Math, Puzzles and Computers

By Fernando Rodriguez Villegas

In the early 2000’s while monkeying around with lattice polygons, I came up with a puzzle that looked interesting. I named it Blet after my daughter Malena saying one day out of the blue: Blet, suena como un tomat. (To this day nobody can really figure out what she meant by it.)

I discussed the puzzle with my then colleagues at UT, Austin, Felipe Voloch and Lorenzo Sadun, and together worked out pretty much the whole thing and published the results. (In 2018 I gave two general talks about Blet in Vienna and at the Basic Notions Seminar at ICTP.)

Somehow the Mathematics behind the puzzle and its solution (lifting $SL(2,Z)$ to the universal cover of $SL(2,R)$ and so on) is more sophisticated than the puzzle itself, which is innocent enough.

It occurred to me then that it might be a good idea to teach a course involving interesting Mathematics with puzzles as a motivation. It turns out that there is a fair number of puzzles, some very well-known, that fit the bill. The result was the undergraduate course Math, Puzzles and Computers that I developed and taught at UT several times.

Here are the actual lecture notes for the Spring 2007 version and these are the class notes for the Spring 2004 version.

My personal goal was to use puzzles as an excuse to explain some basic mathematical concepts to scientific minded students.

If you read portuguese you may have fun with this account (Jogos e feijoada no São Paulo’s on p.13 of the Eureka! magazine No 27 of 2017 of the Olimpíada Brasileira de Matematicas) by E. Carneiro (then graduate student at UT Austin) on our discussion about puzzles and math.

I gave a Basic Notions Seminar talk at ICTP on impartial games, one of the topics of the course.