Pack or sack

Reply Fri 12 Nov, 2004 09:51 am
Grubby an elf who is doing the packing for Santa is looking to a set packages who are increasing in size. Their measurements are 1x1x1 dm^3, 2x2x2 dm^3, 3x3x3 dm^3, ..., 9x9x9 dm^3.

Santa has told him to pack the 9 boxes as economically as possible into a bigger box, because of limited space in the sled. I mean into a box as small as possible.

He could pack the 1x1x1 and the 2x2x2 together into a 2x2x3 box.
If he wanted to add the 3x3x3 box he needed a 3x3x5 box. etc.

So the question is what is the smallest box to fit all 9 boxes?

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Reply Fri 12 Nov, 2004 08:23 pm
The sum of the boxes is 2025 (I'll omit units) - so that's a lower bound.

I can get to 2430 with this arrangement:

Bottom layer viewed from above:

6 5 7
9 1 8

Place the 4 on top of the 5. Place the 3 and the 2 on top of the 6.

The dimensions are 9x15x18 = 2430
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Reply Sat 13 Nov, 2004 05:13 am

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