Explanation 31x31 magic square

The 31x31 magic square is odd and a prime number. To construct a 31x31 magic square use the same methods to construct a 5x5, 7x7, 11x11, 13x13, 17x17, 19x19, 23x23 and 29x29 magic square. Most perfect magic 31x31 square is panmagic and symmetric.

For more detailed explanation see the 5x5 magic square.

Construction methods

The methods to construct an 31x31 magic square are:

• Diagonal method
• Siamese method
• Knight movement method
• Symmetric transformation
• Lozenge method
• Shift method
• Ultra magic
• Pan 29x29 in 31x31 (1)
• Pan 29x29 in 31x31 (2)
• Concentric
• Concentric with diamond

With the first five methods you can construct simple, symmetric 31x31 magic squares.

Use the shift method to construct panmagic 31x31 squares.

The ultra magic 31x31 square is panmagic and symmetric.

Pan 29x29 in 31x31 and concentric [with diamond] are specials.