Suppose there are 100 students on a cruise ship. The ship gets wrecked on an island and only the 100 students survive. The students get captured by a tribe of cannibals. The cannibals tell them the following: We make you sit in a row on this hillside so that each of you can see all the folks in the row that are in front of you but nobody who is behind you. All of you get hats in two colors: black or white. You can see the hats of the folks in front of you, but not your own or the hat of anyone behind you. We start at the top and moving down each of you can say one word only – either black or white. If you guess the color of the hat you are wearing then you will live, if you are wrong we will eat you! You have 20 minutes to talk about a strategy. Then we begin. The students are very clever and so they have an idea to save as many of them as they can. How many can be saved?
Any help is appreciated.