Trimagic square, 64th-order

After the 128th-order trimagic square of Gaston Tarry, the square researchers have tried to find squares of a smaller order. Strangely, it is more difficult to find small multimagic squares than big ones. The first 64th-order trimagic square was found in 1933 by the French general Eutrope Cazalas.

 Eutrope Cazalas (Ribérac 1864-Versailles 1943), son of a controller of the French Direct Taxation (really, after Gaston Tarry…), is a brilliant mind which, after the Ecole Polytechnique year 1884, rapidly became captain of the French army, translated in 1899 a Russian book Towards India, and published in 1909 a booklet The Military Balloon Captured in Wurzbourg in 1796. No, all this has no connection with magic squares. He continued to rise in military rank, participated with high success in the first world war, and became general in 1921. We can add that several honorific distinctions: Croix de Guerre (War Cross) with bar, and Commandeur de la Légion d’Honneur. And he is polyglot: German, Italian, Spanish, Russian. An impressive man!

Our general, then retired from the army, built in 1933 the first known 64th-order trimagic square, that he calculated by hand and integrally published in a folding paper inserted at the end of his remarkable Les Carrés Magiques au Degré n book. Our general thought -wrongly- that smaller ones cannot exist.

64th-order trimagic square of Cazalas published at the end of his book.

In May 2002, we have reconstruct the General Cazalas' square in order to verify it. Hmmm... it is not really trimagic... since in the square as it was published in his book, there is an error... a very small error, but sufficient to all fall through: in column 62, row 14, the number 3769 is incorrect and should be 3739. But be at ease, once this anecdotal error corrected, the square is really trimagic! We will forgive it, because it means that the 64x64 - 1 = 4095 other numbers, all hand computed and hand written in 1933, are true: bravissimo.

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