There Are Magic Hexagons of Every Order

Magic hexagons are hexagonal grids where numbers in straight lines across three directions all sum to the same value, analogous to magic squares. While only one non-trivial normal magic hexagon (with consecutive numbers starting from 1) exists—the order-3 hexagon with 19 cells—relaxing the constraint to allow consecutive numbers starting from any integer enables many more solutions, with the largest known being order-9, discovered in 2024. Finding these "abnormal" magic hexagons is computationally difficult because of the tension between requiring consecutive numbers and equal line sums across lines of different lengths.