Consider one of the 880 order 4 magic squares. .6, 12, .9, .7, 15, .1, .4, 14, .3, 13, 16, .2, 10, .8, .5, 11 If these weights are placed on the odd-odd vertices from (-3,-3) to (3,3), then this will balance perfectly on the center point (0,0). Square each number, and it will still remain perfectly balanced. There are 48 4x4 magic squares with this property. .36, 144, .81, .49, 225, ..1, .16, 196, ..9, 169, 256, ..4, 100, .64, .25, 121 Cube each number, and this magic square is still perfectly balanced. And the same when the numbers are raised to the 4th powers. (But not the 5th or 6th powers) This is the only magic square that remains balanced at powers 3 and 4. .216, 1728, .729, .343, 3375, ...1, ..64, 2744, ..27, 2197, 4096, ...8, 1000, .512, .125, 1331 --Ed Pegg Jr