Three Switches, One Bulb
The problem
A windowless room contains a single incandescent bulb. Outside the room, in a corridor, are three switches labelled A, B and C. Exactly one of them controls the bulb; the other two do nothing. You may flip switches as much as you like, but you may enter the room only once. Once inside, how do you determine which switch controls the bulb?
- You may enter the room exactly once, and you cannot see the bulb from the corridor.
- The bulb is an old filament bulb; it is not visible through any gap or window.
Take a minute
Reveal hint 1
A switch has two states, but a filament bulb carries more than two observable properties.
Reveal hint 2
The bulb's temperature is a second channel of information — but you need to distinguish three cases, so you need to keep the three switches in three distinct states.
Solution
AnswerTurn A on for several minutes, turn it off, turn B on, then enter: the lit bulb means B, a warm unlit bulb means A, and a cold unlit bulb means C.
Derivation
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Recognise the information channel.
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Assign one state per switch.
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Execute the sequence.
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Read the state.
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Why one entry is enough.