A Room square (named after T. G. Room) of order (for even) is an arrangement in an square matrix
of 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.
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(for 
even) is an arrangement in an 
square matrix
of 
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.
." J. Combin. Th. 13, 306-314, 1972.Room,
T. G. "A New Type of Magic Square" (Note 2569). Math. Gaz. 39,
307, 1955.Wallis, W. D. "Solution of the Room Square Existence
Problem." J. Combin. Th. 17, 379-383, 1974.Wallis,
W. D.; Street, A. P.; and Wallis, J. S.