A lightbulb is turned on by one of three switches, but you cannot see the bulb from the switches.
real-life/three.switches Added material
Problem
A lightbulb is turned on by one of three switches, but you cannot see the bulb from the switches. How can you determine which switch turns on the bulb if you only want to go from the switches to the bulb once? Assume that the switches are clearly marked indicating which orientation is on, that the lightbulb is an ordinary household incandescent bulb, that you do not have assistants or apparatus such as mirrors available, and in general that this is not a trick question. Can you solve it for four switches?
Show solution
Leave switch 1 off all the time. Turn switch 2 on for a couple of minutes, then turn it off. Turn switch 3 on and leave it on. Now, go to the bulb. If the lightbulb is on, switch 3 controls it. Otherwise, if the lightbulb is hot to the touch, switch 2 controls it. Otherwise, switch 1 controls it. Since incandescent bulbs do not get hot immediately, it is possible to distinguish between four switches. The trick is to turn switch 4 on just before you go into the other room. If the lightbulb is on and hot, than switch 3 controls it, but if it is only warm, then switch 4 controls it.
Additional material
[ Editor: an objection to the assumption that the switches are marked: ] It seems that everyone who answers this question seems to know how to turn off all the switches. If I see switches and do not know what they control, how can I know when they are on? There could be another door to this mystery room with the identical 3 switches. I have many similar setups in my humble abode. Then there are times when a given switch in one position turns a light on, but by toggling the other switch the same position on switch one has the light off. This winded explanation gets back to the orignal problem.... How do I know which is the off position? -- Wayne B Hacker <wbh@math.ufl.edu> [ Editor: a 1995 version of the puzzle as a riddle, with a reply giving the usual heat solution (omitted here, as it is the one above) and a second method. ] Brad Grace (bradx@ix.netcom.com) wrote: : The king took the man down into a dungeon area where there was a : hallway, and at the end of the hallway there was a steel room with a : single lightbulb hanging from the wire which gave it power. The room : was sealed by a large steel door which had no window, and when closed : allowed no view into the room. Where the king and peon were standing : there were three switches in the down position. The king told him that : he had one hour to tell him which switch turned on the light. He said : the door would be closed in the room, and he would only be able to open : the door once after he played with the switches, at which time he would : have to make his guess. If he guessed wrong the king would cut off his : head. The light was off at the beginning of the riddle. : : Can you win the princesses hand in marriage?? If you are allowed to go back to the room and play with the switches again before guessing (shutting the door behind you, of course), then there is another possible solution. This relies on the fact that you can usually hear if a switch is actually breaking/making a circuit if you fiddle with it so as to make a spark. So the solution would be to fiddle with each switch to check if it is actually connected to something. If only one is connected, that is the controlling switch. If all three are connected, open the door, remove or break the lightbulb, close the door and find the switch that is no longer completing a circuit. That switch is the controlling switch. -- Peter Suzman <suzman@netcom.com>