A set of n magic circles is a numbering of the intersections of the n circles such that the sum over all intersections is the same constant for all circles. The above sets of three and four magic circles have magic constants 14 and 39. For n circles, the constant is n^3 + n^2 + n, for n = 1, 2, ... corresponding to 3, 14, 39, 84, 155, 258, ... (OEIS A027444).

magic graph | magic square