Antimagic square
From Wikipedia, the free encyclopedia
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.
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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.
Antimagic squares form a subset of heterosquares which simply have each row, column and diagonal sum different. They contrast with magic squares where each sum is the same.
[edit] 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?
