This problem concerns a square that is the opposite of a magic square (which has equal row and column sums).

Find a 446 x 446 matrix with entries from {-1, 0, +1} such that the 892 row and column sums are all distinct?

Source: Richard Guy, from a translation by Loren Larson of a Swedish problem book of Paul Vaderlind.Enthusiasts: The odd case seems to be unsolved (though it is easy to deal with the 3 x 3 case by a computer search).

© Copyright 1999 Stan Wagon. Reproduced with permission.

22 September 1999