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

16 |
20 |
18 |
192 |

180 |
81 |
90 |
15 |

108 |
135 |
150 |
9 |

2 |
160 |
144 |
24 |

- Using the Morgenstern's 4x4 and 9x9 powerful methods, and my own 8x8 method, I generated:

- 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.
- 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.

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 |

- 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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