31x31 magic square


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:


With the first three 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.


A concentric 31x31 magic square is a 3x3 in 5x5 in 7x7 in 9x9 in 11x11 in 13x13 in 15x15 in 17x17 in 19x19 in 21x21 in 23x23 in 25x25 in 27x27 in 29x29 in 31x31 magic square.