A Room square (named after T. G. Room) of order n (for n even) is an arrangement in an (n - 1)×(n - 1) square matrix of n objects such that each cell is either empty or holds exactly two different objects. Furthermore, each object appears once in each row and column and each unordered pair occupies exactly one cell. The Room square of order 2 is shown below. 1, 2 The Room square of order 8 is given in the following table.

design | Latin square