List of the site's news added April 4th, 2006
- New research on multiplicative magic
cubes (after the multiplicative magic squares
presented in the previous updates). Among the results:
- the best known cube using smallest possible
integers, maximum number used = 416.
- the two best known pandiagonal perfect cubes
- using smallest possible magic product = 89,518,183,823,250,314,294,722,560,000.
- using smallest possible integers, maximum number used =
- and thanks to Edwin Clark, USA, for his checkings of all
my multiplicative magic cubes!
- First known 6x6 bimagic
square using distinct
integers, by Jaroslaw Wroblewski, Poland. See also
table. An important and long-awaited result: first known example of
a bimagic square smaller
than the 8x8!
- First known pandiagonal bimagic square
using consecutive integers, by Su Maoting, China.
A lot of people (including me...) thought that this problem was perhaps
- A lot of first known bimagic squares, orders:
- 13, by Chen Qinwu-Chen Mutian,
China, and ... independently, only 3 days
later... by Jacques Guéron, France
- 14, by Chen Qinwu-Jacques Guéron
- 15, by Chen Qinwu
- 17 and 19, by Jacques Guéron
- 20, by Su Maoting
- ... and other bigger bimagic squares described in the new page on bimagic/trimagic squares from order 17 to
- Results of new studies on highly multimagic
squares, from 9-multimagic
to 14-multimagic squares, by Pan Fengchu, China.
- About multimagic series, nice compact mathematical proofs by Robert Gerbicz, Hungary:
Mathematics Today, Vol 42, N 2, April 2006:
New open problems added in the Problems page:
- Is it possible to construct better multiplicative magic cubes than my cubes mentionned above? "Better" meaning with smaller constants.
- Is it possible to construct a 6x6 bimagic square using smaller distinct integers, or smaller
magic sums S1 and S2, than the above Wroblewski's square?
- What is the smallest possible order of trimagic squares using distinct integers?
- Is it possible to construct a pandiagonal bimagic square
of order < 32, using consecutive integers? (smaller order than the
above Su Maoting's square)
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