You are standing in front of a room with one lightbulb inside of it. You cannot see if it is on or off. Outside the room there are 3 switches in the off positions. You may turn the switches any way you want to. You stop turning the switches, enter the room and know which switch controls the lightbulb. How?
Turn on switch 1 and leave it on for a few minutes. Turn off switch 1. Turn on switch 2. Open the door. If the light bulb is on, then switch 2 controls it. If the light bulb is off, but warm to the touch, then switch 1 controls it. If the light bulb is off and cold to the touch, then switch 3 controls it. The reason this works is because when you turn on switch 1, the light bulb will start to heat up. Even if you turn off switch 1 after a few minutes, the light bulb will still be warm to the touch. So, if the light bulb is off, but warm to the touch, you know that switch 1 was the one that turned it on. Switch 3 is the only switch that you didn't touch, so if the light bulb is off and cold to the touch, then switch 3 must be the one that controls it.
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