Answer to puzzle 35: Cuboids
There are 20 distinct cuboids such that the number of external cubes is equal to the number of internal cubes. The table below shows the dimensions (a × b × c) and number of external cubes for each such cuboid.
| a | b | c | # external cubes |
|---|---|---|---|
| 5 | 13 | 132 | 4290 |
| 5 | 14 | 72 | 2520 |
| 5 | 15 | 52 | 1950 |
| 5 | 16 | 42 | 1680 |
| 5 | 17 | 36 | 1530 |
| 5 | 18 | 32 | 1440 |
| 5 | 20 | 27 | 1350 |
| 5 | 22 | 24 | 1320 |
| 6 | 9 | 56 | 1512 |
| 6 | 10 | 32 | 960 |
| 6 | 11 | 24 | 792 |
| 6 | 12 | 20 | 720 |
| 6 | 14 | 16 | 672 |
| 7 | 7 | 100 | 2450 |
| 7 | 8 | 30 | 840 |
| 7 | 9 | 20 | 630 |
| 7 | 10 | 16 | 560 |
| 8 | 8 | 18 | 576 |
| 8 | 9 | 14 | 504 |
| 8 | 10 | 12 | 480 |