John Graham-Cumming, of Geek Atlas fame, has posted a piece to answer the perennial question “Why do Christmas lights all go out when one bulb blows?” (the old-school in-series non-LED variety). And he shows ye ol’ “binary chop” technique for quickly rooting out the dead bulb.
Finding the broken bulb
A really fast way to find which bulb is broken is to perform a binary chop. To do that you need a multimeter (or similar meter to test continuity).
0. Unplug the string of lights from the power.
1. Remove the first and last bulbs and check that they are ok.
2. Remove the bulb in the centre of the string of lights. Using the multimeter check to see if there’s an electrical connection between the contacts in the centre bulb socket and each of the end bulb sockets that you remove the bulbs from (you can actually look at the wiring to see which way the wires go and which contact that corresponds to).
3. Pick the half where there’s no connection. The broken bulb is there. Remove the bulb that’s in the middle of that half of the string and check it. If it’s ok proceed to checking the electrical connection between the socket of the bulb you just removed the two nearest bulbs you removed (which will be the middle of the string and one end).
4. Proceed like that following where there’s no electrical connection and dividing in half until you find the broken bulb.