Question

За круглым столом сидят 11 человек. Часть из них — рыцари, которые всегда говорят правду; остальные - лжецы, которые всегда говорят неправду(за столом были и рыцари,и лжецы). Каждого спросили: «Кто твои соседи?». Оказалось, что несколько ответили«Оба – лжецы!», а другие — «Оба — рыцари!». Сколько человек за столом могли бытьлжецами? Перечислите все возможные варианты ответов.Сколько человек за столом могли быть лжецами? Перечислите все возможные вариантыответов.12до 11

Answer 1

Ответ:

оба двое говорят правду

Answer 2

Problem Analysis

In this problem, there are 11 people sitting around a table. Some of them are knights who always tell the truth, while the others are liars who always lie. Each person is asked, "Who are your neighbors?" Some of them answer, "Both are liars!" and others answer, "Both are knights!" We need to determine how many people at the table could be liars and list all the possible answers.

Solution

Let's consider the possible scenarios:

1. If all the people who answered "Both are liars!" are knights, then all their neighbors must be liars as well. This means that there are at least two liars sitting next to each other. However, this contradicts the fact that knights always tell the truth. Therefore, this scenario is not possible.

2. If all the people who answered "Both are knights!" are liars, then all their neighbors must be knights as well. This means that there are at least two knights sitting next to each other. However, this contradicts the fact that liars always lie. Therefore, this scenario is not possible.

3. If some of the people who answered "Both are liars!" are knights and the others are liars, then there must be at least one knight sitting next to a liar. In this case, the number of liars at the table can be any number from 1 to 10, except for 11 (since there must be at least one knight). Therefore, there are 10 possible answers for the number of liars at the table.

Possible Answers

The number of people at the table who could be liars can be any number from 1 to 10, except for 11. Here are all the possible answers:

- 1 liar - 2 liars - 3 liars - 4 liars - 5 liars - 6 liars - 7 liars - 8 liars - 9 liars - 10 liars

Note: The answer cannot be 11 liars, as there must be at least one knight at the table.

Conclusion

In summary, there can be any number of liars at the table from 1 to 10, except for 11. The possible answers are 1 liar, 2 liars, 3 liars, 4 liars, 5 liars, 6 liars, 7 liars, 8 liars, 9 liars, and 10 liars.