Question

ДАЮ БАЛЛОВ ПОМОГИТЕ СРОЧНО Путешественник прибыл на остров, на котором живут лжецы (Л) и рыцари (Р). Каждый Л на вопрос: "Сколько..." называет число на 2 больше или на 2 меньше, чем правильный ответ, каждый Р отвечает правильно. На вопрос путешественника, встретившего двух жителей острова, сколько Л и сколько Р проживает на острове, первый ответил: "Если не считать меня, то 1002 Л и 1003 Р", а второй: "Если не считать меня, то 1001 Л и 1000 Р". Сколько Р проживает на острове?

Answer 1

В каждой клетке доски  стоят рыцари и лжецы (рыцари всегда говорят правду, а лжецы всегда лгут). Каждый из них утверждает, что среди его соседей ровно один рыцарь.
Ответ: 0 или 6

Answer 2

Solving the Island Puzzle

A traveler arrives on an island inhabited by liars (L) and knights (R). Each L will either state a number 2 more or 2 less than the correct answer, while each R will always provide the correct answer. The traveler asks two island inhabitants how many L and R there are. The first one says, "If you don't count me, then there are 1002 L and 1003 R," and the second one says, "If you don't count me, then there are 1001 L and 1000 R." The task is to determine how many R live on the island.

To solve this puzzle, we can analyze the statements of the two inhabitants and derive the number of knights (R) on the island.

The first inhabitant's statement implies that there are 1002 L and 1003 R if he is not counted. The second inhabitant's statement implies that there are 1001 L and 1000 R if he is not counted.

Solution:

Let's denote the number of L as "x" and the number of R as "y."

From the first statement: - If the first inhabitant is a liar (L), then the actual count would be (1002 - 1) L and (1003 - 1) R. - If the first inhabitant is a knight (R), then the actual count would be 1002 L and 1003 R.

From the second statement: - If the second inhabitant is a liar (L), then the actual count would be (1001 - 1) L and (1000 - 1) R. - If the second inhabitant is a knight (R), then the actual count would be 1001 L and 1000 R.

By analyzing the implications of these statements, we can determine the number of knights (R) on the island.

Calculating the Number of Knights (R):

Let's consider the implications of the statements: - If the first inhabitant is a liar, then the actual count would be 1001 L and 1002 R. - If the first inhabitant is a knight, then the actual count would be 1002 L and 1003 R. - If the second inhabitant is a liar, then the actual count would be 1000 L and 999 R. - If the second inhabitant is a knight, then the actual count would be 1001 L and 1000 R.

By comparing the implications, we can conclude that the second inhabitant is a knight, and the actual count is 1001 L and 1000 R.

Therefore, there are 1000 knights (R) living on the island.

This solution is derived from logical analysis of the given statements and implications.

(#1)