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!
Also the number of outcomes isn’t connected to the solution space reduction the way you say. If you don’t know whether the fake coin is heavier or lighter, both tilt-right and tilt-left are effectively the same result. So at least your first test really only has 2 meaningful outcomes.
In general, you’ll only reduce your solution space DOWN TO (not by) 1/(number of distinguishable outcomes) if the possible solutions are evenly divided among those outcomes. It’s easy to have a problem where “result 1 narrows it down a lot, result 2 doesn’t tell us much”
Like I said, it’s been over a decade, some of the specifics may be lost to me.