An antimagic square is an n×n array of integers from 1 to n^2 such that each row, column, and main diagonal produces a different sum such that these sums form a sequence of consecutive integers. It is therefore a special case of a heterosquare. It was defined by Lindon and appeared in Madachy's collection of puzzles, originally published in 1966. Antimagic squares of orders 4-9 are illustrated above. For the 4×4 square, the sums are 30, 31, 32, ..., 39; for the 5×5 square they are 59, 60, 61, ..., 70; and so on.

antimagic graph | heterosquare | magic square | talisman square