Noughts and Crosses

A Maths Starter of The Day

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

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

 

 

 

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  • Transum,
  • Sunday, October 07, 2007
  • "Another game which is isomorphic (same strategies) to noughts and crosses is the game of “15”. 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."
  • Miss Mears, Stockport
  • Tuesday, November 06, 2007
  • "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
  • Monday, January 14, 2008
  • "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."

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Answers

There are nine different places the first "X" can be drawn. This leaves eight different places for the first "O" to be drawn.

The total number of different ways the first two symbols can be drawn is:

9 x 8 = 72