| proposed by | Toby Walsh tw@cs.york.ac.uk |
There are several interesting variations. For example, we may insist on certain values in certain squares (like in quasigroup completion) and ask if the magic square can be completed. In a heterosquare, each row, column and diagonal sums to a different value. In an anti-magic square, the row, column and diagonal sums form a sequence of consecutive integers.
A magic sequence of length n is a sequence of integers x0 . . xn-1 between 0 and n-1, such that for all i in 0 to n-1, the number i occurs exactly xi times in the sequence. For instance, 6,2,1,0,0,0,1,0,0,0 is a magic sequence since 0 occurs 6 times in it, 1 occurs twice, ...