eliovson@aecom.UUCP (05/02/84)
On 5/1 I was introduced to a technique for developing
the magic square, where all columns, any direction (including diagnols)
add up to the same sum- for example:
_________________________________________________________
generation : O 3 3 3 |
of a : OOO OOO 2OO 2 6 2 6 276 276 |
3 X 3 : OOO OOOOO 1OOOO 1 5OO 1 5 9 1 5 9 951 |
magic : OOO OOO OOO 4OO 4 8 438 438 |
square : O O O 7 |
----------------------------------------------------------
When I sat down to write a program for the following I ran into
a small problem- does this only work with ODD squares? ie-
1 2 3 4 4
5 6 7 8 3 8
9 10 11 12 2 7 12
13 14 15 16 1 6 11 16
5 10 15
9 14
13
1st 2nd
leaves me blind-
So all you puzzlers out there- a formula or subroutine
would be much appreciated, and as our system doesn't
give access to net.sources any answers should be directly
mailed to me.
Thanks alot, "Today is the Tommorrow
moshe eliovson you worried about
yesterday."
{spike|rocky2|philabs|pegasus|esquire|cucard}!aecom!eliovsonmerlyn@sequent.UUCP (05/04/84)
> From: eliovson@aecom.UUCP > Message-ID: <551@aecom.UUCP> > Date: Tue, 1-May-84 19:30:38 PDT > > On 5/1 I was introduced to a technique for developing > the magic square... > ...When I sat down to write a program for the following I ran into > a small problem- does this only work with ODD squares? Yes, only ODD squares are possible with this method. It appears to be isomorphic with a method I learned long ago: 1. Starting at the middle square of the top row, label that square "1". 2. For each successive number, go up one and right one square, wrapping right side to left and top to bottom as necessary. 3. If the square in step 2 is already taken, backup and go DOWN one instead (from the original square, not the up-right one). 4. Fill in that square with the next higher number, and repeat. This one automatically generates any ODD-sized magic square. Evidently, even ones are harder to generate. I haven't seen an algorithm for them yet. I have a few special case ones, but that's about it. Randal L. ("Entertainment = MagiC^2") Schwartz, esq. (merlyn@sequent.UUCP) (Official legendary sorcerer of the 1984 Summer Olympics) Sequent Computer Systems, Inc. (503)626-5700 (sequent = 1/quosine) UUCP: ...!XXX!sequent!merlyn where XXX is one of: decwrl nsc ogcvax pur-ee rocks34 shell teneron unisoft vax135 verdix Original Material (C) 1984 by Randal L. Schwartz [ALL RIGHTS RESERVED]
colonel@gloria.UUCP (05/05/84)
[Find the flaw in this proof: ""] There is no "easy" way to make an even magic square. See any standard reference on puzzles. -- Col. G. L. Sicherman ...seismo!rochester!rocksvax!sunybcs!gloria!colonel