32. Find the Right Switch in One Trip Near the front door on the ground floor there are three unlabeled switches. One—and only one—of them controls the ceiling light in a room on the fourth floor. You would like to determine which switch it is, but you want to climb the stairs only once.How can you identify the correct switch with a single trip upstairs? Added 3 October 2010 Show Hint Show Solution Hint: The bulb does more than give off light when it is on. Solution: Turn on the first switch and leave it on for about 10 minutes. This will allow the bulb, if connected, to heat up. After 10 minutes, turn the first switch off and immediately turn on the second switch. Now walk upstairs.• If the light is on, it is controlled by the second switch.• If the light is off but the bulb is warm to the touch, it is controlled by the first switch (which was on long enough to heat the bulb).• If the light is off and the bulb is cool, it must be controlled by the third switch.Thus you discover the correct switch with only one trip upstairs.
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