# Sudoku and latin squares

Today our guests Liljana Babinkostova and Marion Scheepers (both BSU math professors) led a discussion of sudoku and counting.

The discussion began with the popular game of Sudoku. How many valid Sudoku boards are there? How many after we identify the ones that are obviously equivalent (such as by reordering the columns)? How many have a unique solution?

We then saw that Sudoku boards are a special type of Latin square, which just means a square with numbers in its cells such that every row and every column has no repetitions. What are some natural ways to generate a Latin square? When and why does it work? Why are mathematicians interested in Latin squares and what do they investigate about them?