Santa has packed up all his presents into 16 boxes. Each box is a cube: the first is 1m×1m×1m, the second 2m×2m×2m, the third 3m×3m×3m, … up to the largest which is 16m×16m×16m. He wants to ft all the boxes onto two sleds but is bound by the Elf Safety Regulations. These state that on each sled he must have the same number of boxes. In addition to this on each sled the sum of the side-lengths of the boxes must be the same, the sum of the areas of the bases of the boxes must be the same and the sum of the volumes of the boxes must be the same.
Is this possible?
Reveal Solution
Santa has packed up all his presents into 
boxes. Each box is a cube: the first is 
, the second 
, the third 
, … up to the largest which is 
.
He wants to fit all the boxes onto two sleds but is bound by the Elf Safety Regulations. These state that on each sled he must have the same number of boxes. In addition to this on each sled the sum of the side-lengths of the boxes must be the same, the sum of the areas of the bases of the boxes must be the same and the sum of the volumes of the boxes must be the same. Is this possible?
One possible solution to this puzzle is
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| 1 | 1 | 1 | 2 | 4 | 8 | ||
| 4 | 16 | 64 | 3 | 9 | 27 | ||
| 6 | 36 | 216 | 5 | 25 | 125 | ||
| 7 | 49 | 343 | 8 | 64 | 512 | ||
| 10 | 100 | 1000 | 9 | 81 | 729 | ||
| 11 | 121 | 1331 | 12 | 144 | 1728 | ||
| 13 | 169 | 2197 | 14 | 196 | 2744 | ||
| 16 | 256 | 4096 | 15 | 225 | 3375 | ||
| Total | 68 | 748 | 9248 | 68 | 748 | 9248 |
