Homework 1 is intended as a ``warmup'' for the course. It has two problems and is due the class period after it is assigned. In my experience, most students get both problems wrong. The purpose of the problems is to alert students that thinking and writing logically is not as easy or obvious as they may think.

I don't include this homework in the grade.

The first problem is a simple logic quickie. The second is a nice puzzle that most students get wrong. There is a fairly obvious strategy that works in 4 rounds; in the first 3 rounds one reduces the number of mismatches by half at each step, and in the last round there are 2 remaining players who need to swap hats. Most students claim this is optimal, and argue that at each step they maximize the number of people who get the correct hat. Of course optimizing each round separately does not necessarily optimize the process, and indeed, there is a solution that works in two rounds, based on the observation that every rotation of the circle is the product of two reflections.

Later in the course, when students complain about having to prove statements that are ``obvivous'', I use this as one example where the obvious is not always true.

The first problem of assignment 2 is a follow up to this one, where those who gave a ``proof'' of an answer other than 2 are asked to find the flaw in their argument.