The authors consider the problem of partitioning a given square (in the Euclidean plane) into n rectangular pieces having equal area. This problem has direct applications by the organization of manufacturing processes. In order to get information about how the number \(A_ n\) of these partitions depends on n, especially such partitions (number \(B_ n\leq A_ n)\) are investigated which can be realized by “guillotine cuts” (i.e. by a series of straight lines that extend from one edge of a rectangle to the opposite edge, being parallel to the other two edges) or even by using only cross guillotine cuts but no length guillotine cuts with respect to the square (number \(C_ n\leq B_ n)\). Estimates in the latter subproblem lead to the result that the number \(C_ n\) of partitions - and the numbers \(B_ n,A_ n\) all the more - increase exponentially in n.