As you can see exactly one half of the string is lit and the other isn't. This is the problem with most strings of Christmas lights. They are constructed on a single (or in this case two) series circuit. This means that every bulb is attached to the same circuit, and if any bulb goes bad, the entire circuit goes out. Since I didn't want to deal with these strings I went to the store and bought new ones. An hour later, the lights were on the house.
Later in the evening I decided that it would be silly to throw away the bad strings without first seeing if I could fix them. There are really only two ways to fix these strings. The first, and easiest method is to check the fuses. Each string has two fuses, so I replaced the fuses with fuses that I know work. Unfortunately, this fixed none of the stands, meaning the fuses were all good.
The second method is to individually test each bulb. So I took each potential bad bulb and place it in the working strand to see if the working strand still worked. In 2 of the 5 "broken" stands, I found a bad bulb, replaced it, and the stands worked. The the other 3 strands, the bulbs all worked, meaning that something else is wrong with the circuit. Two of these strands are 50% operational, so I can still use them by bunching up the "broken" side. The 0% operational strand is now serving as a bulb replacement strand. Since the bulbs work, I can use them to replace bad bulbs in the future.
I'm glad the lights are up on the house, but checking each bulb was a frustratingly tedious process. Sometimes physics is annoying!