Dissections into 1:2 rectangles (Q1910542)

The author considers dissections of a square and of a 1:2 rectangle into elements that are themselves 1:2 rectangles no two of which are of the same size. The order of such a dissection is by definition the number of dissecting elements. He proves that for every \(n\geq 9\), there is such a dissection of order \(n\) in case of the square, while the bound is \(n\geq 8\) in case of the 1:2 rectangle. In both cases there is no dissection of a smaller order.