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Question 1134175: A 4x4x4 cube is ruled on all six of its faces with 16 congruent squares. How many paths are there along the faces of the cube from A to B, travelling along the lines and always moving closer to point B? (Remember, : the paths are drawn on all six faces!)
Here is the link to the diagram : http://tinypic.com/r/166m8si/9
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
To get from A to B, you have to move, in some order, 4 units forward ("F"), 4 units left (L"), and 4 units down ("D").
The number of different paths from A to B is the number of different orders in which you can make those moves. That is, the number of different paths is the number of different ways of ordering the moves FFFFLLLLDDDD.
By a well-known counting principle, the number of different ways to arrange those moves is
ANSWER: 34,650 different paths. (don't try to count them all......)
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