## Switches and lights variant.

A forum for good logic/math puzzles.

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ericgrau
Posts: 92
Joined: Sat Dec 13, 2008 7:14 pm UTC

### Switches and lights variant.

Instead of 3 switches there are 10 switches... and 10 corresponding lights in a random order. The switches are in one room, the lights are in the next room, following a convoluted hallway and a closed door. You may fiddle with the switches as much as you want, go to the light room, examine the lights and return to the switches, but once you leave the light room the door closes and locks behind you in some irreversible way. Your job is to properly label all the switches, identifying which light each one belongs to so that the Powers that Be may control the lights from afar. Disrupting their ability to do so or otherwise causing them costly property damage results in a failure.

You may bring any tools or other objects you can carry in a single trip. No people. You have access to a 120 VAC 60 Hz power outlet and ethernet port near the switches. The lights are all 100 W, 120 V white incandescent bulbs. The switches are typical wall mounted switches with screw on plates.

I don't have an answer to it but I bet I could find one soon enough. I'm more interested in the many solutions others will come up with.

jakerman999
Posts: 55
Joined: Thu May 29, 2008 2:14 am UTC

### Re: Switches and lights variant.

Is there a second Ethernet port in the light bulb room? If yes, is it connected to the same local area network? what are the walls constructed of(wood, plastic, brick, other)? Is there a gap underneath the door(and/or around a different edge)?

And just to get the nonsense answers out of the way:
Spoiler:
1)Bring in a weight that will prevent the door from closing.
2)Wire all the switches into one and label it master switch.
3)Same as above but on the bulbs end.
And the science fiction methods
Spoiler:
2)Create a recursive time loop through the worlds smallest time traveling device
If all the worlds my stage let's go to intermission

ericgrau
Posts: 92
Joined: Sat Dec 13, 2008 7:14 pm UTC

### Re: Switches and lights variant.

The light bulb room has neither an ethernet port nor 3 pronged outlet. Though accessing the bulbs and standard lightbulb sockets shouldn't be difficult. Those are the only things you know are in that room ahead of time. Technically you only know about the screw-in bulbs, but bulb sockets are probably a safe assumption. The walls are indoor walls so they're drywall (weaker than wood).

The "Powers that Be" phrase is meant to prevent excessively destructive answers and to anchor this into a semi-realistic modern world where the higher ups want a real solution, to prevent nonsense and sci fi answers. For the sake of argument they have also declared that the door most close and lock behind you. Umm, I dunno, in case of zombie attack (and shotguns might damage the hallway paint).

ircmaxell
Posts: 44
Joined: Wed Dec 24, 2008 3:06 am UTC

### Re: Switches and lights variant.

Well, if you can bring ANY object(s) into the switch room:

Spoiler:
I'd bring in an Arduino and a bunch of servos. I'd hook each servo up to each light switch. Each light switch would stand for a bit. Then, I would have the Arduino execute a sequence displaying each step for 30 seconds and then turning off for 30 seconds. I'd start it on a 5 minute delay and immediately go into the room with the lights. The first light that goes on is associated with the first switch. Then watch the order of the lights as they turn on and off, and you should be able to deduce the exact pairing.

As for what the sequence is, it could be simple binary addition (but this could get quite long as 10 bits yields a lot of combinations). It could be the Fibonacci sequence. It could be something else I'm not thinking of... I would prob do the Fibonacci sequence, as it grows large enough fast enough that it shouldn't take forever, but still should hit every bit a number of times that even if you miss one step you should still be able to figure out the sequence...

redrogue
Posts: 116
Joined: Tue Dec 15, 2009 9:17 pm UTC

### Re: Switches and lights variant.

Well *I'd* bring...
Spoiler:
...a thermal camera and a baseball bat.

I'd turn all of the switches on for 10 minutes, then turn them all off in one minute increments. Then I'd wander into the room, scan the bulbs with the thermal camera, and remember the order coolest to hottest. The coolest bulb corresponds to the first switch I turned off, etc.

The baseball bat is for the electrician who decided it was appropriate to wire things this way.

ircmaxell
Posts: 44
Joined: Wed Dec 24, 2008 3:06 am UTC

### Re: Switches and lights variant.

Well, on that note, you could always:

Spoiler:
Get 10 resisters. In the switch room, replace each switch with a resistor. Then turn them all on and walk into the light room. You'd see each light at a different brightness. So order them by brightness, and you found your relationship.

But in reality:

Spoiler:
I think there are an infinite number of "correct" answers. The stipulation that you're allowed to bring anything in kinda spoils it.

I am curious what the ethernet port was intended to be for...

ericgrau
Posts: 92
Joined: Sat Dec 13, 2008 7:14 pm UTC

### Re: Switches and lights variant.

Infinite correct answers was the goal. There was no predetermined solution nor necessarily a purpose for anything. Though I thought about it for a little bit and got an answer similar to a couple here. Maybe next people could think up the simplest / fastest / easiest / least chance of a mistake solutions.

jakerman999
Posts: 55
Joined: Thu May 29, 2008 2:14 am UTC

### Re: Switches and lights variant.

Well at this point I'd say
Spoiler:
Bring a laptop, for several different possibilities.

1)Run wires from the switch room to the light room, while bringing with you a camera. Set everything up so that you can all of the light bulbs in one shot(using the camera's viewfinder), then walk back to the switch room and use the laptop to identify which light co-responds to which switch.

2)Same as above, but using a wireless camera. The drywall shouldn't provide too much of a challenge for a wireless signal to transmit through. Make sure the camera has a long lasting battery.

3)Plug the laptop into the Ethernet port(and possibly an electrical outlet) and visit this thread for other possible solutions(bonus points for meta?).

although option three might leave you a little empty handed.
If all the worlds my stage let's go to intermission

math
Posts: 29
Joined: Sun Oct 24, 2010 4:25 am UTC

### Re: Switches and lights variant.

Spoiler:
I would just bring a remote camera of some sort... pretty obvious the second I noticed *any objects*
Ghostly, she stood in front of him and looked into his eyes. "I am here," she said. "I am here. I want to touch you." She pleaded: "Look at me!" But he would not see her; he only knew how to look at the outside of things.

balr
Posts: 54
Joined: Mon Dec 07, 2009 5:29 pm UTC

### Re: Switches and lights variant.

The traditional three bulb / three switch solution hinges on a three-way partition that depends on:
Spoiler:
one bulb off; one bulb on; one bulb that had been on, as determined by a hand check that it is warmer than ambient

I could extend that to look for a ten-way partition:
Spoiler:
one bulb on; one bulb off; eight bulbs which had been on, each at a different temperature. I could arrange that by switching eight switches ON and then switching one OFF every 30 seconds. Then switch one other ON. Then I nip into the bulb room with a battery powered infrared thermometer and measure how warm each bulb is.

However, that solution depends on all bulbs being ON or OFF at the start (as does the traditional three bulb problem). ericgrau does not explicitly state that is a starting condition (it is vaguely implied). Without initial assumption, a solution is likely to be harder.

ircmaxell
Posts: 44
Joined: Wed Dec 24, 2008 3:06 am UTC

### Re: Switches and lights variant.

balr wrote:However, that solution depends on all bulbs being ON or OFF at the start (as does the traditional three bulb problem). ericgrau does not explicitly state that is a starting condition (it is vaguely implied). Without initial assumption, a solution is likely to be harder.

Well, if you can assume that each switch is clearly labeled on and off, then you could simulate the initial assumption by turning them all off and waiting like 30 minutes to an hour. If they are not clearly labeled, but are consistent (up means the same for each switch), then it would be quite a bit harder since you can't determine if up is on or not, so the method wouldn't be guaranteed to work considering that you could be turning the bulbs on in sequence (assuming again that a bulb warms up fully quite fast, less than the 5 minutes used by your solution).

Either way, it's an interesting problem... A further extension based on the above would be to state a similar problem:

There are 10 light-bulbs in one room, and 10 light switches in another (and you can't see between the rooms at all, they are separated by a hallway). You are only allowed to be in one room at a time, and can't leave anything in the other room when you're not there. The switches are neither marked (on-off) nor consistent (one switch might be up-on, and the next down-on). You can bring any tools that you want that you can carry, but no destructive tests are allowed (and remember, you can't leave anything behind when you leave either room). Starting in the switch room, what is the smallest number of times that you must enter the bulb room to 100% determine both the association between each switch to each bulb and the associated switch configuration (up-on vs down-on)?