In a recent series of papers published in Mathematics Magazine, Brother U. Alfred investigates the conditions under which the sum of the squares of N consecutive odd integers can be a square. He derives several theorems to eliminate many values of N, and finds solutions for other values. Eight numbers below 1000 (193, 564, 577, 601, 673, 724, 772, and 913) remain unsolved in his work. Also, there are 17 values in his table of solutions for which the solution exceeds 10 digits. In this Paper, the eight cases are resolved, and solutions are presented for the 17 cases, only one of which contains as many as 7 digits. A systematic procedure for finding these solutions is demonstrated. 7 pp. Refs.