The three-way intersection problem for latin squares Original Research Article

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n2−k cells different in all three latin squares, denoted by I3[n], is determined here for all orders n. In particular, it is shown that I3[n]={0,…,n2−15}∪{n2−12,n2−9,n2}, for n⩾8.