Boxes

Imagine a room full of boxes. Each box has a length, width, and height. Since the boxes can be rotated those terms are inter- changeable. The dimensions are integral values in a consistent system of units. The boxes have rectangular surfaces and can be nested inside each other. A box can nest inside another box if all its dimensions are strictly less than the corresponding dimensions of the other. You may only nest a box such that the corresponding surfaces are parallel to each other. A box may not be nested along the diagonal. You cannot also put two or more boxes side by side inside another box.