# Math Meets Art, Quarto, and Snow!

Welcome to this week’s Math Munch!

… And, if you happen to write the date in the European way (day/month/year), happy Noughts and Crosses Day! (That’s British English for Tic-Tac-Toe Day.) In Europe, today’s date is 11/12/13– and it’s the last time that the date will be three consecutive numbers in this century! We in America are lucky. Our last Noughts and Crosses Day was November 12, 2013 (11/12/13), and we get another one next year on December 13 (12/13/14). To learn more about Noughts and Crosses Day and find out about an interesting contest, check out this site. And, to our European readers, happy Noughts and Crosses Day!

Speaking of Noughts and Crosses (or Tic-Tac-Toe), I have a new favorite game– Quarto! It’s a mix of Tic-Tac-Toe and another favorite game of mine, SET, and it was introduced to me by a friend of mine. It’s quite tricky– you’ll need the full power of your brain to tackle it. Luckily, there are levels, since it can take a while to develop a strategy. Give it a try, and let us know if you like it!

Looking to learn about some new mathematical artists? Check out this article, “When Math Meets Art,” from the online magazine Dark Rye. It profiles seven mathematical artists– some of whom we’ve written about (such as Erik and Martin Demaine, of origami fame, and Henry Segerman), and some of whom I’ve never heard of. The work of string art shown above is by artist Adam Brucker, who specializes in making “unexpected” curves from straight line segments.

Another of my favorites from this article is the work of Robert Bosch. One of his specialities is making mosaics of faces out of tiles, such as dominoes. The article features his portrait of the mathematician Father Sebastien Truchet made out of the tiles he invented, the Truchet tiles. Clever, right? The mosaic to the left is of the great mathematician Gauss, made out of dominoes. Check out Robert’s website to see more of his awesome art.

Finally, it snowed in New York City yesterday. I love when it snows for the first time in winter… and that got me wanting to make some paper snowflakes to celebrate! Here’s a video by Vi Hart that will teach you to make some of the most beautiful paper snowflakes.

Hang them on your windows, on the walls, or from the ceiling, and have a very happy wintery day! Bon appetit!

# 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!