How many different three-step paths along the edges of a cube are there that take you from vertex $A$ to vertex $B$? (A step is from a vertex to an adjacent vertex sharing an edge.) size(101); import three; currentprojection=orthographic(1/2,-1,1/4); draw((0,0,0)--(1,0,0)--(1,0,1)--(0,0,1)--(0,0,0)); draw((1,0,0)--(1,1,0)--(1,1,1)--(1,0,1)); draw((1,1,1)--(0,1,1)--(0,0,1)); label("A",(0,0,1),(-1,0,0)); label("B",(1,1,0),(1,0,0));
