“Did you hear the one about the alligator and the moat?” For most people, this sounds like the start of a joke. (Not necessarily a good joke, admittedly).
But when you have math friends, there’s a chance that it’s the start of a good problem. Problems like the Alligator and the Moat have circulated for years and years–in today’s parlance, they’re mathematical memes.
They are also community builders. You hear about a weird problem, you tell your friends, you try something, you share ideas. Usually these problems are tricky, and seemingly hard (although once you get them you stop thinking that). You share your failure to solve the problem, you ‘throw things at the wall.’ Often you solve the problem in a way that was different from the method used by the person who asked, which is great because then you own the problem too. Over time you develop a ‘club’ of people with whom you share these problems.
Bill Schmit, a former student of mine, gave me an all time favorite: You are blindfolded (not an unusual start to this kind of problem). You have two groups of 5 dice. One group of dice sums to 15, and the other to 13. Make two groups of dice with the same sum. Reminder–you’re blindfolded.
I mulled this over for a couple of days. I expressed annoyance with Bill for posing it (if you know Bill, also not unusual). And then I mentioned it to another former student, Justin Huang, who said, “I don’t know how to do it, but I know another similar problem that I also don’t know how to do.” And then I solved Justin’s problem right away, and then together we immediately solved Bill’s problem. That’s how problem solving goes some times.
As for the Alligator and the Moat, my colleague and mathematician Lynn Narasimhan started with her usual preface, “Here’s another one from my nephew.” “You are on an island that has radius r that is surrounded by a narrow moat, so that you can cross it almost instantly. Unfortunately, there is an alligator in the moat, and it moves 4 times as fast as you, and you cannot jump directly over it without loss of limb. In general, can you get off the island safely?”
Welcome to the club–good luck!