You are in a room with three switches, labeled $A$, $B$, and $C$. Initially, each switch is in an off state. In an adjoining room, there are three incandescent light bulbs. Your task is to correctly label which switch goes to which bulb.
The catch: you may only enter the bulb room once. You have as long as you need in the switch room, and you may flip any switch as many times as you'd like, but once you leave the switch room, you may not enter it again.
There is a way to know for certain which bulb goes to which switch. How?
Answer
The answer:
Turn switches A and B on. Wait about a minute. Turn switch B off. Go to the bulb room. The bulb that is on corresponds to switch A. The bulb that is off, but warm, corresponds to switch B. The bulb that is off, but cold, corresponds to switch C.
The explanation:
Incandescent bulbs produce a significant amount of heat. In the amount of time it takes you to walk from one room to the other, the bulb will have not had time to cool down, unless the rooms are unreasonably large.
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