The squares are Orthogonal with respect to each other, i.e., added without repetition. Have a regular pattern of characters in each row, and column Irregular. Panmagic squares which cannot be decomposed into regularly patterned Latin squares are called Irregular Pan-Magic Squares . Mutsumi Suzuk has recently described Abe Gakuho's construction technique for these squares which he called Pairwise Exchange .
Irregular squares are nor further considered here.
In addition, so can the subsequent assembly of the Latin squares into one Graeco-Latin square. The two Latin squares are identical but rotated. With larger prime number magic squares, there are more options. A generalized Knight's move consists of any length of step forward and one step to the side, e.g., 1x1, 2x1, 3x1, 4x1, etc. 6x1 Order-7 Latin Squares.