My younger son was working on a problem in the Wolfram Programming Challenges that is best solved using generating functions:

Yesterday we did an introduction to generating functions but unfortunate our camera’s memory card died and the videos were lost. Instead of repeating that introduction we just dove into some of the examples from the book we are using.

The first problem was about distributing juggling balls. It takes a few minutes for the ideas we talked about yesterday to click in, but eventually we were able to work through this problem:

Next is a really neat example of the kind of problem generating functions can solve – counting solutions to relatively simple equations (sorry for forgetting the camera was zoomed in at the beginning – we finally zoom out around 2:45):

Now we tried out a few of the exercises. The first one I chose was about distributing juggling balls. With the work we’d put in on the first example, this problem wasn’t too hard:

Finally, we tried out a new problem asking about the number of integer solutions to an equation. The ideas about generating functions seemed to be really sinking in now and this problem didn’t give them too much trouble:

Introducing the boys to generating functions made for a really fun weekend of math – happy that working through the Wolfram Programming Challenges gave us this opportunity.