Question

Помогите! 30 баллов! 10 людей похитили инопланетяне. Людям сказали, что на них наденут колпаки белого и черного цвета, и каждый не будет знать, какой колпак у него на голове. Их посадят в ряд, то есть самый левый может видеть цвет колпаков всех, кто спереди него, следующий за ним видит всех, кроме самого левого, так как он левее и.т.д. Каждый может говорить только одно из двух слов и только один раз (белое или черное), т.е. он должен сказать цвет своего колпака. Поворачиваться или как то хитрить нельзя. Если хотя бы 9 человек скажут правильный цвет, то инопланетяне их отпустят. Как им так договориться, чтобы всех отпустили?

Answer 1

To solve this puzzle, let's break it down step by step:

Step 1: Analyzing the Situation

We have 10 people who have been kidnapped by aliens. The aliens have put white and black hats on their heads, and each person can see the hat colors of the people in front of them but not their own. Each person can only say one word to indicate the color of their own hat.

Step 2: Establishing a Strategy

The goal is for at least 9 people to correctly state the color of their own hat. Since each person can only see the hats in front of them, they need to come up with a strategy to communicate the colors effectively.

Step 3: Developing a Communication System

To solve this puzzle, the people can agree on a communication system where they use their words to indicate the number of hats of a certain color they see in front of them. Here's how they can do it:

1. The person at the back, who cannot see any hats, will say the number of white hats they see. Let's call this number X. 2. The next person, who can see the hat of the person in front of them, will listen to the first person and count the number of white hats they see in front of them. Let's call this number Y. 3. Based on the numbers X and Y, the second person can deduce the color of their own hat. If X and Y are the same, the second person's hat is black. If X and Y are different, the second person's hat is white.

Step 4: Extending the Strategy

The process continues down the line, with each person using the information they hear from the person behind them to deduce the color of their own hat. By the time the information reaches the person at the front, they will have enough information to correctly state the color of their own hat.

Step 5: Ensuring Success

To ensure that at least 9 people state the correct color, the person at the back should count the number of white hats they see. If the number is 9 or more, they should say "white." If the number is less than 9, they should say "black." This way, even if the person at the back cannot see their own hat, they can guarantee that at least 9 people will state the correct color.

Conclusion

By using this strategy, the group can communicate effectively and ensure that at least 9 people state the correct color of their own hat. This will lead to their release by the aliens.

Please note that this solution assumes that the aliens will follow the agreed-upon rules and release the people if at least 9 of them state the correct color.