Three Switches Problem

> There is only a light bulb in a room.   You can only observe the
> room through a door which is closed.  Outside this room, you see
> 3 switches, and you are told that one of the 3 controls the light
> bulb in the room.  Now, with just _one_ opening of the door, how
> do you determine which switch is the live one?
>
> (Of course, you can touch the switches when the door is open.)
>
> (I was given a clue that you could actually go into the room, but
> the relevancy eludes me.)

What the rec.puzzles FAQ says:
 logic/three.switches moved to real-life/three.switches.

==> logic/three.switches.p <==
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 can only visit 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.


==> logic/three.switches.s <==
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.


<> variation <>

A Scientist uses 3 lamps to illuminate experiments in his laboratory.
They are currently turned off and unfortunately the switches for each of
them are in a different room, from where you cannot see into the lab. He
visits the room with the switches once, does as he pleases with the
switches, then goes back to his laboratory. Without the help of anyone else,
he is then able to identify exactly which light switch turns on whch lamp.
So how does he do it?

<> Spoiler <>

The scientist goes into the room with the switches and turns on the
first one.  Then he sits around for about five minutes, flicks off the
switch, then flips on the second one.   He immediately walks into the
room with the lamps.  If a lamp is on, it's the second switch.  If the
lamp is off, but the bulb is hot, it's the first switch.  Otherwise,
it's the third.

This 3 bulb puzzle is in the Tomorrow's World magazine 
launch issue dated April 1998.