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More Fermi Problems

I am not a fan of Fermi Problems. At least that is the category of interview question that interviewers have come to ask in the absence of true relevant interview questions. The first reason that this is bad is (i) because the interviewer rarely has the question written down and so reciting the question from rote memory is a guess at best. (ii) very few is only the most elite interviewers know exactly how to quantify this very subjective measure.

Here are some examples:

(1) You are at one end of a long hallway with two light switches. At the other end of the hallway is a closed door. Behind the closed door is a lightbulb, currently off.  Which light switch controls the lightbulb.

(2) You have 3 egg cartons labelled S, M, and L. Inside the cartons the eggs are marked S, M, L. Each carton has 12 eggs of the same type. The cartons are all mislabeled. What is the minimum number of cartons that you need to open in order to correct the labels?

(3) You have 3 jars of uniformly colored jelly beans. The beans are flavored Cherry, Grape, and Mixed. The jars are all mislabeled Cherry, Grape, and Mixed. What is the minimum number of jars/beans you need to sample in order to correct the labels?

(4) Your friend has 5 fair coins and you have 6 fair coins. You win if you flip at least one more head than your friend. What are your chances to win? (or something like that)

(5) You are 1 of 50 prisoners. The warden is going to play a sadistic game. He places a black or white hat on each prisoner's head and lines the prisoners front to back such that each prisoner can only see the other prisoners in front. Each prisoner must guess what color their hat is. If the prisoner guesses wrong he is executed. If he guesses correctly then he is freed. Before the game starts the prisoners can decide on a strategy. What is the best possible outcome and what is the strategy?

(6) You are one of three prisoners from the same prison. The deputy warden is also sadistic and has a new game. He gives each prisoner a black or white hat. Everyone can see each other's hat, except their own. This time, however, the prisoners must write down what color they think their own hat is or nothing at all; their guesses are revealed at the same time. If none of the prisoners write anything down they are all executed. If even one guess is wrong they are all executed. What is the best possible outcome and what is the strategy?

Someone needs to explain to me what the value of these questions are and justify it.

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