Can you construct a square of sixteen different numbers so that it shall
be magic (that is, adding up alike in the four rows, four columns, and
two diagonals), whether you turn the diagram upside down or not? You must
not use a 3, 4, or 5, as these figures will not reverse; but a 6 may
become a 9 when reversed, a 9 a 6, a 7 a 2, and a 2 a 7. The 1, 8, and 0
will read the same both ways. Remember that the constant must not be
changed by the reversal.