Polyomino Tiling Recurrences
One of the struggles at JRMF has been finding arithmetic activities that are as popular as our logical and geometric activities in a festival setting. Kids see an activity table with numbers and tend to want to flock to the other tables. I don't think the activity I'll present today is a great festival activity as-is, but I like it because it deals with recurrence relations disguised as a geometric problem. I've run it over the years and my colleague Steve Heller has a well-loved version he has dressed as brick-laying on the Yellow Brick Road. Math circle kids love it, but our goal with math festivals is to give kids that don't normally end up at math circles a bite-sized version that invites -- but doesn't demand -- a ton of careful handwritten work. The reasons I'm hesitant to think of this activity as a great festival activity are (1) there's a some book-keeping required to arrive at the arithmetic content, which younger students don't often th...