# Tic, Tac, and Toe

Who moved first?

Welcome to this week’s Math Munch!  We’re taking a look at several Tic-Toe-Toe related items.

To the right you can see a little Tic-Tac-Toe puzzle I found here.  If the board below shows a real game of Tic-Tac-Toe, then which player moved first?  Think. Think!!

Now let’s talk about the basic game itself.  Tic-Tac-Toe is fun for new players, but at some point, we can all get really good at it.  How good? Well, there’s a strategy, which if you follow without making mistakes, you will never lose!  Amazing, right?  So what’s the strategy?  The picture below shows half of it.  Here’s how to play if you’re X and get to move first. (instructions below.)

### Strategy for X (1st player)

Randall Munroe

“Your move is given by the position of the largest red symbol on the grid. When your opponent picks a move, zoom in on the region of the grid where they went. Repeat.”  Now find a friend and try it out!

This image comes from xkcd, a sometimes mathematical webcomic by Randall Munroe.  (We featured his Sierpinski Heart last Valentine’s Day.) Randall talks about his Tic-Tac-Toe strategy guide and several other mathy comics in this interview with Math Horizons Magazine, which is certainly worth a read.

The undefeated Tic-Tac-Toe player, a Tinkertoy computer

The existence of strategies like the one above mean that a computer can be perfect at Tic-Tac-Toe.  In fact, in Boston’s Museum of Science, there is a computer made entirely of Tinkertoy (a construction system for kids like LEGO) that has never lost a game of tic-tac-toe. It was designed and built by a team of college students in the 1980′s. For more on this impeccable toy computer, read this article by computer scientist A.K. Dewdney.

Finally, I stumbled across a wonderful Tic-Tac-Toe variation game, sometimes called “Ultimate Tic-Tac-Toe,” but here called TicTacToe10.  Here’s a video explaining, but basically in this version, you have a Tic-Tac-Toe board of Tic-Tac-Toe boards.  That is, you have the 9 little boards, and the one big board that they make together. On your turn you make a move on one of the small boards.  Where you decide to go decides which of the nine small boards the next player gets to play in.  If you win a small board, it counts as your shape on the big board.  Crazy, right!?!?  If that’s confusing you’ll have to watch the video tutorial or just start playing.

Here’s a link to a 2-player version of Ultimate Tic-Tac-Toe so that you can play with a friend, although you could also do it on paper, you just have to remember where the last move was.

I hope you found something tasty this week.  Bon appetit!