A magic hexagram is a hexagram such that each outer point and each crossing point is assigned a number so that different points are assigned different numbers. The sum of the numbers on any line is required to be the same for all lines. In a pure magic hexagram, the set of assigned numbers is the set of consecutive integers from one to twelve. Finding magic hexagrams is a popular recreation.

In any pure magic hexagram, the sum of the numbers of the corners of each large triangle must be the same. Here is the proof. Let M be the magic number. From the diagram follows these six equations:

• 1. B = M - I - L - J
• 2. C = M - B - A - D
• 3. E = M - C - K - J
• 4. F = M - E - D - G
• 5. H...