Finding the shortest path in a n-dimensional grid
It's easy: first get the 1st dimension right, then the 2nd dimension, then the 3rd dimension, etc.

For example, if you want to get from $(1,3,0)$ to $(3,4,1)$, you go via the following sequence of points: $(1,3,0), (2,3,0), (3,3,0), (3,4,0), (3,4,1)$.