Noughts and Crosses

A versatile game for youngsters ~ also called Tic-Tac-Toe

This simple game has potential to do more than amuse. As beginners to the game mature ~ it may take a dozen games ~ they may begin to realise that there are strategies that ensure victory every time. Some years of development later they may even be able to analyse the game completely such that by following a flow chart ~ or some other guide ~ victory ~ or a draw ~ is ensured for one of the players.

I describe the pencil and paper version, but point out a variety of suitable alternatives that might be more attractive.

Draw two parallel lines, and two others at right angles, so that they intersect with rotational symmetry and form nine squares.

Player 1 places a mark ~ a cross or a circle ~ in any one of the nine squares. That mark remains the identifier for player 1 for the rest of the game.

Player 2 places the alternative mark on any unoccupied square.

Player 1 places the appropriate mark on any unoccupied square.

The game is won by the player who manages to complete a line ~ orthogonally or diagonally ~ of three similar marks. If all nine suqres are filled with no winning line then the game is an honourable draw. I leave it to the reader to discover ~ recall ~ or re-discover the various mini strategies that ensure victory, or avoid loss.

If paper is in short supply then a suitable grid can be drawn ~ and re-used ~ by players placing small items as their 'moves' ~ coloured counters ~ dried beans and peas ~ nuts and washers.

When I was at teacher training college I combined maths and craft course work by making a board from a square of plywood and lollipop sticks. This could be used for playing noughts and crosses, and another variation ~ whose name I forget ~ whereby each player has three counters, once they are all played they take it in turns to pick and replace one of their counters. There are ~ I believe ~ numerous variations on n x m boards. Recreational mathematicians have a lifetime of work doing stuff around these. It is sufficient to mention the hitorical Japanese game Gomoku ~ played with as many counters needed to obtain five-in-a-row on a 19x19 board. This game is taken very seriously ~ on a par with chess ~ and there are World championships held annually. I will write some notes on it, sometime.

Once noughts and crosses becomes trivial it might be useful to move ahead to Dots and Squares [113808]. Or, at much the same level of ability, Sprouts takes a more creative direction [113805].

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