Inspired by Hexagonal Tortoise Problem, we treat the problem of the magic hexagon. See Puzzle 927. Prime solutions to HTP According to the wiki, "A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M." Arsen Zahray discovered these order 4. See Magic hexagon wiki Magic constant=111 and start number=3. The order 4 hexagon starts with 3 and ends with 39. The numbers in the hexagon are consecutive, and run from a to a+36. Sum=37(2a+36)/2=37(a+18). Hence magic constant M=Sum/7=37(a+18)/7. Since M needs to be integer, a+18=0 Mod 7. Then a=3 Mod 7. If we take a=3, then M=111. We searced the solutions for the order 4 hexagon starts with 3, there were many solutions. We show only 4 solutions below. Though we searced the solutions for the order 4 hexagon starts with 10, no solution was found. M=111 M=111 M=111 M=111

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