From: phil kenny Newsgroups: sci.math Subject: Re: Magic square Date: Sun, 25 Jan 1998 12:10:19 -0800 Baptiste Heyman wrote: > > Does anyone know if there is a 6x6 magic square ? > > -------------------==== Posted via Deja News ====----------------------- > http://www.dejanews.com/ Search, Read, Post to Usenet Here is a 6x6 magic square with an unusual property. If you strip off the outer border of cells, a 4x4 magic square remains. 1 35 30 5 34 6 33 11 24 25 14 4 28 18 21 20 15 9 10 22 17 16 19 27 8 23 12 13 26 29 31 2 7 32 3 36 This appeared in a Dover publication: "Magic Squares and Cubes" by W. S. Andrews, 1960. Sorry, no ISBN. Several other examples of 'concentric' magic squares also are listed in this reference. Regards, phil kenny ============================================================================== From: Baptiste Heyman Newsgroups: sci.math Subject: Re: Magic Squares Date: Sat, 28 Mar 1998 21:36:39 +0100 Anton Ivanov wrote: > > I am working on an age-old problem: magic squares. I have found the > procedure for the 3x3 squares, but I can't seem to find one for 5x5 and > so on. Does anyone know of one? 5 4 10 !---!---!---!---!---! ! 3 ! ! 9 ! !15 ! !---!---!---!---!---! 2 ! ! 8 ! !14 ! !20 !---!---!---!---!---! 1 ! 7 ! !13 ! !19 ! 25 !---!---!---!---!---! 6 ! !12 ! !18 ! !24 !---!---!---!---!---! !11 ! !17 ! !23 ! !---!---!---!---!---! 16 22 21 !---!---!---!---!---! ! 3 !16 ! 9 !22 !15 ! !---!---!---!---!---! !20 ! 8 !21 !14 ! 2 ! !---!---!---!---!---! ! 7 !25 !13 ! 1 !19 ! !---!---!---!---!---! !24 !12 ! 5 !18 ! 6 ! !---!---!---!---!---! !11 ! 4 !17 !10 !23 ! !---!---!---!---!---! ============================================================================== From: jasonp@Glue.umd.edu (Jason Stratos Papadopoulos) Newsgroups: sci.math Subject: Re: Magic square Date: 26 Jan 1998 08:13:47 GMT GSimp95605 (gsimp95605@aol.com) wrote: : isn't there an algorithm for "all" nxn magic squares where n>2 and the : individual squares are filled with the numbers 1,2,3,... n^2? : I know it for odd n, and about a month ago I saw one for even n. This was posted here a long time ago. Note also that the International Obfuscated C Code Contest had a magic square generator win the "most obfuscated algorithm" award a while back. The program is pretty neat, but don't learn the algorithm from it! Anyway, the most general method I've seen is given in "Magic Squares and Cubes", but requires solving (what seems to me) a really complicated combinatorics problem. Rather than repeat myself, look in DejaNews for a post with "thorny combinatorics problem" in the title. jasonp PS: Many more magic squares of odd size are possible than what the poster mentioned; in particular you can start from anywhere in the square except the middle, but the rules change slightly depending on where you start. -------------------------------------------------------------------------- From: "Shin, Kwon Young" Newsgroups: sci.math Subject: Perfect Magic Square Solution Date: Tue, 01 Apr 1997 01:35:53 +0900 THE SOLUTION FOR "THE MAGIC SQUARE" =================================== Have you ever heard of the 'Magic Square'? It's a mathematical 'brain-twister' where the sum of the numbers of a row, column or diagonal in a square n*n is always equal. For example, look at