Question

50 человек, каждый из которых рыцарь или лжец, встали в круг, после чего двое из них сказали, что "Оба моих соседа - лжецы", остальные же заявили, что "Оба моих соседа - рыцари". Сколько рыцарей может быть среди всех? (В ответе запишите сумму возможных значений).

Answer 1

Может быть 48 рыцарей (и 2 лжеца)

Answer 2

The Problem

The problem states that there are 50 people standing in a circle, and each person is either a knight or a knave. Two of them claim that "both of my neighbors are liars," while the rest claim that "both of my neighbors are knights." The question is: how many knights can there be among all the people in the circle?

Analyzing the Statements

Let's analyze the statements made by the two groups of people:

1. Group 1: Two people claim that "both of my neighbors are liars." 2. Group 2: The remaining people claim that "both of my neighbors are knights."

To solve this problem, we need to determine if the statements made by Group 1 and Group 2 are consistent with each other.

Analyzing Group 1's Statement

Group 1 consists of two people who claim that "both of my neighbors are liars." Let's consider the possibilities:

1. If both people in Group 1 are knights, their statement would be false because knights always tell the truth. Therefore, this possibility is not valid. 2. If both people in Group 1 are liars, their statement would be true because liars always lie. Therefore, this possibility is valid.

Based on the above analysis, we can conclude that both people in Group 1 are liars.

Analyzing Group 2's Statement

Group 2 consists of the remaining people who claim that "both of my neighbors are knights." Let's consider the possibilities:

1. If both people in Group 2 are knights, their statement would be true because knights always tell the truth. Therefore, this possibility is valid. 2. If both people in Group 2 are liars, their statement would be false because liars always lie. Therefore, this possibility is not valid.

Based on the above analysis, we can conclude that both people in Group 2 are knights.

Conclusion

From our analysis, we have determined that both people in Group 1 are liars, and both people in Group 2 are knights. Since there are 50 people in total, and two of them are liars, the remaining 48 people must be knights.

Therefore, the number of knights among all the people in the circle is 48.