On March 22, 2007 I first heard about a new magic square discovery in The Netherlands
“Three Dutch secondary school pupils have created the ‘most magical magic square in 5,000 years’,…” [1]
Order12 HSA Square

A lively discussion among magic square friends ensued over the next week. The result? While these students should be complimented on their accomplishment, their imaginative claim was slightly (?) exaggerated. The square in question is a bentdiagonal (Franklintype) order12 square with rows and columns summing correctly. Also present are many other magic patterns found in Franklin type squares. The creators excitement seemed to be due to the fact that the main diagonals also summed correctly, making this a true magic square. This was a feature Ben Franklin did not accomplish in his published squares. It is also symmetric across the central horizontal line. 

Order12 from D. Morris page

I found this square with identical features to the HSA square at Donald Morris’s Franklin Squares site [2]. This was published in 2005 and included a complete method of construction! The HSA square is identical to this square reflected across the leading diagonal !!!! Well... after first swapping columns 5 and 7, then 6 and 8.This pointed out by Jo Geuskens on May 27/07 and Frans Lelieveld on May 30/07. Thanks fellows. 

Order12 from my Mostperfect page

Finally, I compared the HAS square to an order12 Mostperfect magic square on my site. [3] In
the comparison, my square fails on My square also is The HSA (and the Morris) square fails on the mostperfect diagonal test! Strangely, if my square is transposed so that the 1 is in the upper left corner, all horizontal bent diagonals become magic! 

Order12 From Morris email of April
2,2007

Announcement! On April 2, 2007 I received an email from Donald Morris with an order 16 Mostperfect Bent diagonal magic square! [4] Even more surprising was this order 12 square also included in the attachment. It also is a Mostperfect Bent diagonal magic square! To the best of my knowledge, these are the first such squares published! Don tells me he constructed this square in late 2005. 
The Morris Order16 Mostperfect Bent diagonal magic square
Order16 On April 2, 2007, Donald Morris
sent me this order16 magic square that has almost all of the features (68)
found in Franklin's unpublished order16 on my Franklin page. [5]

Order8 Recently Daniel
Schindel,Matthew Rempel And Peter Loly (Winnipeg, Canada) counted the
basic Franklin type bentdiagonal squares of order8. [6] BTW The Peter Loly's count has
been independently corroborated by other sources in Canada and Argentina. Review of requirements to be classed as mostperfect: 1. Doublyeven pandiagonal normal magic squares (i.e. order 4, 8, 12, etc using integers from 1 to n^{2}) 2. Every 2 x 2 block of cells (including wraparound) sum to 2T (where T= n^{2} + 1) (compact) 3. Any pair of integers distant ½n along a diagonal sum to T (complete) 
[1] Announcement of the HSA square
http://www.eurogates.nl/?act=shownews&nid=1856
[2] Donald Morris's Franklin squares site
http://www.bestfranklinsquares.com/franklinsquaresmcm4.html
Not available?
[3] My Mostperfect magic squares page
http://www.geocities.com/~harveyh/mostperfect.htm#Examples
[4] Donald Morris's email address (with his permission) is
donald.morris4@sbcglobal.net
[5] My Franklin magic squares page
http://www.geocities.com/~harveyh/franklin.htm#Comparison
[6] Proc. R. Soc. A (2006) 462, 2271–2279,
doi:10.1098/rspa.2006.1684. Enumerating the bent diagonal squares of Dr Benjamin
Franklin FRS
Published online 28 February 2006. Obtainable by
download from Peter Loly's
home page
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site!
Harvey Heinz harveyheinz@shaw.ca
This page last updated
September 12, 2009
Copyright © 2002 by Harvey D. Heinz