All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 The Plan (Posted on 2003-03-21)
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.

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.

 See The Solution Submitted by Gautam Rating: 4.3000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 The Plan Comment 16 of 16 |
Call the person in the back A, the next person B, and so on. If A sees an odd number of black hats, then A says, "Black." If A sees an even number of black hats, then A says, "White." Then, B will know whether there is an even or odd number of black hats out of B, C, D, E, F, G, H, I, and J. If B sees the same parity of black hats, then B says, "White." If B sees a different parity of black hats, then B says, "Black." Now, C will know the parity of the number of black hats out of C, D, E, F, G, H, I, and J. If C sees the same parity of black hats, then C says, "White." If C sees a different parity of black hats, then C says, "Black." Then, D, E, F, G, H, I, and J do the same thing. A has a 1/2 probability of getting his hat correct. All the others will definitely get their hat correct.

Edited on July 25, 2012, 7:50 pm
 Posted by Math Man on 2012-07-25 19:41:45

 Search: Search body:
Forums (0)