You have been hired to build the Temple of Heterodoxy for a fixed fee. The Temple must be rectangular, divided into two or more rectangular interior rooms, with each side an integral number of bozols. The outer dimensions and the dimensions of each room must all be different. For example, you could not have both a 5x9 room and a 9x11 room. The thickness of the walls is negligible.
What is the smallest possible area for the floor of the temple?
While this was in the queue I had a nagging thought in the back of my mind that we had a problem like this, but I could not find it until I randomly stumbled across it today.
Over there I have a solution of 1x10, 2x9, 3x6, 4x11, and 5x8. Forming 10x13=130 area, which is smaller than broll's 150 area.
+---+----------+
| 3 | 1x10 |
| x +----------+
| 6 | 5x8 | 2 |
+----------+ x |
| 4x11 | 9 |
+----------+---+
Both my 130 area and broll's 150 area have an interior room with one of its dimension matching one for the whole building, so I will then do as broll did and present an adjusted plan to avoid that match.
Stretch the 1x10, 4x11 and 5x8 by three units along their longer sides. Then I can have 1x13, 2x9, 3x6, 4x14, and 5x11 forming 10x16=160 temple area.
Possible Solution
