Vampire Numbers and other Interesting Things

In a Facebook post recently, Gerald Thurman, a computing/math instructor at Scottsdale Community College located in Scottsdale, Arizona introduced me to Vampire Numbers. I’d never heard of them before and if you haven’t either there is a YouTube video you can watch that is a nice introduction.

It’s a tricky problem and Gerald’s students didn’t quite get it finished before the lab period ended. The problem apparently was false positives and a few more minutes would have given them time to finish. That’s the problem with hard deadlines of course.
There are probably a lot of ways to generate an answer to this sort of problem. Brute force is obvious. I’m sure that a real mathematician (I don’t even play one in school) could come up with a good efficient formula as well. Right?
A simpler but similar problem is Alexander’s Numbers. Alexander’s Numbers are numbers whose value is the same as the total of their digits cubed. For example, 1³ + 5³ + 3³ equals 1 + 125 + 27 which equals 153. This is easier because you don’t have to try so many possibilities. I’ve used this with high school students with some success.
Mathematical puzzles like this don’t appeal to everyone of course but even some students who are not “in to” math find the puzzle nature of the exercise to be interesting.
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