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Design and Copyright : George Bell (2011).
|
A |
| Pieces | 6 |
| Selection | complete |
| Goal | 4×4×4 |
| Holes | 0 |
| Solutions | 5 |
Here is the idea: Take all L-shaped polycube pieces of width 1 (called Lominoes) which fit in an n × n square. There are n(n-1)/2 pieces and their total volume is (n3-n)/2. Now make them all 2 tall (twice as thick). The total volume is now n3-n. Finally, take one of the pieces of volume 2n and make it 3 tall. We now have n(n-1)/2 pieces with total volume n3.
| n | Pieces | 3 tall | Sols | Remark |
|---|---|---|---|---|
| 3 | 3 | 2×2 | 0 | |
| 4 | 6 | 3×2 | 5 | Fats Lomino 4 |
| 5 | 10 | 3×3 | 5 | Fats Lomino 5 |
| 4×2 | 0 | |||
| 6 | 15 | 4×3 | many | Fats Lomino 6 |
| 5×2 | many | |||
| 7 | 21 | 4×4 | ? | Fats Lomino 7 |
| 5×3 | ? | |||
| 6×2 | ? |
|
A |
| Pieces | 7 |
| Selection | complete |
| Goal | 4×4×4 |
| Holes | 0 |
| Solutions | 107 |
