Question

В классе учатся N школьников: несколько отличников и 7 хулиганов. Отличники всегда говорят правду, а хулиганы всегда врут. Однажды все ученики этого класса сели за круглый стол, и каждый из них заявил всем остальным «как минимум треть из вас — хулиганы!» Чему может быть равно N? Укажите все возможные варианты. ​

Answer 1

Ответ:

22

Пошаговое объяснение:

7 умножаем на 3 и плюс 1 итого

Answer 2

Analysis and Solution

To solve this problem, we need to consider the statements made by the students and determine the possible values of N. Let's break down the information given:

- There are N students in the class. - Some students are excellent (always tell the truth), and 7 students are troublemakers (always lie). - All the students are sitting around a round table. - Each student declares to the others, "At least one-third of you are troublemakers."

We need to find the possible values of N.

Solution:

Let's consider the possible scenarios:

1. If N is divisible by 3: - In this case, let's assume that N = 3k, where k is a positive integer. - The number of troublemakers (T) would be 7, which is less than one-third of N. - Since the troublemakers always lie, their statement would be false. - The excellent students always tell the truth, so their statement would be true. - This scenario is not possible because the statement made by the excellent students contradicts the statement made by the troublemakers.

2. If N is not divisible by 3: - In this case, let's assume that N = 3k + r, where k is a positive integer and r is the remainder when N is divided by 3. - The number of troublemakers (T) would be 7, which is less than one-third of N. - Since the troublemakers always lie, their statement would be false. - The excellent students always tell the truth, so their statement would be true. - This scenario is possible because the statement made by the excellent students does not contradict the statement made by the troublemakers.

Based on the above analysis, the possible values of N are those that are not divisible by 3.

Possible Values of N:

- N can be any positive integer that is not divisible by 3.

I hope this explanation helps! Let me know if you have any further questions.