List of the site's news added June 2nd, 2020

• TEN YEARS after their opening (April 2010), there still remain eight unsolved enigmas for winning €6,500 and eight bottles of champagne!
  The remaining enigmas are on small squares, from 3x3 to 6x6. Here are the most interesting recent results on them:
• #1 (3x3 magic square of squares, or using at least 7 distinct squared integers), new researches (Feb. 2017 - May 2020) from Lee Morgenstern, Randall Rathbun, Christian Woll, Joseph Hurban, Adrian Suter, Benjamin Bartsch, Eddie Gutierrez, Giancarlo Labruna, Vlad Volosatov, Arkadiusz Wesolowski, Onno Cain, Ben Asselstine, Sunil Kumar.
• Maybe, for some (x, y), a cell below in red can become the required 7th squared integer? It would be a solution of the enigma!
  Wesolowski's 3x3 magic square of 6 squares

(xy - z)²	(xz + y)²	x² + y²z²
(x + yz)²	(x² + y²)(z² + 1)/2	(xz - y)²
x²z² + y²	(yz - x)²	(xy + z)²

• #2 (5x5 bimagic square), "special" bimagic squares using 6 sets of numbers by Frank Rubin, or modulo 41 by Christian Boyer
• #4a (5x5 magic square of cubes), no solution with S3 < 400,000,000 computed by Nicolas Rouanet, but 44 semi-magic squares without any magic diagonal
• #4b (6x6 magic square of cubes), no solution with S3 < 3,000,000 computed by Nicolas Rouanet, but 45 semi-magic squares with one magic diagonal
• #6 (5x5 add-mult magic square), 63 examples of add-mult semi-magic squares which are also add panmagic Graeco-Latin squares, by Keith Lynch and Christian Boyer

• On bimagic squares
• Semi-bimagic squares of prime numbers, orders 5, 6, 7 by Nicolas Rouanet
• Bimagic squares of prime numbers, orders 8 to 25 by Nicolas Rouanet (only excluding orders 12 and 14)
• Bimagic squares of consecutive prime numbers, orders 24 to 28 by Huang Jianchao
• Margaret Kepner's work is a bimagic square of order 25, as reported by Reijo Sund, Ka Lok Chu, and George P. H. Styan
   Margaret Kepner and her work
• Big bimagic squares, orders 65 to 100, by six Chinese researchers

• On trimagic squares
• New researches on trimagic squares of order 12 by Walter Trump, sixteen years after his first square
• Square of order 13 with 13 trimagic rows, 11 trimagic columns, 1 trimagic diagonal by Nicolas Rouanet, better than the previous best known square...
  ....but fully trimagic square of this order still unknown!

• On magic squares of powers
• 11 parametric solutions of 4x4 magic squares of squares found by Seiji Tomita
• Magic squares of squares of prime numbers of orders 6, 7, 8, by Nicolas Rouanet
• Magic squares of cubes of orders 13 to 31, by Nicolas Rouanet (only excluding already known orders 16 and 24)
• Nearly-magic squares of consecutive 4th powers, order 10 and order 12, by Nicolas Rouanet

• On multimagic series
• Updated impossibility proofs of multimagic series for squares up to order 44 and up to octamagic, by Lee Morgenstern
• Formula for estimating the number of trimagic series for cubes, by Dirk Kinnaes
   

• On multiplicative magic squares and cubes
• New best known pandiagonal multiplicative magic squares of orders 9 and 16, by Elbert Krison, only 15 years old!!!
• Two new best known multiplicative semi-magic cubes of order 3, with one magic triagonal, by Elbert Krison, a surprise that this small order can still be improved

3	28	80		8	105	18
160	6	7		21	48	15
14	40	12		90	3	56
16	5	84		30	6	84
21	32	10		12	35	36
20	42	8		42	72	5
140	48	1		63	24	10
2	35	96		60	9	28
24	4	70		4	70	54

• New best known multiplicative magic cubes of orders 8, 9, 10, 11, by Elbert Krison, mentionned (c) in the table

• And also...
• Biographical sketch of Lee Morgenstern, a big contributor of researches and results, since 2006, in these webpages
• Extended biographical sketch of Walter W. Horner, author of the first add-mult magic squares, thanks again to his son Robert
• New page listing website's biographies, with direct access to this page from the main menu on the left, part "To know more"
• Claude Bégin's webpages (Canadian, in French) added in the links, and many thanks for his various references to my work and webpages!
• Thanks to La Recherche and Philippe Pajot, publishing in July-August 2017 (pages 101-104, 110-111) my paper and problems on magic squares and cubes (also on their website)
• John Conway passed away April 11, 2020, from complications related to COVID-19. The mathematician, author of the famous Game of Life, did this lecture on magic squares in 2014:
   https://www.youtube.com/watch?v=ZK-RXLJT7eM

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