# Which switch goes to which bulb?

You are in a room with three switches, labeled $A$, $B$, and $C$. Initially, each switch is in an off state. In an adjoining room, there are three incandescent light bulbs. Your task is to correctly label which switch goes to which bulb.

The catch: you may only enter the bulb room once. You have as long as you need in the switch room, and you may flip any switch as many times as you'd like, but once you leave the switch room, you may not enter it again.

There is a way to know for certain which bulb goes to which switch. How?

• Why did you ask this? Moreover, why did you answer it yourself? It is a fairly well-known challenge, but you could have at least let someone else answer it. – TheDoctor May 15 '14 at 3:25
• @TheDoctor Self-answering is encouraged on SE, and especially during private beta I think it's popular to seed the site with some (quality) questions you can self-answer. The quality is of course important, but this question seems ok to me, and regardless: the fact that it's self-answered should not be the problem, we should focus on the question content itself. – WendiKidd May 17 '14 at 1:42
• An entertaining analysis: blogs.msdn.com/b/ericlippert/archive/2011/02/14/… – A E Sep 3 '15 at 6:58

Turn switches A and B on. Wait about a minute. Turn switch B off. Go to the bulb room. The bulb that is on corresponds to switch A. The bulb that is off, but warm, corresponds to switch B. The bulb that is off, but cold, corresponds to switch C.

The explanation:

Incandescent bulbs produce a significant amount of heat. In the amount of time it takes you to walk from one room to the other, the bulb will have not had time to cool down, unless the rooms are unreasonably large.

• You should also accept your own answer if this is just your own Q&A knowledge sharing. – Joe Z. May 15 '14 at 0:17
• Alas, another beautiful puzzle succumbs to the advance of technology. LED bulbs make this fail. – Ross Millikan May 15 '14 at 13:28
• @JoeZ. - It's not allowed to accept your own answer until 48 hours after. – Xynariz May 16 '14 at 2:01
• Oh, really? I don't think I've ever actually accepted my own answer before, so I didn't really know. – Joe Z. May 16 '14 at 2:22
• @Joez. - Neither did I, until I asked this question. – Xynariz May 20 '14 at 22:51

A late solution for LED lights as well, or if you can't touch these hot bulbs :P

Since all of the bulbs are new and identical with the exact liftetime:

1 -

Turn on the first switch.

2 -

Wait 24 hours.

3 -

Turn on the second switch.

4 -

Get into the room, wait until a bulb turns off.

5 -

The bulb that turns off first corresponds to the first switch.

The one which is still on corresponds to the second switch.

That way you can have LED lights and you don't get a burn, but you might have to wait long time.

• "you might have to wait long time" - Approx 50,000 hours? – Richard Dec 5 '14 at 0:34
• @Richard what's 6 years between friends? – Joe Dec 5 '14 at 21:05
• @Joe - I'm just thinking that you might want to bring a few books while you wait. – Richard Dec 5 '14 at 21:07
• @Richard a small sacrifice to work out which bulb is which, I'm sure you'll agree – Joe Dec 5 '14 at 21:08
• You can speed up the process by jiggling the first switch on and off constantly, which Mythbusters found can reduce the lifespan to mere weeks if you do it 24/7. – Vitruvius May 1 '15 at 4:57

A solution for 4 lightbulbs, A B C D.

turn on A and B. wait ten minutes. turn A off. turn C on. run upstairs. touch the lit bulbs. the hot one is B. the cold one is C. touch the dark bulbs. the warm one is A. the cold one is D.

• Why would you go upstairs? The puzzle says the lights are in an adjoining room. ;) – Trevor Powell Mar 23 '18 at 8:49

Pardon the extremely (extremely!) late answer, but it occurs to me that there's a much easier and faster solution to this puzzle than has yet been suggested. All it requires is noticing that the puzzle specifies that...

...the lights and switches are in adjoining rooms.

In the normal formulation of this puzzle, that's not the case. Normally...

...the switches are in the basement and the bulbs are in the attic, separated by half a dozen rooms, specifically to cut off line of sight.

But this puzzle explicitly isn't set up in that usual way, and as a result we can solve the puzzle much more easily! (And some might say 'trivially')

All we have to do is flip a switch, peek through the door into the bulb room (without actually leaving the switch room), and take note of which bulb turned on.

Repeat for each switch, and we're done! And our non-burnt fingers will thank us. :)

• Clever outside-the-box thinking! – Xynariz Feb 12 at 18:59