• Magic
• Order 3
• Order 4
• Order 5

Magic Square Orders

Order Classification

The availability of recognized types of magic squares is related to the order of the squares. Orders are generally divided as odd and even, with even orders being further split into singly even (4k+2) and doubly even, (4k), k≥1. One type, Franklin, requires a further split of doubly even to doubly doubly even, (8k).

Order Types

Order 3: See type summary.
Order 4: See type summary. The pandiagonal are all most-perfect, (compact + complete).
Order 5: See type summary. There are 16 ultramagic, (associative + pandiagonal).

Notes:

• Associative:  There are near-associative squares for singly even order.
• Pandiagonal: There are near-pandiagonal squares for singly even order.
• Symlateral:   There are near-symlateral squares for even order.
• Self-complement: Refers to side-to-side symmetric; associative squares are also self-complementary.