List of the site's news added October 6th, 2006

• Sudoku's French ancestors, article published in Pour La Science, June 2006. And soon in The Mathematical Intelligencer! See also the Michel Feuillée's letter, France, including an interesting 16x16 sudoku problem.

• A lot of new impressive discoveries, by Lee Morgenstern, USA:
• first known 7x7 bimagic squares using distinct positive integers (eight different squares!)
• two 6x6 bimagic squares with smaller sums than the Jaroslaw Wroblewski's squares
• a 5x5 nearly bimagic square with 23 correct sums out of 24
• construction method of 4x4 magic squares of n-th powers, with the first known 4x4 semi-magic square of cubes:

163	203	183	1923
1803	813	903	153
1083	1353	1503	93
23	1603	1443	243

• other discoveries on 5x5, 6x6, 7x7, 8x8, 9x9 squares of cubes (including 6x6 and 9x9 methods)

• Using the Morgenstern's 4x4 and 9x9 powerful methods, and my own 8x8 method, I generated:
• first known 9x9 semi-magic square of cubes
• first known 4x4 , 8x8 and 9x9 semi-magic squares of fourth powers

• On multiplicative magic squares:
• Games for you! I discovered that G. Pfeffermann, France, published multiplicative squares in 1893. But they were published as games: will you succeed to fill his 3x3, 4x4 and 5x5 multiplicative squares? He found the smallest possible 3x3 square twenty years before Harry Sayles.
• Pandiagonal multiplicative magic square of order 6 are possible. Here is my new 6x6 record using the smallest known magic product. It is also a "most-perfect" square.

5	720	160	45	80	1440
4800	12	150	192	300	6
9	400	288	25	144	800
320	180	10	2880	20	90
75	48	2400	3	1200	96
576	100	18	1600	36	50

• With this order 6, a lot of new other best known pandiagonal multiplicative magic squares built in 2006: orders 8, 9, 10, and more...
  Look at the table summarizing the best known pandiagonal multiplicative squares.

• On multiplicative magic cubes:
• Best known multiplicative magic cube of order 6.
• Added image of multiplicative magic cube of order 3.

• Latest research on trimagic squares:
• 13th-order square with some trimagic properties, by Fredrik Jansson, Finland. Who will construct the first known 13th-order trimagic square?
• 48th-order "very nearly" trimagic square, by Louis Caya, Canada. Who will construct the first known 48th-order trimagic square?

• A lot of first known bimagic squares, orders < 64:
• 18, 21, 22, 23, by Jacques Guéron, France
• 26, 31 by Chen Qinwu, 23, 29 by Chen Qinwu-Chen Mutian, China
• 30, 33 by Su Maoting, 39, 50, 54, 56 by Gao Zhiyuan, 42, 51, 57 by Gao Zhiyuan-Su Maoting, China
• 44, 52, 60, 63 by Pan Fengchu, 55 by Li Wen, China
• but... see the new updated table of bimagic/trimagic squares from order 17 to 64, a lot of bimagic and trimagic squares are still unknown

• Two new photos (years 1969 and 1981) added in the biography (in French) of Charles Devimeux. Thanks to Mrs Annick Devimeux.

• ??!!??  REMINDER of some of the most wanted problems on "small" objects, extracted from the updated Problems page:
• is it possible to construct a 3x3 magic square of squares? (using distinct integers)
• is it possible to construct a 4x4 magic square of cubes? (using distinct positive integers)
• is it possible to construct a 5x5 bimagic square? (using distinct integers)
• is it possible to construct a ?x?x? multiplicative magic cube using distinct integers < 416?

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