Puzzle: There is one bulb inside a room but three switches outside the room. Only one of these switches operates the bulb. There is no way to see the state of the bulb from outside the room.
You have to fiddle with the switches, enter the room once and only once, and have to be able to tell which switch operated the bulb. What will you do?
If you have answered the first question, extend the problem to four switches.
Solution: The first problem with 3 switches was already known to me. The idea is simple. Flick on one of the switches, say switch 1, for quite some time, say about half an hour. Flick it off and flick on a different switch, say switch 2. And then enter the room.
- If the bulb is glowing, switch 2 is the correct switch
- If bulb is not glowing, but is hot, then switch 1 is the correct switch
- If bulb is not glowing and is not hot, then switch 3 is the correct switch
We now have to extend this problem to four switches. The underlying idea is simple. Note that there are two parameters involved - state(on/off) of the switch, and temperature(hot/cold) of the switch. Together, they form 4 distinct combinations. Once this is realized, we have to now figure out a strategy such that each of these combinations points to a unique switch.
The strategy is as follows. First, turn on 2 switches for quite some time, say half an hour (say switch 1 and switch 2). Then, turn one of them off (switch 2) and turn a different switch on (switch 3). With abated breath, enter the room.
- If bulb is glowing and is hot, switch 1 is the correct switch
- If bulb is glowing but not hot, switch 3 is the correct switch
- If bulb is not glowing but is hot, switch 2 is the correct switch
- If bulb is not glowing and is not hot, switch 4 is the correct switch
Enough of flicking switches and examining bulbs now. Lets flick them all off and retire for a nice slumber.
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