There is an island with 10 inhabitants. One day a monster comes and says that he intends to eat every one of them but will give them a chance to survive in the following way:

In the morning, the monster will line up all the people - single file so that the last person sees the remaining 9, the next person sees the remaining 8, and so on until the first person that obviously sees no one in front of himself. The monster will then place black or white hats on their heads randomly (they can be all white, all black or any combination thereof). The monster will offer each person starting with the last one (who sees everyone else's hats) to guess the color of his/her own hat. The answer can only be one word: "white" or "black". The monster will eat him on the spot if he guessed wrong, and will leave him alive if he guessed right. All the remaining people will hear both the guess and the outcome of the guess. The monster will then go on to the next to last person (who only sees 8 people), and so on until the end. The monster gives them the whole night to think.

The Task:

Devise the optimal strategy that these poor natives could use to maximize their survival rate.

Assumptions:

1. All the 10 people can easily understand your strategy, and will execute it with perfect precision.
2. If the monster suspects that any of the people are giving away information to any of the remaining team members by intonation of words when answering, or any other signs, or by touch, he will eat everyone.
3. The only allowed response is a short, unemotional "white" or "black".
4. Having said that, I will add that you can put any value you like into each of these words.

I am going to add to Fernando's answer to ensure that the last guy will be saved. He will simply add up the numbers (1's and 0's) of 8,7,6,5,4,3, and 2. If the number is different than 9's answer than he is a one; if it is the same than he is a 0. For example, if 9 said 0, that means he saw an even number ahead of him. If the last guy only counts three 1's then he must be a 1. If he counts four then he is a 0. If 9 answered with a 1, then he must have seen an odd number ahead of him, so the same method can be used by the last guy.

Posted by Ryan on 2003-03-25 08:22:12