magic circles

Given $n$ circles which intersect $k$ times, the set of circles is referred to as magic circles if there exists a numbering (using $\{1,\mathrm{\dots },k\}$) of the intersections of the $n$ circles such that the sum of the numbers at the intersections along each circle is the same constant for all circles.

Further reference:http://www.cgl.uwaterloo.ca/ smann/Magic/