I just came across this XKCD comic.
Though I can happily report that so far, I managed to avoid getting hit by a truck, it is a life situation in which I found myself quite a number of times in my life.
In fact, ever since I’ve seen this comic an hour or so ago, I’ve been wondering about the resistor network. Thankfully, in the era of the Internet and Google, puzzles like this won’t keep you awake at night; well-reasoned solutions are readily available.
Anyhow, just in case anyone wonders, the answer is 4/π − 1/2 ohms.