This is the game of "Noughts and Crosses" or "Tic Tac Toe".
In how many different ways can the first "X" and "O" be placed on the grid?
Topics: Starter  Combinations  Puzzles
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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?
Instead of using paper and pencil, play noughts and crosses with people! You can find instructions on the People Maths page.
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Teacher, do your students have
access to computers? 

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