Magic Venn Diagrams

A magic Venn diagram (MVD) of order n , size r , degree d and magic sum m is a Venn diagram of n sets A 1 , A 2 , . . . , A n , in which r of the 2 n non-overlapping Venn regions are weighted 1-1 by the numbers 1, 2, . . . , r in such a way that each set A i contains d weights adding up to the constant m . After demonstrating how MVDs arise and how they encompass a broad array of magic figures, we give results on the frequencies of different MVD’s of orders 3 and 4, by combinatorial type and magic sum. Illustrations and explanations are given for several of the smaller types.