Concentric Magic Squares


Concentric Magic Squares have nested centered sub-squares that are all, (not normal), magic. The innermost nested sub-square of odd order concentric magic squares is the order 1 square. The innermost nested sub-square of even order concentric magic squares is an order 4 square.

The order 1 square is not concentric because it does not have a sub-square.
Order 4 squares are not concentric because the center 2x2 is not magic.

A special kind of concentric magic squares is known as Bordered Magic Squares. For even order, there are also Bordering Magic Squares.

Odd Order

There are 174,240 order 5 concentric magic squares. These are group 2 of the Complement Pair Pattern Groups.

There are 3,835,791,613,181,952,000 order 7 concentric magic squares. Program Order7Ccount.

Even Order

There are 736,347,893,760 order 6 concentric magic squares. Program Order6Ccount.


MagicRectangles makes these squares and non-square rectangles.

Order5Special makes the 174,240 order 5 concentric squares.

Order6CSample makes a sample of the order 6 concentric squares. Order6C makes the 4x4 center squares and border groups for all the squares.