You are in the downstairs lobby o f a house. There are three switches, all in the "off' position. Upstairs, there is a room with a light bulb that is turned off. One and only one of the three switches controls the bulb. You want to discover which switch controls the bulb, but you are only allowed to go upstairs once. How do you do it? (No fancy strings, telescopes, etc. allowed. You cannot see the upstairs room from downstairs. The light bulb is a standard lOO-watt bulb.)
2026-04-04 15:20:38.1775316038
It is possible to find which one is the switch of the light without going upstairs in this recreational problem?
350 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
Well, I wouldn’t call a $100W$ light bulb “standard” :-)
This is not really a mathematical problem. Mathematically speaking, if we were to assume that you can put the switches in some state and observe only one binary result from this (lamp on or off), the task would be impossible, because the information about three possible outcomes cannot be encoded in a binary result.
The solution is to turn one switch on for a while, turn it off, turn another one on and quickly go upstairs. Then the three switches can be distinguished according as the lamp is on, warm or off.