The order-7 Room square was used by Robert Richard Anstice to provide additional solutions to Kirkman's schoolgirl problem in the mid-19th century, and Anstice also constructed an infinite family of Room squares, but his constructions did not attract attention.
In his original paper on the subject, Room observed that n must be odd and unequal to 3 or 5, but it was not shown that these conditions are both necessary and sufficient until the work of W. D. Wallis in 1973.
The columns of the square represent tables, each of which holds a deal of the cards that is played by each pair of teams that meet at that table.
Archbold and Johnson used Room squares to construct experimental designs.
[4] There are connections between Room squares and other mathematical objects including quasigroups, Latin squares, graph factorizations, and Steiner triple systems.