9. Identifying the Light Switch Challenge
9. You're standing downstairs next to a panel of three light switches, all currently in the off position. One of these switches controls an incandescent lightbulb in an upstairs room, while the other two do nothing. Both the downstairs room and the upstairs room are very small, they are both 5 foot (1.5 meters) cubed. You need to figure out which switch controls the bulb, but with some restrictions:
1. You can flip the switches however you like (on or off).
2. After you’re done, you can go upstairs and check the bulb only once.
3. You can’t see the bulb or any light from where you're standing downstairs.
4. You only get one trip upstairs, so no back and forth.
How can you determine which switch controls the lightbulb in a single trip upstairs?
Added 1 January 2007
Hint: The light is in the ceiling, but the ceiling is very low and easily within reach.
Solution:
Here's a clever solution to figure out which switch controls the bulb using only one trip upstairs:
1. Turn on one switch (let’s call it Switch 1) and leave it on for a few minutes.
2. After a few minutes, turn off Switch 1 and immediately turn on another switch (Switch 2).
3. Leave the third switch (Switch 3) in the off position.
4. Go upstairs and check the bulb.
Now, based on the state of the bulb, you can determine which switch controls it:
1. If the bulb is on, then Switch 2 controls the bulb (since it's the only one you left on).
2. If the bulb is off but warm to the touch, then Switch 1 controls the bulb (because it was on for a few minutes and generated heat before you turned it off).
3. If the bulb is off and cool to the touch, then Switch 3 controls the bulb (since it was never turned on).
4. This way, you can definitively determine which switch controls the lightbulb in just one trip!
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