Looking for a challenge beyond Sudoku puzzles? Benjamin Franklin,born 300 years ago on 17 January 1706 (see SlashDot story) , also jotted down a couple of much more complex number puzzles of his own, so called magic squares.
Magic squares are characterised by having the sum of the elements of all rows, columns, and main diagonals having the same sum. Over the years, rows and columns were added to magic squares, rules developed around them as well as competition to figure out how many variations of each magic square are possible.
Counting the number of distinct normal magic squares is a difficult problem in combinatorics., and Benjamin Franklin’s variation on the 8×8 Magic Square, has defeated all such attempts untill now as reported in the Globe and Mail, a University of Manitoba’s department of physics and astronomy professor,Dr. Peter Loly, has computed how many permutations are possible under his distinct mathematical design, 1,105,920, in a paper published online by the Proceedings of the Royal Society :Enumerating the bent diagonal squares of Dr Benjamin Franklin.
Prof Loly was also interviewed by on CBC’s radio’s ‘As It Happens’ (Realplay Ram).
For related information checkout Ben Franklin’s 8×8 Magic Square by William H. Richardson of the Wichita State University.