18 Sep
2008
18 Sep
'08
11:01 a.m.
To connect two distinct discussion threads, Ben Franklin worked on magic squares in his "youth": http://www.mathpages.com/home/kmath155.htm At 08:59 AM 9/18/2008, Ed Pegg Jr wrote:
Two items dealing with both magic squares and combinatorial designs.
Two 4x4 squares containing every double from 1-16. http://demonstrations.wolfram.com/MagicSquaresAndDesigns/
Four 8x8 squares containing every double from 1-64. http://demonstrations.wolfram.com/The26481Design/
Similar constructions have been proven impossible for the 6x6, 10x10, 14x14, 22x22.
Existence of designs for 12x12,18x18, 20x20 are all unsolved problems, in square form or not.
The designs behind a possible set of 16x16 squares exist, but I haven't mapped them to a magic square form.