An antimagic square of order n is an arrangement of the numbers 1 to n² in a square, such that the n rows, the n columns and the two diagonals form a sequence of 2n + 2 consecutive integers. The smallest antimagic squares have order 4.
In each of these two antimagic squares of order 4, the rows, columns and diagonals sum to ten different numbers in the range 29–38.
Some open problems
- How many antimagic squares of a given order exist?
- Do antimagic squares exist for all orders greater than 3?
- Is there a simple proof that no antimagic square of order 3 exists?