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March 24, 2004
The Attic Lamp Switch
A downstairs panel contains three on-off switches, one of which controls the lamp in the attic—but which one? Your mission is to do something with the switches, then determine after one trip to the attic which switch is connected to the attic lamp.
Adapted with permission from Mathematical Puzzles: A Connoisseur's Collection by Peter Winkler. Copyright © 2004 by A K Peters, Ltd. See www.akpeters.com/book.asp?bID=197.
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It's impossible to tell which switch is connected to the attic lamp if all you get is one bit of information from your trip to the attic. However, you can get more information with your hand!
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Turn on switches 1 and 2, wait a few minutes, then turn off switch 2 before ascending to the attic. If the bulb is off, but warm, you conclude that switch 2 is the winner. If the bulb is on, it's switch 1. If the bulb is off, but cold, it's switch 3.
If you can't reach the bulb but have enormous patience, you can achieve the same effect by turning switch 2 on and then waiting a couple of months (or longer) before turning on switch 1 and visiting the attic. If the bulb is burnt out, switch 2 is the culprit.
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