Question

9. (12 баллов) Решите задачу. Встретились четыре старых друга: Белов, Чернов, Рыжов и Седов. Один из них был блондином, другой брюнетом, третий рыжим, а четвертый – седым. «Ни у кого из нас цвет волос не совпадает с фамилией», – сказал Белов. «Ты прав», – подтвердил брюнет. «Тот, у кого цвет волос совпадает с моей фамилией, носит фамилию, совпадающую с цветом волос Белова» – вмешался в их беседу седовласый. Известно, что все они сказали правду. Определите, у кого какой цвет волос. а) Белов – рыжий, Чернов – седой, Рыжов – брюнет, Седов – блондин б) Белов – седой, Чернов – рыжий, Рыжов – брюнет, Седов – блондин в) Белов – рыжий, Чернов – седой, Рыжов – блондин, Седов – брюнет г) Белов – брюнет, Чернов – седой, Рыжов – блондин, Седов – рыжий

Answer 1

Правильный ответ под буквой Г

Answer 2

Problem Analysis

We have four friends: Belov, Chernov, Ryzhov, and Sedov. Each of them has a different hair color: blond, brunette, redhead, and gray. They make the following statements: 1. Belov says that none of them has the same hair color as their last name. 2. The brunette confirms that Belov is correct. 3. The gray-haired friend says that the person whose hair color matches his last name has a last name that matches Belov's hair color.

We need to determine the hair color of each friend.

Solution

Let's analyze the statements one by one and see if we can deduce the hair color of each friend.

1. Belov says that none of them has the same hair color as their last name. - This means that Belov cannot have red hair, as his last name matches the hair color of one of the friends. - Therefore, Belov cannot be the redhead.

2. The brunette confirms that Belov is correct. - This means that the brunette cannot have the same hair color as his last name. - Since Belov cannot be the redhead, the brunette cannot be Belov. - Therefore, the brunette cannot be Ryzhov.

3. The gray-haired friend says that the person whose hair color matches his last name has a last name that matches Belov's hair color. - This means that the gray-haired friend's last name matches Belov's hair color. - Since Belov cannot be the redhead, the gray-haired friend's last name cannot match the redhead's hair color. - Therefore, the gray-haired friend's last name matches the hair color of either the blond or the brunette.

Based on the above deductions, we can conclude the following:

- Belov cannot be the redhead. - The brunette cannot be Belov or Ryzhov. - The gray-haired friend's last name matches the hair color of either the blond or the brunette.

Let's consider the remaining possibilities:

1. Belov – redhead, Chernov – gray, Ryzhov – brunette, Sedov – blond 2. Belov – gray, Chernov – redhead, Ryzhov – brunette, Sedov – blond 3. Belov – redhead, Chernov – gray, Ryzhov – blond, Sedov – brunette 4. Belov – brunette, Chernov – gray, Ryzhov – blond, Sedov – redhead

We need to determine which of these possibilities satisfies all the statements made by the friends.

- In possibility 1, Belov's hair color matches his last name, which contradicts the first statement. - In possibility 2, Belov's hair color does not match his last name, which contradicts the first statement. - In possibility 3, the gray-haired friend's last name does not match Belov's hair color, which contradicts the third statement. - In possibility 4, all the statements made by the friends are satisfied.

Therefore, the correct answer is: Belov – brunette, Chernov – gray, Ryzhov – blond, Sedov – redhead.

Answer

According to the given information, the hair colors of the four friends are as follows: - Belov is a brunette. - Chernov is gray. - Ryzhov is blond. - Sedov is a redhead.

Please let me know if you need any further assistance!