List of the site's news added January 21, 2010

• The 5 enigmas published in 2008, each with a 100€ prize + bottle of champagne, are today still unsolved!
  Republished in 2009 in the Pour La Science website , a new 6th enigma is added.
  Sorry, no, I myself do not have the solutions! Some interesting news (...but none being a solution...) on these difficult enigmas:
• Enigma #1: 3x3 semi-magic squares of squares with S = three times a square found by Lee Morgenstern, USA
• Enigma #1: 3x3 semi-magic squares of squares with two close diagonal sums searched by Frank Rubin, USA
• Enigma #2: 5x5 nearly-bimagic square with 23 correct sums found by Lee Morgenstern, USA
• Enigma #2: no 5x5 bimagic square using 25 distinct integers < 500, computed by Gildas Guillemot, France
• Enigmas #3 and #4: hmmm... nothing interesting...
• Enigma #5: 4x4x4 multiplicative magic cube with MaxNb = 364 found by Max Alekseyev, USA
• Enigma #6: no 5x5 add-mult magic square with MaxNb < 1000 and P < 10^9 * center cell computed by me...
• The paper published in 2008 launching these enigmas is now available through the Internet. See the end of this page.

• On additive-multiplicative magic squares (magic when you add the cells, and again magic when you multiply the cells !) :
• The new 6th enigma already mentionned above is "who can construct a 5x5 add-mult magic square?", meaning that the smallest possible order of add-mult squares is still unknown
• First known add-mult magic squares of orders 27, 28, 30, 32 and of order as BIG as 1024! Thanks to Joshua Zucker and W. Edwin Clark, USA, for their checking of my squares
• Including these new found squares, updated table of known add-mult magic squares, and updated downloadable files among them the full big square of order 1024
• Three historical precisions on add-mult squares:
• Paul Erdös in 1992
  Among problems published in 1974 by J. Dénes - A. D. Keedwell - P. Erdös, one of them was: "For what orders n do addition-multiplication magic squares exist?". This means that my new updated table is the current status on their problem, and that my new 6th enigma is also a part of their problem.
• Walter W. Horner, the first author of this very interesting kind of magic squares in 50's, was in 1966 a retired mathematics teacher of Pittsburgh, Pennsylvania, USA. Sentence found in the Madachy's book. Who can send me his portrait or more biographical information?
• In 1997, the Chinese team Yu Fuxi, Sun Rongguo and Zhang Guiming published the first known add-mult magic square of order 24. Thanks to Zhu Lie, China, who informed me of this paper!

• Results from Lee Morgenstern, USA:
• First know 4x4 nearly-bimagic square with 18 correct sums, and mathematical proof that a 4x4 magic square can't be semi-bimagic
• Exhaustive computing search proving that his 6x6 bimagic square initially found in 2006 is THE smallest possible 6x6 bimagic square.
  This also means that if the Enigma #2 (5x5 bimagic square) is impossible, then the smallest possible bimagic square (of any order) is his 6x6 square of 2006:

72	18	17	16	49	47
13	52	36	5	50	63
38	35	7	66	15	58
20	53	34	39	69	4
55	1	57	56	26	24
21	60	68	37	10	23

• Results from Li Wen, China:
• Panbimagic squares of orders 77, 91, 125 using consecutive integers. Before them, the square of order 36, done by Su Maoting in 2006, was the only known normal panbimagic square.
• First known panTRImagic square, meaning that all its broken diagonals are trimagic!!! Non-normal = using non-consecutive integers. And this big square of order 396 is also a PENTAmagic square!!!
   

• New paper published in Statistical Papers written by George P. H. Styan, Christian Boyer and Ka Lok Chu
• Some comments on Latin squares and on Graeco-Latin squares, illustrated with postage stamps and old playing cards, Vol. 50, N 4, 2009, pages 917-941, http://www.springerlink.com/(...)

• My three papers published in The Mathematical Intelligencer can be ordered through the Internet, and their first page can be freely seen:
• Some Notes on the Magic Squares of Squares Problem, Vol. 27, N 2, 2005, pages 52-64, http://www.springerlink.com/(...)
• Sudoku's French ancestors, Article and Problems, Vol. 29, N 1, 2007, pages 37-44, http://www.springerlink.com/(...)
• Sudoku's French ancestors, Solutions to the Problems, Vol. 29, N 2, 2007, pages 59-63, http://www.springerlink.com/(...)

• On my several papers published in Pour La Science (the French edition of Scientific American), three can be ordered -only 1€ each!- through the Internet, and their beginning can be freely seen:
                                 (my other papers can't be seen, their archives before 2004 being not yet online)
• Les Ancêtres Français du Sudoku, N°344, June 2006, pages 8-11, http://www.pourlascience.fr/(...)
             and their solutions, same issue, page 89, http://www.pourlascience.fr/(...)
• Enigmes sur les Carrés Magiques, Dossier N°59, April-June 2008, pages 22-25, http://www.dossierpourlascience.fr/(...)
• Les Nombres Taxicabs, Dossier N°59, April-June 2008, pages 26-28, http://www.dossierpourlascience.fr/(...)

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