## Magic Star

An n-pointed magic star is a star polygon in which numbers are placed at each of the n vertices and n intersections such that the four numbers on each line sum to the same magic constant.

A normal magic star contains the consecutive integers 1 to 2n.

The magic constant of an n-pointed normal magic star is M = 4n + 2.

No star polygons with fewer than 5 points exist. In addition, the construction of a normal 5-pointed magic star turns out to be impossible. Therefore, the smallest examples of normal magic stars are 6-pointed.

Examples for n = 6, 7, and 8 are presented below.

n = 6:

n = 7: