Question

На острове 2016 аборигенов, каждый из которых либо лжец (лжецы всегда лгут), либо рыцарь (рыцари всегда говорят правду). Некоторые аборигены знакомы друг с другом, причём каждый лжец имеет знакомого среди рыцарей, а каждый рыцарь - знакомого среди лжецов. Каждый абориген сделал заявление:"Среди моих знакомых лжецов больше, чем рыцарей". Затем правитель острова казнил одного из аборигенов и после этого каждый абориген сделал заявление:"Среди моих знакомых рыцарей больше, чем лжецов". Сколько рыцарей было на острове изначально?

Answer 1

1007 вот ответ мой!!!

Answer 2

2016:2=1008
ответ:1008 рыцарей

Answer 3

Problem Analysis

We are given a scenario on an island where there are two types of inhabitants: liars and knights. Liars always lie, while knights always tell the truth. Some of the inhabitants are acquainted with each other, and each liar knows at least one knight, while each knight knows at least one liar. Each inhabitant makes a statement: "Among my acquaintances, there are more liars than knights." After one inhabitant is executed, each inhabitant makes a new statement: "Among my acquaintances, there are more knights than liars." We need to determine the initial number of knights on the island.

Solution

Let's assume there are x liars and y knights on the island initially. We need to find the values of x and y.

From the first statement, we can conclude that each liar knows at least one knight, and each knight knows at least one liar. Therefore, the number of acquaintances for each liar is at least 1, and the number of acquaintances for each knight is at least 1.

According to the first statement, each inhabitant claims that there are more liars among their acquaintances than knights. This means that the number of liars among the acquaintances of each inhabitant is greater than the number of knights among their acquaintances.

Let's consider the case where there is only one liar and one knight on the island. In this case, the liar's statement would be false because there are no liars among the acquaintances of the knight. Therefore, we can conclude that there must be at least two liars and at least two knights on the island.

Now, let's analyze the second statement made by each inhabitant after one inhabitant is executed. In this statement, each inhabitant claims that there are more knights among their acquaintances than liars. This means that the number of knights among the acquaintances of each inhabitant is greater than the number of liars among their acquaintances.

If there are only two liars and two knights on the island, then each liar knows one knight, and each knight knows one liar. In this case, the second statement would also be false because there are no knights among the acquaintances of the liars. Therefore, we can conclude that there must be more than two knights on the island.

Based on the above analysis, we can conclude that there are at least two liars and more than two knights on the island.

Unfortunately, the provided search results do not contain the specific information required to determine the exact number of knights on the island. Therefore, we cannot provide a precise answer to the question of how many knights were on the island initially.

Conclusion

Based on the given scenario, we can conclude that there are at least two liars and more than two knights on the island initially. However, the exact number of knights cannot be determined with the available information.