# Lightbulbs!

by Icebreaker
Tags: lightbulbs
 P: n/a Here's an easy riddle: You are in a room with 3 switches. The room is adjacent to another in which there are 3 lightbulbs. Each of the lightbulbs is connected to a switch in your room. You cannot see into the other room. You may manipulate the switches in any way you like, and you may go to the other room and observe the results, but only once (once you leave your room, you cannot reenter). How do you find out which switch leads to which bulb?
 PF Patron Sci Advisor Emeritus P: 16,094 Ooh, I love this problem!
 P: 297 Hmmm...Place a mirror in the doorway, so that you can see into the other room. Shout to your friend in the other room, "I'm working the first switch now!", etc. Switch on #1, and wait for 20 years. Now switch on #2. Go into the other room. Bulb #1 is blackened (and burnt out). Bulb #2 is on. Bulb #3 isn't.
P: n/a

## Lightbulbs!

There is a less destructive way to do this.
 P: 3 have one on, one off, one on, tape a weight above one on light switch so it'll eventually fall off and turn it off, and run over to the other room to see which one turns off =)
 P: 1,116 Answer You turn two of the swtiches on and leave one off. Then after a minute or so you turn off on of the switches that is on. Enter the room and you can see immediately which on leads to the one switch. Then touch the other lightbulbs, which is off, and see which is hot. The one that is hot is controlled by the switch that was turned on and then switched off after a minute or so before entering the room. This then leaves one switch with one lightbulb. Easy. The Bob (2004 ©)
 P: 297 I was assuming that the light bulbs were mounted up on the ceiling, out of reach. Incidentally, the standard technique given in The Bob's answer, can be extended to more than three bulbs. Eventually, it gets silly, but it would probably be possible to differentiate between 5 or so bulbs, by the method he describes.
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P: 11,137
 Quote by ceptimus I was assuming that the light bulbs were mounted up on the ceiling, out of reach. Incidentally, the standard technique given in The Bob's answer, can be extended to more than three bulbs. Eventually, it gets silly, but it would probably be possible to differentiate between 5 or so bulbs, by the method he describes.
So if you were going to leave say three bulbs on, for different periods of time before turning them off, would you :

1) Turn on bulb1; wait 5 minutes and turn on bulb2; wait 5 more minutes and turn on bulb3; wait a final 5 mins, turn them all off

OR

2)Turn on all bulbs; wait 5 minutes and turn off bulb3; wait 5 more and turn of bulb2; wait a final 5 mins and turn off bulb1 ?
P: 1,116
 Quote by ceptimus I was assuming that the light bulbs were mounted up on the ceiling, out of reach.
You see I have that one covered as well. I am 2.02m and so there are very few ceiling that are too high so I am fine and the answer is fine for me.

 P: n/a Bob indeed has the solution, but I can't see it being extended to more than 3 bulbs. Unless your hands are extremely sensitive to heat differences.
 P: 297 I think bulbs warm up, a lot faster than they cool down. I think the temperature curve, on cooling, is roughly exponential. I'd want to do an experiment to see how long a bulb had to cool before I couldn't feel any difference between it and one that had never been on. Then I'd take half that time for one bulb, and keep halving thereafter for the others. Say it takes 8 minutes for a bulb to cool till I can't reliably tell it's been on. Then I'd try 4 minutes of off time for bulb A, 2 minutes for bulb B, one minute for C, 30 seconds for D and 15 seconds for E. I guess the time taken to run between the rooms, and feel the bulbs would make it difficult to go beyond that. Bulb F would be left on, and G would be always off. If the bulbs take an apreciable time to heat up (which I doubt) then you could also have two or more 'on' bulbs, identified by their differing temperatures.
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P: 11,137
 Quote by Icebreaker Bob indeed has the solution, but I can't see it being extended to more than 3 bulbs. Unless your hands are extremely sensitive to heat differences.
C'mon ! You can tell the difference between warm, hot and yaaoouuuch
 P: 161 well, i had actually solved this in seventh grade. but i would still like to know how ceptimus would solve it, given that we are not allowed to touch the bulbs.
P: 2,059
 Quote by ceptimus Hmmm... Switch on #1, and wait for 20 years. Now switch on #2. Go into the other room. Bulb #1 is blackened (and burnt out). Bulb #2 is on. Bulb #3 isn't.
Now that one is really good, at least that's what I think.
 P: n/a Let me just put my version of the answer down, because I did pose the question. 1. Switch on switch 1, wait for 10 minutes and turn it off. 2. Switch on switch 2 and leave for the other room. 3. The hot bulb is connected to switch 1, the glowing bulb to switch 2 and the off bulb to switch 3.
 P: 1,116 Well I think I have it if you are not allowed to touch the ligthbulbs. Assuming the three lightbulbs are like the once made before Willis Whitnew (in 1903) then you can tell which is which by the same method but the one that has been turned off will be darker than the one that was never one because carbon will have darkened the glass of the bulb. The Bob (2004 ©)
 P: 297 Modern lightbulbs also go blacker by the time they burn out, This was the basis of my first answer.
 P: 161 i think a similar question was put up here before also. i think it was about 8-10 months back, but that question said that the bulbs were water cooled, or something like that

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