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?
The problem requires that: 'The outer dimensions and the dimensions of each room must all be different.' This is presumably meant distributively, i.e the outer dimensions must be different and the dimensions of each room must be different.
By observation, the Temple cannot comprise 1,2,3, or 4 rooms.
If the Temple comprises 5 rooms, they must have 10 different dimensions, with a minimum of {1,2,3,4,5,6,7,8,9,10} (room dimension rule).
The lesser dimension of the Temple must therefore be no less than 10.
The greater dimension of the Temple must then be at least 11 (outer dimension rule).
The following Temple has 5 rooms and dimensions 10x15, for a total area of 150 and the neat property that the numbers 1 to 10 are all used.
4x5 (4x5) 6x7 4+6=10
1x10 3x2 (6x7) 1+3+6=10
(1x10) 9x8 9x8 1+9=10
5+10=15 5+2+8=15 7+8=15
If the phrase referred to above is meant conjunctively, then changing 6x7 to 9x7 and 9x8 to 12x8 produces a much less attractive Temple with outer dimensions 13x15 and area 195.
|
|
Posted by broll
on 2024-07-18 12:24:03 |
Possible Solution
