Three switches downstairs, one bulb in the attic.
Three switches control one attic bulb and you get a single trip upstairs. Which switch is wired to the bulb? Two states of information are not enough for three candidates, so the answer must come from somewhere outside the on-off world.
You stand in a hallway with three ordinary light switches, all off. Exactly one of them controls an incandescent bulb in the attic, two floors up. The other two are connected to nothing. From the hallway you cannot see the attic or any glow from it.
You may flip the switches as much as you like, in any pattern, for as long as you like. Then you climb to the attic once. Once you are up there, you may not come back down to touch the switches again; whatever you observe on that single visit must settle the matter.
Determine, with certainty, which switch controls the bulb.
The information-theoretic tension is worth stating plainly, because it is what makes the puzzle feel impossible for a minute. When you walk into the attic, the bulb shows one of two states: lit or dark. Two observable states cannot distinguish three hypotheses. So either the puzzle is unsolvable, or the bulb carries more observable state than on versus off. It does, and the puzzle specified the bulb type on purpose.
Stuck? Open hints one at a time
Each hint gives away one more layer. Stop the moment something clicks.
Hint 1 a nudge
Count states. You need to distinguish 3 possibilities with one observation, so you need at least 3 distinguishable outcomes in the attic. On and off make two. What third observable does an incandescent bulb offer?
Hint 2 the key move
An incandescent filament converts most of its power to heat, and that heat lingers after the current stops. A bulb that was on until recently is dark but warm. You control time with the switches; use it.
The solution
Reveal the full solution
Flip switch 1 on and leave it on for ten minutes. Then flip it off, flip switch 2 on, and go straight up to the attic.
- Bulb lit: switch 2 is the one.
- Bulb dark and warm to the touch: switch 1.
- Bulb dark and cold: switch 3.
The scheme works because it widens the observation channel. The bulb's electrical state carries one bit, but its thermal state carries another, and the two are independent enough to combine: lit or dark crossed with warm or cold. You only need three of those four combinations, and the ten-minute soak guarantees the warm reading is unambiguous.
What this puzzle is really testing
Interviewers who ask this are probing whether you challenge the frame you are handed. The trap is accepting "the bulb is a boolean" as a premise when the puzzle never said it; the physical object has richer state than the abstraction suggests. Engineers hit the same wall constantly: a system that seems to expose too little information often leaks more through side channels, timing, or history. The counting-states discipline in hint 1 is the same argument that shows a comparison sort cannot beat n log n: log of n-factorial comparisons are required because each comparison yields one bit and there are n-factorial orderings to distinguish. The counting sort deep-dive walks that lower-bound argument properly, and the sorting module places it in context.
Follow-ups to expect
Two natural extensions: with an LED bulb (nearly no heat), can it still be done? And what is the maximum number of switches identifiable in one trip? With heat available you get up to four (two bits: lit/dark times warm/cold); without it you are back to two. If you liked the "how many outcomes can one observation carry" framing, the bulb-toggling puzzle from yesterday exercises the complementary skill: extracting structure from a process instead of an observation.