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Polycube Snakes

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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.

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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, odd, .

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

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Contributed by: Karl Scherer (March 2011)
Open content licensed under CC BY-NC-SA

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