# Some fun with Latin Squares

I found a cute, playful bit paper on arXiv.org. Fun with Latin Squares, by Michael Han, Tanya Khovanova, Ella Kim, Evin Liang, Miriam (Mira)Lubashev, Oleg Polin, Vaibhav Rastogi, Benjamin Taycher, Ada Tsui, and Cindy Wei, appears to be the result of a school research project. A Latin Square is an arrangement of numbers. Like, if you have the whole numbers from 1 to 5, you can make a five-row, five-column magic square, with each number appearing once in each row and column. If you have the numbers from 1 to 10 you can make a ten-row, ten-column magic square, again with each number appearing once per row and column. And so on.

So what the arXiv.org paper does is look at different types of Latin Squares, and whip up some new ones by imposing new rules. Latin Squares are one of those corners of mathematics I haven’t thought about much. But they do connect to other problems, such as sudoku, or knights-tour and similar problems of chess piece movement. So we get enlightenment in those from considering these. And from thinking how we might vary the rules about how to arrange numbers. It’s pleasant, fun exercise.