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 быть лжецами? Перечислите все возможные варианты ответов. Сколько человек за столом могли быть лжецами? Перечислите все возможные варианты ответов. 1 2 3 … До 11

Answer 1

Ответ:

оба двое говорят правду

Answer 2

Problem Analysis

In this problem, there are 11 people sitting around a round table. Some of them are knights who always tell the truth, while the others are liars who always lie. Each person is asked about their neighbors, and some say that both of their neighbors are liars, while others say that both of their neighbors are knights. We need to determine how many people at the table could be liars and list all possible answers.

Solution

Let's consider the possible scenarios:

1. If the person who claims that both of their neighbors are liars is a knight, then both of their neighbors must be liars as well. However, this contradicts the statement that there are knights at the table. Therefore, this scenario is not possible.

2. If the person who claims that both of their neighbors are knights is a liar, then both of their neighbors must be liars as well. However, this contradicts the statement that there are liars at the table. Therefore, this scenario is not possible.

3. If the person who claims that both of their neighbors are liars is a liar, then one of their neighbors must be a knight and the other must be a liar. This scenario is possible.

4. If the person who claims that both of their neighbors are knights is a knight, then one of their neighbors must be a knight and the other must be a liar. This scenario is possible.

Based on the above analysis, there are two possible scenarios where some people at the table could be liars:

1. Scenario 1: One person claims that both of their neighbors are liars, and the rest of the people at the table are knights.

2. Scenario 2: One person claims that both of their neighbors are knights, and the rest of the people at the table are liars.

In both scenarios, there is only one person who could be a liar. Therefore, there can be 1 person at the table who could be a liar.

Summary

In the given scenario, there can be only one person at the table who could be a liar. All other people must be knights.