Polycube Snakes

The , and cubes can be filled with a polycube "snake" that turns by right angles at every step. The solutions for these three cubes are given here.

The polycubes as such are not shown, but their positions are represented by colored points connected by a polyline.

Such a path can be found for all cuboids except for the following cases:

and ,

odd, odd, .

(Karl Scherer 1982; the proof is very easy.)