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## 'Cube Paths' printed from http://nrich.maths.org/

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.)