Came to know about the following problem from a friend which can be simplified to the following: A1, A2, ....Am and B1, B2,...Bn are two groups of sets each group spanning the sample space. Now there are p elements in each of Ai and each element is in exactly p1 of the sets of the A group. Again there are q elements in each of Bi and each element is in exactly q1 of the sets of the B group. We have to write, 'n' in terms of m,p,p1,q,q1. Thanks for any ideas.