Three switches puzzle: Determine which light corresponds to each switch.

You are standing in a hallway next to three light switches, all of which are off. Each switch operates a different incandescent light bulb in the room at the end of the hall. You cannot see the lights from where the switches are. Determine which light corresponds to each switch. You may go into the room with the lights only once.

The crux of this problem comes quickly to the fore: There are only two possible positions for each switch (on or off) but there are three lights to identify. You can easily identify one light, by setting one switch differently than the other two, but this leaves you no way to distinguish the two left in the same position.

When confronted with a seemingly impossible task, you should go back to basics. The two key objects in this problem seem to be the switches and the lights. What do you know about switches and light bulbs? Switches make or break an electrical connection. When a switch is on, current flows through it. A light bulb consists of a resistive filament inside an evacuated glass bulb. When current flows through the filament, it consumes power, producing light and heat.

How can these properties help you solve the problem? Which of them can you detect or measure? The properties of a switch don’t seem too useful. It’s much easier to look at the switch to see whether it’s off or on than to measure current. The light bulbs sound a little more promising. You can detect light by looking at the bulbs, and you can detect heat by touching them. Whether there is light coming from a bulb is determined entirely by its switch - when the switch is on, there is light; when it’s off, there isn’t. What about heat? It takes some time for a light to heat up after it’s been switched on, and some time for it to cool after it’s switched off, so you could use heat to determine whether a bulb had been on, even if it were off when you walked into the room.

You can determine which switch goes with each bulb by turning the first switch on and the second and third off. After ten minutes, turn the first switch off, leave the second off, and turn the third on. When you go into the room, the hot dark bulb corresponds to the first switch, the cold dark bulb to the second, and the lit bulb to the third.

Although there’s nothing truly outlandish about this question - it’s not just a stupid play on words, for instance - it is arguably a trick question. The solution involves coming up with something somewhat outside the definition of the problem. Some interviewers believe that questions like this will help them identify people who can “think outside the box” and develop nontraditional, innovative solutions to difficult problems. In the authors’ opinion, these problems are cheap shots that don’t prove much of anything. Nevertheless, these problems do appear in interviews, and you should be prepared for them.

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