Prove that one can pack precisely forty one 1x2x4 bricks into a 7x7x7 box.
Can precisely forty two 1x2x4 bricks be packed into this box?
If so, show how. If not, prove that it canít 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.
The bonus question was proved to be impossible, the key point was that there were only 7 empty voids in the box, no two of which could be coplanar.