Can you create a 4x4 magic square that still works with the same total when turned upside down?

[A Magic Square is a grid of numbers whose rows, columns and long diagonals add up to the same total. All the numbers in the square must be different.]

[By 'turned upside down' I mean that if 106 is the number in the top left corner in the original magic square, then 901 is in the bottom right corner of the inverted square]

Since 1s and 8s look the same when flipped and 6s and 9s switch, if you have one of each number in the ones place and in the tens place it would work.

Using the grids of ABCD magic squares, you can construct one of these.

ABCD Simply using reflections and rotations on this grid will give
DCBA another grid of the same type. Just replace A through D with
BADC a number 1, 6, 8, 9 and it should work. Then put the two grids
CDAB together with one digit equalling the tens place and the other
grid equalling the ones place, and you have a magic square created.
Other places can be added in the same way. :)

Maybe someone could devise a program that creates these this way? :)

Posted by Gamer on 2003-11-22 14:16:55