# Types of Magic Squares

• Normal Magic Square: A normal magic square is one in which only the natural numbers 1, 2, 3, ...n*n are used to fill an n by n grid. The lo-shu is an example of a normal magic square; only the numbers 1 through 9 are used to fill the 3 by 3 grid.

 8 1 6 3 5 7 4 9 2

• Even/Odd Order Magic Squares: Magic squares of even order contain an even number of rows and an even number of columns while magic squares of odd order contain an odd number of rows and an odd number of columns.
• Doubly Even Magic Squares: Doubly even magic squares are all those whose order (for an n by n, the order is n) is a multiple of 4.
• Singly Even Magic Squares: Singly even magic squares are all other even order magic squares.
• Pandiagonal Magic Squares: Pandiagonal (a. k. a. panmagic or perfect) magic squares occur when the entries of the broken diagonals also sum to the magic constant. The magic square in Durer's Melancholia is one example of a pandiagonal magic square.

 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1

• Regular Magic Squares: A regular (a. k. a. associated) magic square occurs when the sum of any two numbers located in cells diametrically equidistant from the center of the square equals the sum of the first and last terms of the square. Both the lo-shu and Durer's magic square are examples of regular magic squares.