MULTIMAGIE.COM - May 2011 news

List of the site's news added May 18th, 2011

NEW RECORD! New smallest known magic square of 4th powers, by François Labelle, with:

First known 16x16 magic square of 4th powers, much smaller than Li Wen's 36x36 (the previous record)

François Labelle

Squares of powers by Christian Boyer with:

New smallest known semi-magic square of 5th powers, with a 25x25 semi-magic square of 5th powers, smaller than Li Wen's 36x36 (the previous record)
First known 15x15 semi-magic square of cubes and first known 15x15 semi-magic square of 4th powers

With the new results above, here is the updated table of smallest known magic squares of powers:

Edouard Lucas	Smallest known squares	semi-magic	magic	Leonhard Euler
	of squares	3x3, Edouard Lucas (1876)	4x4, Leonhard Euler (1770)
	of cubes	4x4, Lee Morgenstern (2006)	8x8, Walter Trump (2008)
	of 4th powers	4x4, Morgenstern-Boyer (2006)	16x16, François Labelle (2010) NEW!
	of 5th powers	25x25, Christian Boyer (2011) NEW!	36x36, Li Wen (2008)

But smallest possible squares not yet known! Who will find smaller squares? Only 3x3 semi-magic squares of squares are proved impossible to improve (2x2 being of course impossible!).
The goal of several enigmas (#1, #3, #4, #4a, #4b, #4c) is to improve this table.

There still remain ten enigmas for winning €6,900 and ten bottles!
Here are the most interesting results received on the remaining enigmas, but still unsolved:

From Lee Morgenstern

#1 (3x3 magic square using at least 7 distinct squared integers), a search method

From Toshihiro Shirakawa, the winner of enigmas #3a and #5, very close to solve enigmas #4b, #4c and #6b with only one missing diagonal:

#4a (5x5 magic square of cubes), no solution with magic sum < 46656000. Only semi-magic squares, without any magic diagonal.
#4b (6x6 magic square of cubes), two 6x6 nearly magic squares of cubes each with one magic diagonal
#4c (7x7 magic square of cubes), his 7x7 nearly magic square of cubes, previously found in May 2010, has the smallest possible magic sum allowing one magic diagonal
#6b (7x7 add-mult magic square), a 7x7 nearly add-mult magic square with one add-mult diagonal AND one mult or add diagonal!

From Javier Cilleruelo and Florian Luca

#6 (5x5 add-mult magic square), coincidence, without any contact between us, the problem 2 of their paper in The Electronics Journal of Combinatorics, is the same as this enigma #6!

After the two solved enigmas in 2010, papers reported Toshihiro Shirakawa's solutions. Thanks to Akira Iino, Sugaku Seminar, and Michel Criton, Tangente.

Photo of Jószef Dénes with Paul Erdös taken in summer 1990.
Maybe discussing of their add-mult magic square problem? ;-)...

Photo kindly provided by Donald A. Keedwell. This is probably the first published photo of Jószef Dénes!

G4G October 21, 2010, Paris. Organized by François Dubois (Kafemath) and Pierre Berloquin.
During this event, one of the lectures was on magic squares and cubes:
Deux problèmes de Martin Gardner - Two Gardner's problems, one solved, one unsolved.
PowerPoint file (1.5Mb) in French, by Christian Boyer.

New papers on bimagic squares, from South America:

by Professor Inder Jeet Taneja, Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis, Brazil (his homepage www.mtm.ufsc.br/~taneja)

http://arxiv.org/abs/1010.2083 "Universal Bimagic Squares and the day 10th October 2010 (10.10.10)"
http://arxiv.org/abs/1010.2541 "DIGITAL ERA: Universal Bimagic Squares"
http://arxiv.org/abs/1010.4186 "Upside Down Numerical Equation, Bimagic Squares, and the day September 11"
http://arxiv.org/abs/1102.2394 "Upside Down Magic, Bimagic, Palindromic Squares and Pythagoras Theorem on a Palindromic Day - 11.02.2011"
http://arxiv.org/abs/1102.3052 "Bimagic Squares of Bimagic Squares and an Open Problem"

by Miguel Angel Amela, La Pampa, Argentina

Pfeffermann IXOHOXI Bimagic Square (PDF file, 142Kb)
Universal H-IXOHOXI Magic Squares of Order Eight (PDF file, 154Kb)

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