Trimagic Squares

A trimagic square is a bimagic square, where in addition, the rows, columns and diagonals have the same sum, when all the numbers are taken to the third power. The first trimagic square was given by Gaston Tarry in 1905 vor. It had the order of 128. Cazalas then improved this method and succeeded in creating trimagic squares of orders 64 and 81

A another great step was made in 1976, when Benson and Jacoby published a trimagic square of order 32.

The great sensation took place in 2002, when Walter Trump published a trimagic square of order 12. In the meantime it is well-known that this is the lowest order for which a trimagic square can exist.

122334162667983104112123144
9119451151079352383010026136
75141354857141318897110470
748106491243102133963913771
1401011244260371088510321445
12276142866712619785936923
552795135130895615105011890
132117689111994613454772813
736421211093211336241438172
58988411613816129729614787
803410569212718531394011165
5163312025128171201251148294

His trimagic square is self-complementary and the numbers are horizontally symmetrical. This means that numbers which are symmetrically in the same row always have the same sum n2 + 1, which is 145. This trimagic square has the constant sums S12=870, S122=83 810 and S123=9 082 800.

Read more on the multimagic pages of Christian Boyer about the discovery of this sensational trimagic square.

The first known 16th-order trimagic square was created in 2005 by Chen Qin-wu and Chen Mu-tian. This square is also self-complementary and the numbers are again horizontally symmetrical.

343028261468385115142172174111231229227223
524012464234110207219385014723193133217205
17816822621216924515142215106128845318979
12520152491129149103154208166145825256132
1961801762321995996241161611985825817761
627882118247214114152421434310139175179195
203253107127974413102155244213160130150454
11955711892102362016493237214768186202138
255991856766762389416319181191190721582
137157251129241821711823986752331286100120
13113518318791733624017221842487074122126
533149691921482431561011410965188108254204
224228230140159197144372201136098117272933
1121737481651621531049592209250184136256
80903246871110521641152246170211225167177
206218134194572222214111635235200631233951