Noughts and Crosses

This is the game of "Noughts and Crosses" or "Tic Tac Toe".

  First Type Wins Record

In how many different ways can the first "X" and "O" be placed on the grid?

A Mathematics Lesson Starter Of The Day

Topics: Starter | Combinations | Puzzles

  • Transum,
  • Another game which is isomorphic (same strategies) to noughts and crosses is the game of Fifteen. The numbers 1 to 9 are written on cards. Players take it in turns to take a card. The first person who can make a total of 15 with the cards they have is the winner.
    If you arrange the nine numbered cards to form a magic square you will see the similarities with noughts and crosses.
    We have invented a game called Trilett. Play it a few times and see if you can work out why it is isomorphic to noughts and crosses.

    Here are links to the related interactive activities:

    Noughts and Crosses | Fifteen | Trilett
  • Miss Mears, Stockport
  • A nice starter - we then extended the idea to the general case of an nxn grid and used some algebra as well.
  • Mark, New Zealand
  • Surely there are only three ways that the first cross can be placed: centre, side or corner. In any meaningful analysis of the game the sides are all identical and should not be distinguished.
  • Mrs. S. Farragonda, Fernan Elementary, CDA, ID
  • This game is very mental, and fun for both teachers and students! We now do the "secret student" thing with our class laptops. If the secret student is playing and X wins, the class wins. So everybody is motivated to do well.

    [Transum: There's no better way to select a 'secret student' than to use the Random Student Generator.]

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
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In how many different ways can the first three moves be placed on the grid? First four moves etc.?

How many different games are there?

How many different arrangements of noughts and crosses are possible on a full grid?


People Maths

Instead of using paper and pencil, play noughts and crosses with people! You can find instructions on the People Maths page.

Person Maths

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Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:

However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to a similar activity.

Student Activity

Ultimate Noughts and Crosses is the new game that I get really excited about playing. It's magnificent, have a look!

Student Activity

The javascript for this game above was kindly made public by Stephen Ostermiller (GNU General Public License as published by the Free Software Foundation) who also provides an excellent description of Tic-Tac-Toe Strategy.


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