**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:

« So far is known, this is the first trimagic square ever to be constructed of an order lower than 64. It has been completely checked by the use of IBM equipment and proved to be correct. The method is perfectly general and flexible. Any number of trimagic squares of the 32nd (64th, 128th, etc…) order can be constructed by its use. »

- Captain W. H. Benson, ex-professor, dies, by the Carlisle Sentinel, local newspaper, December 29, 1984
- William H. Benson, biographical sketch, by Samuel Alston Banks, President of the Dickinson College, January 2, 1985.
It has been very difficult to find information about William
H. Benson. The light came with this sentence found in the foreword
written by « Now it was easy to contact the Dickinson College! Many many
thanks to |

2 |
831 |
1017 |
… |
587 |
653 |
436 |

59 |
774 |
964 |
… |
626 |
696 |
393 |

931 |
158 |
92 |
… |
490 |
304 |
529 |

… |
… |
… |
… |
… |
… |
… |

220 |
997 |
803 |
… |
657 |
599 |
362 |

836 |
125 |
187 |
… |
265 |
463 |
754 |

889 |
72 |
130 |
… |
308 |
502 |
715 |

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.

- Download the image of the 32nd-order trimagic square of William Benson, zipped BMP file of 58Kb
- Download the 32nd-order trimagic square of William Benson, zipped Excel file 39Kb.

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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