I love this! We are always looking for ways to iterate problems and extend them, but there's nothing to extend with this problem. It's all ready for the wolverine wrangler to do his stuff. I'm looking for the guy who can make this wolverine sit and quit bearing its teeth so my 8th graders can pet it for a second. GeoGebra does this. Mr. H's applet makes this problem accessible to an 8 year old. In fact, my son was so mesmerized by the animation that I swear I heard him muttering, "Heffalumps and Woozles. Heffalumps and Woozles." Heck, I found a strange urge to put on some Pink Floyd myself.
Can you imagine starting a problem in middle school and finishing it with calculus? That's how beautiful (that's right I said it!) this problem is. Why can't we let these younger kids see the beauty of the wolverine without actually having to be the one to handle it? I can see posing the problem, setting the kids up with GeoGebra (with minimal prerequisites) and turning them loose. They'll see the pattern, make a conjecture and inductively decide the answer. Show the applet which demonstrates the first 360 cases and inevitably, the question will be:
Now, talk about storytelling. The table's been set for the sequel that the kid's gonna have to wait a couple of years to see. precalculus kids can actually calculate the answer and the trilogy will be complete once they have the tools to actually prove that for n chords, the product is n+1. This problem can span four years. At least.
 Apologies if I misused the metaphor.