356: Nerd Sniping
Title text: I first saw this problem on the Google Labs Aptitude Test. A professor and I filled a blackboard without getting anywhere. Have fun.
Nerds have a way of getting distracted easily and focusing on one thing and ignoring the rest, when they feel their specific skills are challenged by an interesting problem. Black Hat has decided to make this into a disturbing game of getting nerds, in this case a physicist, to stop in the middle of a street and get crushed by a truck by showing them an interesting problem to solve.
The problem Black Hat shows is an electronics engineering thought experiment to find the resistance between two points. In normal wiring, a one ohm resistor would result in one ohm of resistance. Two resistors connected in a series, where electricity has to go through each, has two ohms of resistance. Two resistors in parallel give the circuit only half an ohm since you average the resistance of the path (1 ohm of resistance over 2 paths). With an infinite grid of resistors, you have an infinite number of paths to take, and for each path an infinite number of both series and parallel paths to consider, so much more advanced methods are needed. The exact answer to the question is 4/π − 1/2 ohms, or about 0.773 ohms. See .
The Google Labs Aptitude Test is a collection of puzzles published by Google as a parody of tests such as the SAT. Google is known for using logic & math puzzles in their job interviews. Randall explained in a speech at Google five days before this comic, that he was nerd-sniped, in a way, by that problem in this test, and got quite irritated when he ultimately found that it was actually a modern physics research problem, requiring very advanced math, far more complicated than the other puzzles it figured among.
- [Black Hat is sitting on a chair, Cueball is standing next to him. Across the street another man is coming from a building.]
- Black Hat: There's a certain type of brain that's easily disabled. If you show it an interesting problem, it involuntarily drops everything else to work on it.
- [The man across the street is about to enter a crosswalk.]
- Black Hat: This has led me to invent a new sport: nerd sniping. See that physicist crossing the road?
- [Black Hat holds up a sign.]
- Black Hat: HEY!
- [There is an image of a grid with resistors on every connection, two nodes a knight's move apart are marked with red circles.]
- Sign: On this infinite grid of ideal one-ohm resistors, what's the equivalent resistance between the two marked nodes?
- Physicist on the street: It's... Hmm. Interesting. Maybe if you start with... No. Wait. Hmm... You could—
- [A truck is zooming past, apparently where the physicist just stood.]
- Cueball: I will have no part in this.
- Black Hat: C'mon, make a sign. It's fun! Physicists are two points, mathematicians three.