There is a famous puzzle, asked several times on this site, regarding a light bulb hidden in a room. There are three switches outside. You can flip them however you want, but you cannot continue flipping them once you've opened the door to the bulb. How do you figure out which switch connects to the bulb? The answer, which I'll put in spoilers for those who don't know yet, is:
You flip one switch on, wait a few minutes, flip it off, and flip another switch on, then open the door. If it's on, it's the second switch. If it's off, but it's hot, it's the first switch. If it's off, but cold, it's the switch you didn't touch.
My question is as follows: Assuming you don't have a thermometer, can you increase the total number of switches beyond three and still be able to tell which switch connects to the bulb?
Once you're done with this one, check out the sequel.