The Three Switches Puzzle
Three switches sit in a hallway. One of them controls a bulb in a closed room. You may flip them as you like, then open the door once. Which switch runs the bulb?
If you only think about the bulb being on or off, the job looks impossible. One visit gives you two possible observations, on or off, and you need to tell three switches apart. So you need a third kind of observation.
Stop reading here if you want to try it
Take a real minute. The fun is in the moment the extra clue appears.
The answer
- Turn switch A on and leave it for ten minutes.
- Turn A off and turn B on.
- Open the door.
If the bulb is lit, it is B. If it is dark but warm to the touch, it is A. If it is dark and cold, it is C.
What the puzzle teaches
Most stuck problems are stuck because of a quiet assumption. Here the assumption is that a bulb only has one property worth measuring. When a problem seems to need more information than you can collect, ask what else you could observe.
A modern LED barely warms up, so a stickler may object. Good. Checking the conditions of a puzzle is exactly the habit we are here to build. Assume an old-fashioned incandescent bulb.