Tromino Tiling Deficient Cubes of Any Side Length

Details Tromino Tiling Deficient Cubes of Any Side Length Tromino Tiling Deficient Cubes of Any Side Length

2008-06-03

arxiv.org/abs/0806.0524v1

"Tromino Tiling Deficient Cubes of Side Length 2n", Geombinatorics XVIII(2) (2008), 72-87

Mathematics

Combinatorics

15 pages, 27 figures

Scientific paper

We show that three dimensional cubes of any size can be tiled with trominoes and, when necessary, one or two singletons in any positions. Cubes of side length a multiple of three can always be tiled with trominoes (known), cubes of side length congruent to 1 mod 3 can always be tiled with an arbitrary single cube and trominoes, and cubes of side length congruent to 2 mod 3 can always be tiled with two single cubes in arbitrary locations and trominoes.

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