Trimagic square, 32nd-order

William H. Benson (Halethorpe, Maryland USA, 1902 - Carlisle, Pennsylvania USA, 1984)

The first known order-32 trimagic square is owed to the American William H. Benson. The whole square was published for the first time in the book New recreations with Magic Squares (pages 86-87) by William H. Benson and Oswald Jacoby, with the method used. Here is an extract of their talk:

Here are the two biographies, and photos, provided courtesy of the Archives and Special Collections, Dickinson College, Carlisle, Pennsylvania, USA:

It has been very difficult to find information about William H. Benson. The light came with this sentence found in the foreword written by Oswald Jacoby (1902-1984, exactly like Benson!) in Intriguing Mathematical Problems, first published in 1962 under the title Mathematics for Pleasure, book cowritten by Oswald Jacoby and William H. Benson:

    « Mathematics for Pleasure is the result. In its preparation I had the help of the perfect co-author, William H. Benson, Associate Professor of Mathematics at Dickinson College - an old friend I had first known when he was Captain Benson, USN, and I was Commander Jacoby, USNR. In addition to his faculty for turning out highly accurate work of all sorts, Professor Benson has long made a hobby of mathematical recreations and ranks with the world's top experts on magic squares. »

Now it was easy to contact the Dickinson College! Many many thanks to Jim Gerencser, College Archivist at Dickinson College, for his efficient help.

The sums of the rows, columns and diagonals are equal to 16,400. The sums of the squares of the rows, columns and diagonals are equal to 11,201,200. The sums of the cubes of the rows, columns and diagonals are equal to 8,606,720,000.

We know today how to construct other 32nd-order trimagic squares. Our method used for our tetra and pentamagic squares can also construct numerous 32nd-order trimagic squares for which we provide a sample.

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