Latin and cross Latin squares

Abstract

Latin squares were first introduced and studied by the famous mathematician Leonhard Euler in the 1700s. Through the years, Latin squares have been used in areas such as statistics, graph theory, coding theory, the generation of random numbers as well as in the design and analysis of experiments. Recently, with the international popularity of Sudoku puzzles, Latin squares are in the spotlight as every solution to a Sudoku puzzle is a Latin square. This article describes Latin, diagonal Latin and cross Latin squares, as well as a method of constructing such squares.