27x27 magic square

 

Explanation 27x27 magic square

The 27x27 magic square is odd and a multiple of 3 (3x9). Use 3x3 an ultra magic 9x9 square to construct an ultra magic 27x27 square.

 

Construction methods:

Methods to construct the 27x27 magic square are:

Composite (1) and (2) lead to simple magic 27x27 squares.

 

Composite (3) leads to a magic square consisting of 81 (semi)magic 3x3 squares, so each 1/9 row/column gives 1/9 of the magic sum. The 27x27 magic square is 3x3 compact too.

 

Composite (4) leads to a magic square consisting of 9 ultramagic 9x9 squares, so each 1/3 row/column/diagonal gives 1/3 of the magic sum. The 27x27 magic square is also panmagic, 3x3 compact and symmetric, and that is ultramagic.

 

Diagonal method,  Siamese method and knight movement method lead to simple, symmetric magic 27x27 squares.

 

Use the shift method to construct panmagic 27x27 squares.

 

The ultra magic 27x27 square is panmagic, 3x3 compact, symmetric and each 1/9 row/column gives 1/9 of the magic sum and each 1/3 diagonal gives 1/3 of the magic sum.

 

Ultra 25x25 in 27x27 and concentric are specials.