  We consider partitions of n-dimensional boxes in R^n, n>1, into a finite
number of boxes with pairwise disjoint interiors. We study sets X \subseteq
(0,\infty) with the Property (W_n): for every n-dimensional box P and every
partition of P, if each constituent box has one side with the length belonging
to X, then the length of one side of P belongs to X. We prove that the set X
\subseteq (0,\infty) has Property (W_n) if and only if X is closed with respect
to the operations: x+y and x+y+z-2min(x,y,z).
