MULTIMAGIE.COM - October 2010 news

List of the site's news added October 11, 2010

Martin Gardner, the master of mathematical recreations, unfortunately died May 22, 2010. He was 95. See for example The New York Times.

In 2003 with Walter Trump, we had been happy to be the first to solve a Martin Gardner's problem posed in Scientific American in 1976: “Is there a perfect magic cube of order 5? No one knows”. Orders 3 and 4 were previously proved impossible.
Fermat worked also on the subject, sending to Mersenne in 1640 a nearly-perfect magic cube of order 4.
A few weeks after our discovery, we were very proud to receive a letter from Oklahoma: Martin Gardner sent us some kind handwritten words, now scanned with emotion.
My enigma #1 is inspired by one of his other problems, but not yet solved: construct a 3x3 magic square of squares. The enigma should be easier, only 7 squared integers are asked...

Toshihiro Shirakawa solved two enigmas, winning a total of €1,100 and two bottles of champagne:

#5, first known multiplicative magic cube using integers < 364, with a very ingenious method needing no computing!
>>> Here winning his first Moët & Chandon bottle, with his cube! >>>

#3a, first known 7x7 semi-magic square of cubes, but this time with a computer

After these two solved enigmas, there still remains ten enigmas for winning €6,900 and ten bottles!

#5

#3a

First known 12x12 semi-magic square of 4th powers, by François Labelle.
Updated table of first known magic squares of powers with above Shirakawa's 7x7 and Labelle's 12x12 results. But a lot of cells of this table are still waiting the first discoverers!

Here are the other most interesting results received on enigmas, but enigmas still unsolved:

#1 (3x3 magic square using 7 distinct squared integers), Lee Sallows constructed a 3x3 magic square having 7 distinct squared... Gaussian integers!
#2 (5x5 bimagic square), Michael Quist found a 5x5 nearly bimagic square with 23 of 24 sums correct. With smaller integers and sums than the square previously found by Lee Morgenstern, one year earlier.
#3 (3x3 semi-magic square of cubes), Lee Morgenstern proposed two new methods which may perhaps solve this enigma
#4b (6x6 magic square of cubes), best possible 6x6 semi-magic square of cubes, by Toshihiro Shirakawa, confirmed by Lee Morgenstern
#4c (7x7 magic square of cubes), 7x7 nearly-magic square of cubes, with one magic diagonal, by Toshihiro Shirakawa
#6 (5x5 add-mult magic square), Jérôme Crétaux, famous for cracking the French e-health insurance card, found a 5x5 add-mult semi-magic square

Toshihiro Shirakawa found other excellent results:

first known 7x7 add-mult semi-magic squares
first known 10x10, 11x11, 14x14, 22x22, 26x26 add-mult magic squares
new best known 5x5x5, 6x6x6 and 7x7x7 multiplicative magic cubes
with these results, updated tables and updated Excel files of:

first known add-mult magic squares of orders < 10 and best known of orders >= 8 for a better (but still partial) answer to the Dénes - Keedwell - Erdös problem
best known multiplicative magic cubes

Many thanks to
Ivars Peterson, Ian Stewart, Ed Pegg Jr, David Larousserie, Christoph Pöppe, Philippe Ribeau, Michel Criton, Jean Moreau de Saint-Martin, Jean-Paul Delahaye, Roger Mansuy, with and others... for their announcements of the twelve enigmas and prizes

Because the statistics on multimagie.com clearly show that the pages in English are much more seen than the pages in French, the default language of www.multimagie.com is now English. Both French and German pages are always available, but if you want to have your language directly selected, you now have to enter with:

www.multimagie.com for English (or www.multimagie.com/en.htm, or www.multimagie.com/indexengl.htm still working)
www.multimagie.com/fr.htm for French (and no more www.multimagie.com)
www.multimagie.com/de.htm for German (or www.multimagie.com/indexdeut.htm, as before)

Anyway, it is always possible to change the language at any time during your connection, simply clicking on the flag or or in the banner.

Return to the home page http://www.multimagie.com