Tictacktoe: Do You Have a Problem with This?

After ten months of responding to teacher’s questions, it’s time for two months of freedom. Summer is an opportunity to spend unlimited time answering your OWN questions.

In December, MC2 runs QED: Chicago’s Youth Math Symposium, a celebration of math question posing. For many students, the biggest challenge is getting started. School doesn’t always do a good job of giving students practice coming up with their own questions (teachers, I recommend Make One Change: Teach Students to Ask Their Own Questions).

Let’s do an exercise (with thanks to Martin Gardner’s Wheels, Life and Other Mathematical Amusements) where we start with something familiar and routine, and use that as a spark to generate mathematical questions for exploration. Let’s talk about ticktacktoe.

Ticktacktoe is familiar to everyone, and it’s easy to analyze. When both players play strategically, the game ends in a tie. You couldn’t do a QED project about ticktacktoe.

But you COULD do a project IF YOU CHANGED THE RULES:

  • What if you only played with x’s? (Whoever gets 3 x’s in a row wins).
  • What if you played on a 4×4 grid, but still needed to get 3 in a row? Or now needed to get 4 in a row? Or needed to make an L-shape?
  • What if you LOSE if you get 3 in a row? (This is called “toetacktick”.)
  • What if either player is allowed to play an x or an o? (This is called “wild ticktacktoe”.) Or, under those rules, you lose if you get three in a row (“wild toetacktick”)?
  • What if one player wins if there are no 3 in a rows at the end of the game, and the other wins if there are?
  • What if you played in a 3x3x3 cube? What if you played within such a cube, but no one was allowed to mark the central cube?

QED will be held on December 2nd. Check out our QED page for examples of past year’s projects and other resources. And think of some math problem or some mathematical game and extend it. Or make it simpler. Or four dimensional.

I’ll end with three quotes from our end of the year Math Circles of Chicago surveys:

  • I learn new things about math every time I come to math circles
  • I also like that it’s not just memorizing facts
  • I like changing the rules to a problem

Enjoy your summer–Ask your own questions!



TicktackToe image by nneonneo (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons