Some Bunny Board Notes

For all of my career I have been posing off-topic problems to students. And for most of my career Ghost the Bunny has been my favorite.

Laura’s pet bunny, Ghost, hops up a flight of 12 stairs. Ghost can hop up one or two steps at a time, and never hops down. How many ways can Ghost reach the top step?

I just offered the problem to a class – but it was a little close to some regular work on a skill that could be applied here – so I got – boring – mostly one solution – a solution that was practical, but not the most interesting. I made groups try for a second solution, and most stumbled on the usual first solution. It was ok, but not very satisfying.

Friday the class had a game day (3-D tic tac toe with visualization challenges and embedded combinatorial questions, and sequence issues, it’s still a math class, even if they love it). And I walked over to the board, and sketched some solutions from previous years, solutions that emphasized an interesting and important (says me) aspect of Ghost. And I interrupted their game play (they were all spread out) and made them come over and take a look, and a few saw something they found interesting, but no one found anything as interesting as 3-D tic tac toe, which they quickly returned to….

By the way, that solution on the right, I am pretty certain that three freshmen, maybe 6 or 7 or 9 or 10 years ago, they drew that solution all the way out to 12 steps…