A magic hexagon of order n is an arrangement of close-packed hexagons containing the numbers 1, 2, ..., H_(n - 1), where H_n is the nth hex number such that the numbers along each straight line add up to the same sum. (Here, the hex numbers are i.e., 1, 7, 19, 37, 61, 91, 127, ...; OEIS A003215). In the above magic hexagon of order n = 3, each line (those of lengths 3, 4, and 5) adds up to 38. It was discovered independently by Ernst von Haselberg in 1887, W. Radcliffe in 1895 (Tapson 1987, Hemme 1990, Heinz), H. Lulli (Hendricks, Heinz), Martin Kühl in 1940 (Gardner 1963, 1984; Honsberger 1973), Clifford W. Adams, who worked on the problem from 1910 to 1957 (Gardner 1963, 1984; Honsberger 1973), and Vickers (1958; Trigg 1964).

hexagon | hex number | magic graph | magic hexagram | magic square | Pascal's theorem | talisman hexagon