Imagine a three-dimensional version of noughts and crosses where two players take it in turn to place different coloured marbles into a box. The box is made from 27 transparent unit cubes arranged in a 3-by-3-by-3 array. The object of the game is to complete as many winning lines of three marbles as possible. How many different winning lines are there? Once you have thought about how you might tackle the problem, click below to see four different methods for working out the number of winning lines in a 3×3×3 cube.
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