Mathematics and Statistics Colloquium
Title: How to Solve Euler's (Impossible) 36 Officers Problem
In 1782 Euler asked whether it's possible to arrange 36 officers in a square with certain properties, and 118 years later Tarry proved the answer is no. In this talk we will describe how to construct the square Euler wanted. Along the way we'll meet Latin squares, alternating sign matrices, a conjecture of Euler's which turned out to be false, an unusual linear algebraic definition of orthogonality, a perfect rectangle, and a couple of (mathematically) interesting quilting patterns. If there's time, then we'll also discuss a few related open problems.