Room squares and generalizations have been extensively studied for over 40 years. In 1974, Mullin and Wallis showed that the spectrum of Room squares consists of all odd positive integers other than 3 or 5; however, many other related questions have remained unsolved. (For an extensive survey from 1992 of Room squares and related designs, we refer the reader to .) In the 1994 paper by Dinitz, Stinson and Zhu , the authors studied three well-known spectra of designs closely related to Room squares and in each instance left exactly one unsolved case. In this paper we will prove the existence of each of these designs...