On This Infinite Grid of Ideal 1-ohm Resistors...

This is from one of xkcd's recent comics, talking about stopping people dead in their tracks with intriguing problems... "nerd sniping". It's about on the same level of effectiveness as a weapon as the world's deadliest joke, which even has a mention in Wikipedia. Going back to the comic, the problem of an infinite grid of resistors is apparently from the Google Labs Aptitute Test, which I looked up. The questions were harder and more ingenious than I thought they would be, especially the numeric-acoustic ones.

I remain, however, one of the people who are easily nerd sniped (computer scientist for one point?). Here's an example. I thought about the actual question for a bit, using my rusty physics skills, and could only narrow it down to the resistance being larger than 0 but smaller than 3 (since the two nodes are on a parallel circuit, and the resistance has to be smaller than the smallest resistance).

There's a fairly popular flash game called Desktop Tower Defense, a strategy game of sorts. I played it for a bit, then did the "fun" version where you start with 10000 gold. I spent the next few hours (or days) trying to create as long a path as possible for the creeps. That would mean more towers and more time for me to deal damage. I think my last version lasted up till level 40+ before I had to upgrade the towers...



Clearly, this is one of the xkcd comics which real life should not imitate.

1 comment :

  1. Apperently, the answer is R = 2/pi for each diagonal position! I dont understand it myself - but an explaination is here: http://www.geocities.com/frooha/grid/node2.html