The game uses a 3x3 square board. 2 players take turns to play,
either placing a red on an empty square, or changing a red to
orange, or orange to green. The player who forms 3 of 1 colour in a
This game for two players comes from Ghana. However, stones that were marked for this game in the third century AD have been found near Hadrian's Wall in Northern England.
Some puzzles requiring no knowledge of knot theory, just a careful
inspection of the patterns. A glimpse of the classification of
knots and a little about prime knots, crossing numbers and knot
Fifteen is a game for two players that you can play anywhere, anytime. Try it without writing anything down. You take it in turns to choose one of the whole numbers 1 to 9 (and each number can only be chosen once). To win you have to pick 3 numbers that add up to 15.
Can you beat the computer?
Can you analyse the structure in the following games and the correspondences between them? Describe the patterns that show they are equivalent games that can be played using equivalent strategies.
We suggest tackling them in the order given.