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Cube Paths

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

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.)

Cube Paths diagram