A group of individuals are living on an island when a visitor arrives with an unusual order: all blue-eyed people must leave the island immediately. Every evening at 8:00 p.m., a flight will depart. Everyone can see everyone else's eye colour, but no one knows their own (nor is anyone allowed to tell them). Furthermore, they have no idea how many people have blue eyes, but they do know that at least one person has. How long will it take for the blue-eyed individuals to leave?

A group of individuals are living on an island when a visitor arrives with an unusual order: all blue-eyed people must leave the island immediately. Every evening at 8:00 p.m., a flight will depart. Everyone can see everyone else's eye colour, but no one knows their own (nor is anyone allowed to tell them). Furthermore, they have no idea how many people have blue eyes, but they do know that at least one person has. How long will it take for the blue-eyed individuals to leave?

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter19: Probabilistic Dynamic Programming

Section19.4: Further Examples Of Probabilistic Dynamic Programming Formulations

Problem 7P

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A bunch of people are living on an island, when a visitor comes with a strangeorder: all blue-eyed people must leave the island as soon as possible. There will be a flight out at8:00pm every evening. Each person can see everyone else's eye color, but they do not know theirown (nor is anyone allowed to tell them). Additionally, they do not know how many people haveblue eyes, although they do know that at least one person does. How many days will it take theblue-eyed people to leave?
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