I’m with Robert, I think these interview questions reveal a disrespectful interviewer. Also I don’t really want to work at a place where my coworkers qualifications are that they happen to be good at riddles.

Also, I’d be incredibly insulted if anyone asked me a question like this in an interview.

“Devise a winning strategy when you do not know whether the initial state of the switch is on or off.”
Using the same strategy here would result in a one man uncertainty. If the initial state is on, then the finish count would be the amount of people + 1 (excluding the counter). If the initial state is off, then finish count would be the amount of people (excluding the counter).
This can be solved if everybody turn on the lights two times. Then the finish count would be the amount of people (excluding the count) times two.

example with 3 people and 1 counter
Case 1: The initial state is off. 3 people turn on the switch twice and the counter declares that everybody have been in the room on count 6.

Case 2: The initial state is on (So the count starts at 1). 2 out of 3 flips the switch twice (so the current count is 5). Then counter can’t declare that everyone have been in the room before the last person enters the room and turn the switch on.

Couldn’t solve the one with the sinners without assuming that they knew the amount of sinners though. It’s not forbidden to tell people that they are not sinners right?

Well, I enjoyed the questions but I totally forgot about the rest of your post. *Bookmarked*

Suppose we only knew this: ‘Each prisoner will visit the “switch room” arbitrarily often.’ In such a case, the warden could arrange that the census taker will visit the switch room once at a time when it’s too early to answer, and never visit again. If the warden doesn’t know who the census taker is then the warden picks a bunch of people at random so the warden has a bunch of chances of winning instead of being sure of winning.

We do need this: ‘More precisely, for any N, eventually each of you will visit the “switch room” at least N times.’ Now we are guaranteed that the census taker will eventually get the full count.

If the villagers are allowed to count and communicate, then the problem could be solved on day one by dividing the villagers into groups of and having each villager communicate the number of sinners they see.

There are N villagers. At the first nightly meeting, each person writes down the number of sinners he/she sees and these counts are collected [by the priest perhaps].
One of three scenarios may occur:

*Scenario 1 (trivial): Each villager counts N-1 sinners. In that case all villagers are sinners and must leave on that day.

*Scenario 2 (trivial): Each villager counts 0 sinners. There are no sinners in the village (The priest lied, which did not brand him a sinner however).

*Scenario 3: Some villagers count X sinners and others count X+1 (where X<N). In this case, all villagers who only counted X are themselves sinners and will leave on that day.

This would accomplish the filtering on the 1st day without one villager telling another [directly] about the observed mark.

It seems like this way of solving the problem results in an order of magnitude less complexity than the other posted solutions.

Lastly, it would seem that since we are guessing at the method used by the villager, there is no way of identifying the number of sinners in the original problem as it was stated, as if they had followed this method, 1 day would have been sufficient. (perhaps they spent the extra time packing?)

Or did I miss a constraint?

Great post/comments btw!

At the first nightly meeting, each person writes down the number of sinners he/she sees and these counts are collected [by the priest perhaps]. The highest number recorded [N] will be the count of the number of sinners in the village, which corresponds to the count observed by all non-sinner. This number is announced by the priest and each person who had counted N-1 sinners will know to leave.

This would accomplish the filtering on the 1st day without one villager telling another about the observed mark.

Seems like this way of solving the problem results in an order of magnitude less complexity than the other published results.

Also it would seem that since we are guessing at the method used by the villager, there is no way of identifying the number of sinners in the original problem as it was stated, as if they had followed this method, 1 day would have been sufficient. (perhaps they spent the extra time packing?)

Or did I miss a constraint?

Great post/comments btw!

Also, it’s also important to note that the answer is not the most crucial part but how you work towards the answer. You can tell a lot about the interviewees in the process.