DARA is a variation of Nine Men's Morris, also called The Mill. This game can be traced back to Ancient Egypt, where a game board was discovered carved into a stone roof slab at the temple of Karnak. Today, Egyptians play a modern version of the game, called Seega.
Other versions of this game (for example African Morris) also exist. It is popular throughout Africa. All the games are a variation on Noughts and Crosses, where a line of three in a row wins. In the Egyptian version "three in a row" is called a mill. It is mentioned in Shakespeare's A Midsummer Night's Dream.
This kind of game encourages strategic thinking as it is large enough to be fairly complex (so not as easy to crack as Noughts and Crosses), yet it is relatively simple to provide some analysis. Students could be encouraged to "crack" the game by looking at combinations of moves that are more likely to win, as in Chess. Or they could provide reasons why certain squares are good to fill first and others are not. Filling diagonal lines is one good strategy.
There are several other popular African games. Claudia Zaslavsky's excellent book Africa Counts: Number and Pattern in African Culture (Acappella Publishing, Gazelle Books Service, tel: 01524 68765) describes all the games in great detail. Because much of Africa, from the north down, has historically been ruled by Muslims and has had much contact with Arab traders, the Islamic influence on games, architecture and patterns has been great.
Little recorded history remains from before the time of the Islamic influence, but there are hints of great empires all over Africa. The Ishango bone discovered by a Belgian scientist in Zaire (Democratic Republic of Congo) is the earliest record we have of sequential notation. It can be dated to between 9000 and 6500 BC.
In 1976, the African Mathematical Union was set up. It is now preparing web pges which are currently based at the University of Buffalo's website at www.math.buffalo.edu
AFRICAN CHALLENGE 1: African culture is the oldest on our planet. Sticks used for counting or, like rulers, for measuring date back to almost 9000 BC. Some African culture is Islamic. A famous mathematician in the 18th century was Muhammad Ibn Muhammad, who died in 1741. He did a lot of work on Magic Squares.
Materials: on your worksheet you need a game board with 30 squares (five by six) like the one below, big enough to play on with counters. Make or obtain two sets of 12 numbered counters.
* Dara is a game for two players.
* Each player has a set of 12 numbered counters and before they start the game they take turns laying the counters in the squares on the board.When all 24 counters are down, the game can begin.
* In turn, players move their counters one square vertically or horizontally to an empty square. A player may not move diagonally, and jumps are not allowed.
* For each line of three formed vertically or horizontally, you must first make a note of which counters you used. Then you remove one of your opponent's counters.
* If you made a line of three before all the counters were down at the start, that does not count, nor does any diagonal line of three. And you may not repeat a line of three numbered counters in any permutation.
* A line of four does not count either, but moving a counter off the end of a line of four would make a line of three.
* When your opponent has only got two counters left or cannot move, you have won!
After playing the game a few times, try to work out the best way to win.
Is it best to go first?
Which are the best squares to fill first?
Write down your ideas.
Simon Crivich teaches at Overton Grange School in Sutton. E-mail: SFCrivich@email.com