A windowless room contains three identical light fixtures, each containing an identical light bulb. Each light is connected to one of three switches outside the room. You may manipulate the switches however you wish, but once you open the door, you cannot touch the switches again. How do you determine which switch controls which light?
Common Wrong Answers
“Turn on all the switches and enter the room.”
If you turn on all the switches and enter the room, you won't be able to determine which switch controls which light because all bulbs will be lit.
“Turn on switch 1 and leave it on, then turn on switch 2 before entering.”
If you leave switch 1 on and turn on switch 2, you will only know that one bulb is on (switch 2), but you won't be able to tell if the other bulb is off due to switch 1 or switch 3.
“Just flip switch 1 and then enter the room.”
Flipping switch 1 does not provide enough information to determine the status of the other bulbs. When entering, you would only know that one bulb is on, but not which switch controls which.
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