Enigma 1112: Patio zones
From New Scientist #2268, 9th December 2000
George is building a patio, which will be covered using one-foot-square concrete slabs of seven different colours. He has divided the rectangular patio into seven rectangular zones, without any gaps.
Each zone will be covered by slabs of one colour, with five different colours appearing around the perimeter of the patio, and four different colours at the corners. The seven rectangular zones are all different shapes, but all have the same perimeter, which is less than 60 feet.
What are the dimensions of the patio that George is building?
This puzzle is referenced by Enigma 1221.