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From: eli@uw-june.UUCP
Newsgroups: net.math
Subject: Re: n x n magic squares, even n
Message-ID: <1383@uw-june>
Date: Fri, 4-May-84 15:11:12 EDT
Article-I.D.: uw-june.1383
Posted: Fri May  4 15:11:12 1984
Date-Received: Sat, 5-May-84 01:44:33 EDT
References: <551@aecom.UUCP>
Organization: U. Washington, Computer Sci
Lines: 20

The rules I learned for composing magic squares are indeed different for
even and odd n.  For even n,

    var    square: array[1..20, 1..20] of integer;

    begin
        for i := 1 to n do
            for j := 1 to n do
                if (i = j) or (i = n - j + 1) then
                    square[i, j] := n * (n - i) + (n - j + 1)
	        else
                    square[i, j] := n * (i - 1) + j;
    end;

Conceptually you are numbering the squares not on the main diagonals, from
left to right, top to bottom, counting up from 1 to n^2, and numbering the
square on the main diagonal, from left to right, top to bottom counting
down from n^2 to 1.

... uw-june!eli