Polycube Snakes
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.
2×2×2
4×4×4
5×5×5
The display of the polycubes is optional; their positions are represented by black points connected by a polyline.
Such a snaking path can be found for all cuboids except for the following cases:
a×b×c
a>=b>=3
c=1
a
b
c=3
(Karl Scherer 1982; the proof is very easy.)