# Sled-packing with Santa

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

 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
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