# 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!

### 12 responses »

1. I think I have a similar strategy to win tic tac toe I think my strategy is similar to the one that you posted the one who moved first was the X and if you will like to win bottom right corner or right upper corner.

2. Here’s a post about a game using the “ultimate tic tac toe” board, with contraints involving the multiples of 1-9. http://artofmathstudio.wordpress.com/2013/08/30/multiplication-tic-tac-toe/
There are some parallels, and some added elements, while the essence of tic tac toe remains. I use it with kids who are learning their multiplication facts, but it’s fun for me for the same reason “ultimate tic tac toe” is interesting, the winning strategy is not immediately obvious.

3. In Tic,Tac,andToe you had to find out who moved first. I believed that X moved first because if you go in the middle first you have a lot of different ways to get three in a row. At the last picture you see,X has two ways to get three in a row. I always do that when i play Tic,Tac,Toe.

4. I never thought tic tac toe could be such a complex game with the outcomes. One question, how was a computer created from tinkertoy and how was it “programmed” to be unbeatable in tic tac toe?

5. tie tac toe is a very complexed game but i think X is going first because id go first in the middle and how the compeuter is unbeateable in a game of tic tac toe.

• Hey Anthony the strategy guide here suggests going in the corner first. It is also undefeatable.