The challenge
Three switches are outside a closed room. Exactly one controls a traditional incandescent bulb inside. You may operate the switches however you like, but may enter the room only once. How do you identify the correct switch?
Three Switches and a Light Bulb Puzzle
Solve this medium logic challenge, then compare your reasoning with the hint, checked answer, verification, and variation.
Hint
The bulb can give you information in more than one way.
Map the three observable states
Turn on the first switch for several minutes, then turn it off. Turn on the second switch and enter the room. A lit bulb identifies the second switch. An unlit but warm bulb identifies the first. An unlit, cool bulb identifies the third.
One visit, three signals
- Use the first switch long enough to create heat, then turn it off.
- Leave the second switch on and do not use the third switch.
- Enter once and map lit, warm, and cool states to the three switches.
State coverage check
The three final states are mutually exclusive and cover every switch, so every possible observation identifies exactly one answer.
Why light alone is insufficient
Treating light as the only output leaves just two visible states for three candidates. The constraint is one visit, not one kind of observation.
Information can persist after an action
Look for hidden state. Heat preserves information after the visible signal is removed.
How confident were you?
Plan observations before touching a switch
List every observation available after the single room visit. The bulb can be on or off, but an incandescent bulb also has a temperature. That gives three distinguishable end states, one for each switch.
Change the available signal
Suppose the bulb is an LED that does not become noticeably warm. What additional allowed action or observable signal would be needed to distinguish three switches in one visit?
Study how to solve logic puzzles for the reusable method behind this challenge. Then explore the logic puzzles and deductive reasoning learning path for connected examples and practice.