# Three switches

Question:

There are three switches in a hallway. One switch controls a light fixture in a room at the far end of the hall. The door to the room is closed, and you can’t see whether the light is on or off. You need to find out which of the three switches controls the light. You are allowed only one inspection. How can you be certain of finding out which switch controls the light?

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Solution: The chief constraint is that you are allowed only one inspection. In other words, you need to solve the brainteaser with one and only one opportunity to obtain clues. Many candidates spoil their chances by wasting credibility on trying to defeat the constraint, e.g., Can I set up a video camera? Can I keep the door open? It’s much better to accept the constraint and work within it.

Call the switches 1, 2, and 3. Leave switch 1 off. Turn switch 2 on for five minutes and then turn it off. Turn switch 3 on. Enter the room. If a bulb is on, it’s controlled by switch 3. Feel the light bulb for heat. A warm bulb is controlled by switch 2. A bulb that is off and cold is con-trolled by switch 1.

Answer: Get an additional data point by noting that lightbulbs give off heat.