Office Applications and Entertainment, Magic Squares of Subtraction

Enumeration Magic Squares of Subtraction (4 x 4)

The total number of magic series for order 4 Magic Squares of Subtraction is 1820. The frequency (n4) of the occurring residuum values for these magic series is shown below.

Res4 n4 n9 2 91 0 3 156 0 4 198 2632 5 220 3188 6 225 10868 7 216 3456 8 196 4160 9 168 176 10 135 8 11 100 0 12 66 0 13 36 0 14 13 0 Total 1820 24488

The resulting number (n9) of (unique) Squares of Subtraction per applicable Residuum Value, as counted with routine SubtrSqrs4, is summarised in the table above and confirms the findings of Henryk Fuks (24488).

Attachment 4.1 shows for miscellaneous symmetries (Dudeney Classification) the (unique) Magic Squares of Subtraction, which could be found within this collection for Res4 = 4, 6 and 8.

Attachment 4.2 shows the (unique) Magic Squares of Subtraction (Res4 = 4, 6 and 8), for which the Main - and Broken Diagonals sum to the Magic Sum s4 = 34.