A Room square R of order r is an r x r array each of whose cells may either be empty or contain an unordered pair of objects 0,1,2,...,r, subject to the following conditions:
(i) each of the objects 0,1,2.....r occurs precisely once in each row of R and precisely once in each column of R, and
(ii) every possible unordered pair of objects occurs precisely once in the whole array.
Chaudhry G R and Seberry J, Minimal Critical Set of a Room Square of order 7, Bull. Inst. of Combin. and its Applications 20(1997), 90.