Sharing Robert Kaplinsky’s pipe stacking problem with my younger son

Yesterday I saw a really neat video collection from Robert Kaplinsky

I found clicking through to his blog post and watching all of the videos to be an absolutely fascinating exercise.

My younger son has been working through Art of Problem Solving’s Introduction to Geometry book this year and I thought he’d find Kaplinsky’s problem to be interesting. So, we watched the video in the tweet and then dove into the problem.

Here are his initial thoughts. You’ll see that the problem has confused him a bit and that he doesn’t quite know how to get started:

His first idea was to simplify the problem at look at just two layers of each of the stacks. He was able to solve the simpler problem (!) and then formed a conjecture about the solution to the 20 layer problem.

Next we tested the conjecture.

I would have liked to have gone about 5 min more, but we were already over the time allotted -> he needed to get ready to go to school. I’m pretty happy with his approach to the problem, though. It was really nice to see him work all the way to the complete solution. Thanks to Robert Kaplinsky for this nice problem.