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.
- 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.