Prove that one can pack precisely forty one 1x2x4 bricks into a 7x7x7 box.

Bonus Question:
Can precisely forty two 1x2x4 bricks be packed into this box?
If so, show how. If not, prove that it can’t be done.

I remember seeing this puzzle somewhere years ago.  The trick to packing the 41 bricks was that the empty spaces in box formed three 1x1x5 spaces, forming a sort of path from one corner of the box to its far opposite corner.

Posted by Brian Smith on 2014-05-24 14:08:20