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Which of four switches lights the hidden bulb

Question

Outside a closed room are four switches, all off. Exactly one of them operates a light bulb inside the room, and from outside you cannot see the bulb. What is the minimum number of times you must enter the room to be sure which switch controls it?

Short answer

Once. Turn switches 11 and 22 on and wait several minutes, then turn 22 off and turn 33 on, and go in. The bulb's state (on or off) together with its temperature (hot or cold) gives four combinations: on and hot means 11, off and hot means 22, on and cold means 33, off and cold means 44.

Adapted from Zhou, A Practical Guide to Quantitative Finance Interviews, sec. 2.3 Thinking Out of the Box, 'Light switches', p.13; question and answer rewritten by SelfMadeQuant.com.

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