Stage: 3 Challenge Level: 
The diagram shows a skeletal view of a 2 by 2 by 2 cube with one route 'down' the cube.
How many routes are there on the surface of the cube from A to
B?
(No `backtracking' allowed, i.e. each move must be away
from A towards B.)
Generalising. Cubes. Combinatorics. Visualising. Regular polygons. Construction kits. Interactivities. Mathematical reasoning & proof. Working systematically. Counting.
Published November 1998.
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