We Have PhDs in Nerdiness

Originally published at Live Granades. Please leave any comments there.

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?