Sandeep Koranne <koranne@natlab.research.philips.com> wrote:
+---------------
| Magic Sqares of 3x3 and 4x4 have a lot of differences.
| Odd Magic squares can be easily computed using GO-UP GO-LEFT AND ADD method.
+---------------
Yup. Or as I learned it, UP+RIGHT -- OOPS,STEP-DOWN.
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| Even magic squares a a bit more tricky.
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I vaguely recall some procedure for even magic squares in which you
first factor the square into even and non-even components, so you have
an even supersquare of odd subblocks. Then you:
1. Solve the even supersquare by some method [e.g., see below]
2. Solve one off subblock
3. Put the solved odd subblock wherever the "1" is in the even
superblock solution, and fill in the remaining subblocks with
multiples of odd solution, using the number in the even superblock
position as a multiplier for every element of the subblock.
Or something like that...
-Rob
p.s. Aha! The Web is your friend!
<URL:http://mathworld.wolfram.com/MagicSquare.html> gives a method for
"doubly-even" squares that are 4*m on a side ("draw X's through the four
subsquares...then swap..."), and one for "singly-even" squares 4*m+2 on
a side [for m>1 only!] (which J. H. Conway calls the "LUX" method).
That page also calls the "UP+RIGHT/STEP-DOWN" method for odd squares
"the Siamese method".
-----
Rob Warnock, 41L-955 rpw3@sgi.com
Applied Networking http://reality.sgi.com/rpw3/
Silicon Graphics, Inc. Phone: 650-933-1673
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