Exact Solution of a Simple Cutting Problem

Recently Gilmore and Gomory have discussed in detail cutting stock problems in two and more dimensions. However the generality of their approach seems to obscure the existence of exact solutions to very simple situations given in this paper. We discuss here the problem of optimal dissection of a large rectangular plane area into smaller rectangles having unit width and integral length so as to obtain the least waste. When the strips are of only one or two sizes the problem is solved completely. It is shown that when the strips are of two different lengths then, if the area being dissected is large enough and the two lengths are relatively prime numbers, strips can be cut so as to leave no remainder. Possible future extensions are suggested.