Marbles in a Box

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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 ways can you make a winning line?


A poster of this problem is available here.

Published February 2003.