Finding ways from A to B in 3d objects

[coldcell]

Find the total number of ways to go from A to B, if each way is the shortest route.

http://img151.imageshack.us/img151/9875/010hr.jpg

This is a rough sketch of 2 by 2 by 2 object.

I have to find the number of ways for x by x by x object and x by y by z object.

I tried doing it for 1 by 1 by 1 and 2 by 2 by 2 based on manual calcualting. However I cannot find a general formula for this.

I'm thinking x + y + z, but that's just a pure guess. I tried it on a paper, but it's too hard to show what I tried in this forum.

 

[StatusX]

Well, you can only go down, in, or right (depending on how you orient the figure) if you want to go the quickest way, and conversely, as long as you only go one of these three directions at each step, this is a shortest path. (Do you see why?) It might help you visualize things if you flatten the shape out and turn this into a 2D problem.

 

[coldcell]

Ah yes I see it... but is it that simple?

We are assuming if we go to the right, it's 1 way. But we have in fact, crossed 2 boxes.

To be honest, I don't really understand the question myself :S

 

[StatusX]

What? I don't follow you. There is definitely more than one way.