Simon Whitechapel first contacted me regarding magic stars in an email dated June 26, 2001.
...I've linked to it from a small page on magic stars I've written myself (I've called them magic polygrams): http://www.gwywyr.com/articles/scimaths/polmagic.html
I put the complements of orders 15 to 20
which I took from his site (with his permission) on my
At that time he had found solutions for orders 6 to 20, but only for pattern A. He has now (March 2005) found
a solution for pattern A of all orders up to 100. Also a solution for order 166 with S = 666.
In an email of July 16, 2001, he describes his Pascal program this way.
It's very crude but I hope it will work okay for you. Essentially what it does is set up an array to represent the magic star, count the total of each line, then swap two random points at a time until the (sum of totals) - (magic-total*vertices) drops, ideally to zero. When you've found a magic star, you can save it to disk, then read it again as required. I don't understand magic stars well enough to make the search systematic, so I'd be interested to see your exe program and its Basic listing.
In an August 31, 2003 email he says (in part)
Thanks for your previous reply. Since then I've written a program that finds magic polygrams much quicker than my previous one, and I hope the following is data for magic 21-, 22-, and 23-agrams.
This solution for a 23-v magic polygram was included in the above email:
Line by line values are (35,27,7,25),(30,7,26,31),(25,26,21,22),(31,21,41,1),(22,41,15,16),(1,15,40,38), (16,40,20,18),(38,20,19,17),(18,19,46,11),(17,46,2,29),(11,2,39,42),(29,39,3,23),(42,3,4,45),(23,4,34,33), (45,34,5,10),(33,5,44,12),(10,44,32,8),(12,32,37,13),(8,37,43,6),(13,43,24,14),(6,24,36,28),(14,36,9,35), (28,9,27,30)
Peak values are35,30,25,31,22,1,16,38,18,17,11,29,42,23,45,33,10,12,8,13,6,14,28 Valley values are 27,7,26,21,41,15,40,20,19,46,2,39,3,4,34,5,44,32,37,43,24,36,9.
In an email of September 2, 2003
No, I've been surprised by how quick it is: I found a 21-agram in just under 60 seconds today (and I haven't got a fast computer). Here are three more big stars, each of which took less than half-an-hour to find.
Attached were solutions for orders 24, 25, and 26 stars.
Email of September 8, 2003
I've now got polygrams 6-50, with the 29-agram found in under ten seconds. Funny that last month I was wondering if I'd ever be able to get the 21-agram...
Email of September 9, 2003
I'm attaching the data for the stars in a text file.
I've started at the 15-agram, because this program doesn't use a stochastic search, so the polygrams are found in the same way each time, and one consequence is that they always start with lines 1 and 7 of the set of lines summing to the magic total. The ones I sent previously were found randomly, so there are no obvious patterns like that in them. The program could find all possible polygrams for a particular vertex total too. I'm searching for the 55-agram at the moment, because the magic total is 222, and I'd like to try the 166-agram (mt=666) sometime, but I've started looking at the order-b polygrams now too.
Email of November 1, 2003
I've had no success with order-b polygrams etc, I'm afraid, but I've got 15-100 in order-a now, plus some isolated higher ones (e.g. the 166, mt 666). I've also been working on magic circles and spheres -- an example is attached.
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This page last updated May 19, 2007
Copyright © 2005 by Harvey D. Heinz