I admit it: I am in the Facebook, with the Twittering, the different technology that young people are using today. And occasionally we have very geeky conversations there.

Me: Five kids in the house = combinatoric explosion. No wonder interactive fiction authors avoid NPCs.

Glen: I just recently did that problem. Complexity scales as the number of pair interactions, plus a linear term in the number of children. Therefore two kids is three times as complicated as one; three is six times; four is ten times. I think the general formula is 1 + 2 + … + N for N kids.Oh, and good luck. Having that many rugrats running around is pretty complicated!

Jeff: But aren’t some kids more complicated than others?

Glen: In a word, no. The proof is left as an exercise for the reader.

For bonus points, should this series have higher-order terms? Why or why not?

I think that, for N kids, the formula is actually (N^N)^N

I’m now convinced that the kids’ ages matter as well. Having five kids all between 1.5 and 5 yrs old is very different from having 5 kids who are 1, 3, 5, 7, and 9. More research must be done!

Yay! I made the peer-reviewed journal “Live Granades.” Next stop: “Nature!”

And whenever you want to do that research, let me know–i’ll contribute some kids. I might even provide some funding!

That’ll earn you a merit badge! http://www.scq.ubc.ca/order-of-the-science-scouts-of-exemplary-repute-and-above-average-physique/

I think it’s more like 2^N – 1, Each possible subset of kids has its own unique interaction. You subtract one since the situation where no kids are the room adds no complexity.