A Reversible Magic Square102
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.