------------------+

| |

+>(0,2)|(1,2)|(2,2) >---|+

(0,1)|(1,1)|(2,1) | |

+>(0,0)|(1,0)|(2,0) >--+ |

| |

+------------------------------+

.... and (0,1) and (2,1) "roll around" to each other.

Horizontal "three in a line" conditions would mean any three

consecutive coordinates from below:

(0,0)-(1,0)-(2,0)-(0,2) notice it twisted - (1,2)-(2,2)-(0,0) twist

and back - and so on

and (0,1)-(1,1)-(2,1)

If I define "right and up" diagonal, one of them could be: (1,0)-(2,1)-

(0,2)

But if I define "up and right" diagonal, one of them could be: (1,0)-

(2,1)-(0,0)

That means the operations "up" and "right" are not symmetric to each

other(?) anymore. I coming across two diagonals originating with two

common points.

Which one of the above definition for diagonal is correct?

Confused,

-Bhushit

.

**Follow-Ups**:**Re: Tic-tac-toe on Mobius strip has something counter-intuitive. Please help!***From:*Puppet_Sock

**Re: Tic-tac-toe on Mobius strip has something counter-intuitive. Please help!***From:*Bhushit Joshipura

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