Counting Magic Venn Diagrams

A Magic Venn Diagram is a magic figure where regions of a Venn diagram are labeled such that the sums of the regional labels of each set are the same. We have developed a backtracking search to count the number of Magic Venn Diagrams. The algorithm could determine the number of Magic Venn Diagrams for all Venn diagrams with four sets. This paper presents the algorithm with its applied heuristics and lists the computational results.