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.

(In reply to solution by Charlie)

This is just like a puzzle that was on the other site. The actual answer, which I came up with (but not first of course) was like this:

(Note: I will assume all 'he' for ease of explanation)

The first person says "black" if the number of black hats he sees are odd. (White if the number of black hats he sees are even) Note: This hat and person are just to tell odd or even. (The other 9 hats besides this one will be called "The other 9 hats)

Then, the person that sees 8 hats will know if he sees odd number and the first person said odd number, he must be wearing a white hat. If he sees odd and the first person said even, (or switched) he must be wearing a black hat. So now he can correctly identify his hat.

Now the third person knows all "the other 9 hats" besides his own, and if they are odd and even. This means he can determine his own hat just like the second man did.

All the rest of them can do it the same way.
This leaves a 50% chance that all are saved and 50% chance that 9 are saved (Since the chance of the first person dying is 50%/50%)

I think that was what was described, at least that was my solution.

Posted by Gamer on 2003-03-21 08:25:00