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:
- All the 10 people can easily understand your strategy, and will execute it with perfect precision.
- 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.
- The only allowed response is a short, unemotional "white" or "black".
- Having said that, I will add that you can put any value you like into each of these words.
Hello i got a nice way out of this puzzle. here is it...
NOTE : i'm giving 1....10 for persons from last to front
as somebody said earlier 1 will say BLACK iff he sees odd number of blacks, and he will say WHITE iff he sees odd number of whites (either will be the actual case, as he can see only 9 hats. so ther is no possibility of two odds)
I'm beginning with a hypothetical condition of 7W (7 white hats) and 2B(2 black hats) in front of 1. so he will say W. (he may get killed or may be saved). then, 2 can see either 7W+1B or 6W+2B. If it's the first case, he will definetley say his hat as B, to make B to an even mumber. If it's the second case, he will say W to make W an odd number.
we can proceed further with the first case (2 sees 7W+1B and tells as B). here 3 can have two probabilities - he can see either 7W or 6W+1B). If it's 7W, he will add one B to it, as identified by 2 as the colour of his cap. so it becomes 7W+1B. now both W and B became odd numbers. actually this was not the case. so he will say B as the colour of his hat, to make B an odd number. Again, if it's 6W+1B, he will add B to it as said by 2. then it becomes 6W+2B. to make W an odd number, he will say W as the colour of his hat.
I think there is no need to explain it further. So all the 9 people (from 2-10) can say the colour of their hats correctly and escape from the mouth of the monster. 1 has a probaility of 50% to escape.
I think it makes a reasonable solution. If there is anything wrong in this, plz feel free to contact.
manojezz@yahoo.co.in
9 persons could be saved!
