Bimagic square

Bimagic square

In mathematics, a bimagic square is a magic square that also remains magic if all of the numbers it contains are squared. The first known bimagic square has order 8 and magic constant 260; it has been conjectured by Bensen and Jacoby that no nontrivial bimagic squares of order less than 8 exist. This was shown for magic squares containing the elements 1 to "n"2 by Boyer and Trump.

However, J. R. Hendricks was able to show in 1998 that no bimagic square of order 3 exists, save for the trivial bimagic square containing the same number nine times. The proof is fairly simple: let the following be our bimagic square.

An 8×8 bimagic square.



See also

* Magic square
* Trimagic square
* Multimagic square
* Magic cube
* Bimagic cube
* Trimagic cube
* Multimagic cube

External links

* Aale de Winkel's listing of all 80 [http://home.wanadoo.nl/aaledewinkel/Encyclopedia/DataBase/BiMagicSquare_08.html bimagic squares of order 8] .


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