Latin square love affair

by malmskog

This is what you get when you google “sexy quilt.” Can you believe it?? My faith in the essential wholesomeness of the internet (which should never have existed in the first place) has not been restored, but I do love surprises.

I am writing today about a problem that I described in my last post about how a group of 5 people could pass 5 quilts around so that each person works on every quilt and no person ever passes to the same other person twice.  And of course, I used Latin squares to model the problem, and I am now a little bit in love with Latin squares.  So the exciting thing for today is my new mathematical crush on Latin squares and a solution to the problem at the end of this post.

But first, let me share a few updates about my life.

School is just about to start here at Colorado College. CC has a very unusual course structure.  The academic year is organized into eight three-and-a-half week blocks.  During each block, students take a single course and professors teach a single course.  Classes are intense but the structure gives the opportunity for lots of creativity in teaching and amazing field trips.  I am really looking forward to teaching on the block schedule.  My first class is good old Calculus I, starting Monday and running through September 24.  So goodbye to all my decadent ways.  Goodbye, sleeping late.  Goodbye, reading novels all afternoon.  Sigh. But really tt’s about time I got back to work.  I’m pretty sure I have the best job around so I’m not going to whine (any more) about not being able to sit home and read The Hunger Games all day.

And… forget work, there is another extracurricular activity to take up my time.  I finally visited KRCC 91.5 FM here in Colorado Springs and had a great time talking with Mike Procell and Vicky Gregor.  Did I mention how much I really love that station?  It was one of the (many) things that made me decide to take the job here at CC.  I will go in tomorrow to sit in with Vicky and start training! The prospect of getting on-air at KRCC is totally thrilling.  So wish me luck.  And, I also get to learn about my health insurance tomorrow.  Did I mention how much I love being out of grad school and having health insurance?

I couldn’t resist sticking in a gratuitous picture of this incredibly beautiful place. I work here!

Here is one of the sweet quilts that Judy and her group worked on, though without the passing sequence they dreamed of.

Back to the problem. In the interest of laziness, I will link directly to a pdf of my solution and response to Judy: quiltproblem.

My favorite part about this problem is that it is a real-life problem that is modeled with very useless-seeming mathematics.  I love abstraction and mathematics for the sake of fun and beauty, and I love solving problems, but its not every day that these two loves come together for me.  And this problem promises to be a good source of united fun for a while.  So, I have determined that the quilts can be passed as desired if there are an even number of people.  It is not possible if there are 3 or 5 people.  What about other odd numbers?  That’s my next question: for what sizes of groups is it possible to find a good way to pass the quilts?

I’ll post whatever I figure out.  But probably not until block break.