Wolfram Demonstrations Project

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 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:

and

odd,

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

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Polycube Snakes