// Workers AI · dad joke modeWhat did the hexagonal tortoise problem say? Shell yeah, it's complex.

Choi Seok-jeong's original magic hexagonal tortoise pattern. All the sums of six numbers of each hexagon are the same number, 93. The magic sum varies if the numbers 1 through 30 are rearranged. For example, the magic sum could be 77 through 109.

The hexagonal tortoise problem (Korean: 지수귀문도; Hanja: 地數龜文圖; RR: jisugwimundo) was invented by Korean aristocrat and mathematician Choi Seok-jeong (1646–1715). It is a mathematical problem that involves a hexagonal lattice, like the hexagonal pattern on some tortoises' shells, to the (N) vertices of which must be assigned integers (from 1 to N) in such a way that the sum of all integers at the vertices of each hexagon is the same. The problem has apparent similarities to a magic square although it is a vertex-magic format rather than an edge-magic form or the more typical rows-of-cells form.

His book, Gusuryak, contains many mathematical discoveries.

Related Problems

Analogues of the hexagonal tortoise problem based on other Uniform tilings have also been studied. Yang Hui and Choi Seok-jeong studied related magic figures based on the truncated square tiling. Analogues based on the square tiling, in which the sums of the 2×2 subsquares are equal, have also been studied (sequence A355256 in the OEIS), as have analogues based on the trihexagonal tiling (sequence A391236 in the OEIS).

See Also

• Magic hexagon

Sources used

• Choe, Heemahn; Choi, Sung-Soon; Moon, Byung-Ro (2003). Cantù-Paz, Erick (ed.). A Hybrid Genetic Algorithm for the Hexagonal Tortoise Problem. Proceedings of the Genetic and Evolutionary Computation (GECCO) Conference, Chicago, IL, USA, July 12–16, 2003. Springer. ISBN 978-3-540-40602-0.