Cavenagh, Nicholas JWanless, Ian2015-12-100166-218Xhttp://hdl.handle.net/1885/56238It is well known that if n is even, the addition table for the integers modulo n (which we denote by Bn) possesses no transversals. We show that if n is odd, then the number of transversals in Bn is at least exponential in n. Equivalently, for odd n, theKeywords: Complete mapping; Diagonally cyclic; Homogeneous latin bitrade; Latin square; Magic juggling sequence; Orthomorphism; Random MOLS; Semi-queen; Transversal; Mapping; Recreational facilities Complete mapping; Diagonally cyclic; Homogeneous latin bitrade; Latin square; Magic juggling sequence; Orthomorphism; Random MOLS; Semi-queen; Transversal201010.1016/j.dam.2009.09.0062016-02-24