Question

О каждом из трёх островитян А.В и С известно,что он - либо Рыцарь(всегда говорит правду),либо лжец(всегда лжёт).А говорит:"Мы все лжецы";В говорит:"Ровно один из нас лжец".Можно ли определить,кто такой В(Рыцарь или лжец)?Можно ли определить,кто такой С?

Answer 1

Рассмотрим два случай:

1) Пусть А-лжец

Тогда В будет прав и В рыцарь, а С-рыцарь

2) Пусть А-рыцарь

Но здесь противоречие 

Ответ: В, С - рыцарь

Answer 2

Problem Analysis

We have three islanders, A, B, and C, and each of them is either a Knight (always tells the truth) or a Knave (always lies). A says, "We are all liars," and B says, "Exactly one of us is a liar." We need to determine if B is a Knight or a Knave and if C is a Knight or a Knave.

Solution

Let's analyze the statements made by A and B:

1. A says, "We are all liars." 2. B says, "Exactly one of us is a liar."

If A is a Knight, then their statement "We are all liars" would be false because Knights always tell the truth. Therefore, A cannot be a Knight.

If A is a Knave, then their statement "We are all liars" would be true because Knaves always lie. This means that both B and C must be Knights because they are not liars. Therefore, B is a Knight and C is a Knight.

To summarize: - A is a Knave. - B is a Knight. - C is a Knight.

Conclusion

Based on the given statements, we can determine that B is a Knight and C is also a Knight.