My favorite candy come in packages of 5 or 6. What's the largest number for which I cannot buy exactly that many candies? Can this be generalized?I got a result yesterday. I liked its symmetry but couldn't figure out why it worked. I think I have the why down now, but I'm not sure I could explain it well yet. I thought you and your kids might enjoy playing with it.
The beach is fun, too. :^)
[Edited on April 24: The generalization discussed in the comments involves using two numbers that are relatively prime, ie GCF(A,B)=1. JD blogged 5 years ago about "The McNuggets Puzzle", using 3 numbers, which share some common factors. Cool extension!]