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From: Peter_Gutmann@kcbbs.gen.nz (Peter Gutmann)

Newsgroups: sci.crypt

Subject: Re: About "magic squares"

Message-ID: <25517.829222906@kcbbs.gen.nz>

Date: 23 Mar 92 07:05:17 GMT

Organization: Kappa Crucis Unix BBS, Auckland, New Zealand

Lines: 36

 

 

  

In article <1992Mar18.103506.8546@i2unix.dist.unige.it>,   

    ab@dist.dist.unige.it (Alessandro Berni) writes:  

  

> A friend has shown me the following "magic square"  

>   

>           4 | 9 | 2  

>           ---------  

>           3 | 5 | 7  

>           ---------  

>           8 | 1 | 6  

>   

> the sum of each row/colums/diagonal is 15. The question I was posed  

> was: "does it exists a rule to create a similar square with sum=17 or  

> sum=25" ?  

  

No (well, not as far as I know anyway:-).  The formula for a generalized  

magic square is:  

  

    a-c  a-b+c  a+b  

   a+b+c   a   a-b-c  

    a-b  a+b-c  a+c  

  

where 'a' is 1/3 of the magic number (thus the magic number has to be a  

multiple of 3).  In addition, if the numbers of the square are to be  

consecutive positive integers, 'a' must be >= 5, 'b' must be 1, and 'c' must  

be 3.  

  

--  

    pgut1@cs.aukuni.ac.nz || peterg@kcbbs.gen.nz || peter@nacjack.gen.nz  

                           (In order of preference)  

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