Post:
You have three switches in one room and a single light bulb in another room. You are allowed to visit the room with the light bulb only once. How do you figure out which switch controls the bulb? Write your answer in the comments before looking at other answers.
Comment:
If this were an interview question, the correct response would be "Do you have any relevant questions for me? Because have a long list of things that more deserving of my precious time than to think about this!
The “right” solution doesn’t work. Each light switch can turn the lightbulb on by being up or being down. This means there is 3*2=6 possible cases of which light switch state turns on the light bulb. So we need to make 3 observations to bring it down to one case. An example of the original logic failing is that the light bulb being on could mean either that switch 2 being up turns it on, switch 1 being down turns it on, or switch 3 being down turn it on.
I present an alternative solution. Since the conventional solution says that we can feel its temperature, we know the light bulb is within reach. We can visit the room first, unplug the light bulb, and bring it back to the light switches. Then we can check all 2^3 permutations of light switches to see which one effects the bulb. Of course, it is likely that non affects it after unplugging it, but it could be a wireless light bulb.
What if the light’s on with a combination of different positions spanning 2 or all of the switches? How many possibilities then? Plus the possibility none of these switches have anything to do with that light, and the original question had a fallacious premise. Then even the possibility that the light has different states from different combinations… and/or that the light functions differently at different times, and/or different combinations of other criteria. How many possibilities do we have now? … I can’t be bothered doing the maths. I gotta get breakfast. n_n