ABSTRACT
A Room square of side r (or of order r + 1) is a square array with r cells in each row and each column, such that each cell is either empty or contains an unordered pair of symbols chosen from a set of r + 1 elements. Each row and each column contains each element precisely once, from which it follows that r must be odd; say r = 2n − 1. Without loss of generality, we can take the elements as the numbers 1, 2, . . . , 2n− 1 and the symbol ∞. So each row and each column of the design contains n − 1 empty cells and n cells each containing a pair of symbols. Further, each of the n(2n− 1) possible distinct pairs of symbols is required to occur exactly once in a cell of the square. An example, of side 7, is shown in Figure 15.1.
