```Newsgroups:     rec.puzzles,sci.math
From:           umatf071@unibi.hrz.uni-bielefeld.de (sio)
Subject:        Re: Tiling problem
Date:           Tue, 9 Feb 93 21:28:17 GMT
Organization:   Universitaet Bielefeld
```

```The last tetracube tiling problem: (Update of a previous posting)

______
|\     \               Is it possible to tile a 3*2n*2m box only
| \_____\              with tetracubes shown left?
| |     |____
|\|     |    \         All other (hyper-) box tiling problems with
| *_____|_____\        only alike tetracubes are solved. See:
| |\     \    |         A. L. Clarke, Packing Boxes with Congruent Polycubes,
\| \_____\   |         J. of Recreational Mathematics 10 (1977/78) 177-182
* |     |___|
\|     |
*_____|

You can show 2 | nm.
According to my computations n and m had to be greater then 8.

The 3*4*Z is tileble:
build two times  2 1 1 2 2 1 1 2 2 1 1 2
. . 1 2 2 1 1 2 2 1 1 2 2 1 . .
. . 1 2 2 1 1 2 2 1 1 2 2 1 . .
2 1 1 2 2 1 1 2 2 1 1 2

use the          a a b b a a b b a a b b
dissection       a c c b a c c b a c c b
b c c a b c c a b c c a
b b a a b b a a b b a a

so the 3*N*Z is tileble.

My Conjectures:
- the 3*2n*N box is not tileble.
- the 3*N*N box (3*quadrant) is tileble.

Torsten Sillke
```