Show that it is possible to fill a rectangular box with rectangular blocks so that:
(1) the dimensions of all of the blocks are integers,
(2) no edge of a block coincides with an entire edge of the box, and
(3) no two blocks have identical faces (that is, you could not have blocks of size A×B×C and A×B×D).
Find the box of least volume for which this is possible.
(In reply to
Answer by Brian Smith)
I made a mistake and overlooked one pair of congruent faces. So I bumped up the middle block to 3x5x7. Then I get a set of 1x6x9, 2x4x9, 1x4x7, 2x7x8, 1x5x8, 2x5x6, 1x1x1, 2x2x2, 3x5x7.
These pack into a 6x8x10 box
re: Answer
