These "magic" hexagons were studied by Choi Seok-jeong, a Korean mathematician, over 300 years ago. The N vertices of a hexagonal array are given numbers from 1 to N. The numbers are arranged so that the sums of the six integers at the vertices of each hexagon are the same. See - https://en.wikipedia.org/wiki/Hexagonal_tortoise_problem

Here are examples containing 3,4,5,6, and 7 hexagons. The sums at the hexagonal vertices are 40, 50, 60, 70, 75, and 80. Hexagonal arrays with fewer than about 20 vertices are easy to construct by trial and error; arrays with more than 20 vertices are difficult. Choe, Choi, and Moon have devised an algorithm that creates large arrays - see the wikipedia article.

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