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Bimagic Square of Order 8

Gaston Tarry 13-16. Published in French magazine: L'Echo de Paris, 1903.

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Biography of Gaston Tarry:

Gaston Tarry (Villefranche de Rouergue 1843 - Le Havre 1913) was born in the Aveyron, a region in the center of France. He studied mathematics at the Lycée Saint-Louis in Paris, and spent his working life in Algeria in the French Financial Administration (Contributions Diverses de l’Administration des Finances). France had invaded Algeria in 1830 and French rule was established by 1847. Tarry was part of the French administration in Algeria, retiring in 1902. Although he was an amateur mathematician, Tarry had an amazing ability to analyse combinatorial problems. His passion for magic squares started when he was in his fifties and meet his friend of Alger, Brutus Portier. Together they investigated mathematically problems and, you guessed it, he discovered also the first 16th-order panmagic square. That will say the first bimagic square of order 16. This started his passion for magic squares. Over time, he wrote a large number of articles in various scientific magazines of the period, where the bimagic squares of order 8 where published when he was back in Paris, year 1903. He was searching after algorithm to solve the squares and the first known trimagic square of order 128 is also credited to Gaston Tarry and it was presented in a French magazine 1905. He called his method of magic square construction the "cabalistic condensator" and wrote: This condensator is a real magic machine charged at the limit. In discharging it, we will obtain magical effects. The discharge can only stay in a good conductive environment, a magic field.

Tarry also solved Euler's 36 Officer Problem, proving that two orthogonal Latin squares of order 6 does not exist. The problem as stated by Euler is as follows: How can a delegation of six regiments, each of which sends a colonel, a lieutenant-colonel, a major, a captain, a lieutenant, and a sub-lieutenant be arranged in a regular 6 × 6 array such that no row or column duplicates a rank or a regiment? He showed it in two articles in French magazine that such an arrangement is impossible.

A panmagic square (pandiagonal magic, also called diabolic) is a square which is magic for all its lines, all its columns, and all its full or broken diagonals (not only the two main diagonals).

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