2 15. Let p be a positive integer, and let A = (A1, A2, ..., An) be a family of n subsets of the set Y {41, 42, ..., Yn} of n elements. Suppose that each set Aj of A contains exactly p elements of Y, and each element y; of Y is contained in exactly p sets of A. Prove that A has an SDR. Reformulate this problem in terms of nonattacking rooks on a board with forbidden positions. 2 2 15. Let p be a positive integer, and let A = (A1, A2, ..., An) be a family of n subsets of the set Y {41, 42, ..., Yn} of n elements. Suppose that each set Aj of A contains exactly p elements of Y, and each element y; of Y is contained in exactly p sets of A. Prove that A has an SDR. Reformulate this problem in terms of nonattacking rooks on a board with forbidden positions. 2