How to determine the number of a cube within a bigger cube?

Hi all,

I have a cube, sized 39 x 13 x 8. I need to find out how many of them can fit in a cube of 100 x 100 x 100. I need to find the highest number possible.

Do you know of a way to do that without having to draw them, with trial and error?

Septronic

-
I do not have a definite answer, and I am surely no expert on this topic. But I can say that similar problems are hard: en.wikipedia.org/wiki/Bin_packing_problem In your case, a computer program might be the easiest way out. – jmc May 18 '13 at 14:09
Your latter cube is indeed a cube, but the first-mentioned "cube" is not. Such a rectangular body is called a cuboid. – John Bentin May 18 '13 at 17:42
Do you think trial and error will find the optimal packing? I feel like I have to think "outside the box" to pack 5 unit squares in a 2.8x2.8 square. Hopefully this sort of packing is not necessary for your problem. – Dustin G. Mixon May 18 '13 at 18:59
@John : $\:$ I suspect that what the OP has is a rectangular prism, since a cuboid can be more general. – Ricky Demer May 18 '13 at 20:02
FYI - I asked a follow-up question, and got an answer that might interest you: mathoverflow.net/questions/131084/is-this-cube-packing-possible – Dustin G. Mixon May 19 '13 at 0:25