Years ago I taught a “math for poets” class. (I don’t remember the actual name of the course. Everyone called it “math for poets” because it was the one math class humanities majors had to take.) I taught the students how to mentally figure out days of the week and they loved it. It was easily the most popular topic in the course. It was satisfying to find any topic that was popular in a course that many had put off as long as possible.
I’d thought about turning my old class notes into a blog post, but there’s one minor complication. I taught this course in the 1990’s and the method was designed to make it easiest to work with dates in the 20th century. You could use it to compute days of the week in the 21st century, but doing so would take one more step than revising the method to make it easier to work with 21st century dates.