Question

В классе учатся N школьников: несколько отличников и 8 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. Если ответом являются несколько чисел, то они вводятся все — каждое число в отдельное поле ввода в произвольном порядке.

Answer 1

Ответ:

25, 26, 27

Пошаговое объяснение:

Каждый хулиган соврал, значит среди N-1 школьников хулиганов меньше одной третьей N-1.

7 < (N-1)/3

Остальные сказали правду, значит среди N-1 школьников хулиганов не меньше одной третьей N-1

8>=(N-1)/3

N >= 25

N <= 27

25, 26, 27

Answer 2

Ответ: 23; 24; 25

Пошаговое объяснение:

решал не я, а алгоритм на компе, так что должно быть правильно

Answer 3

Problem Analysis

We are given a class with N students, consisting of several top students and 8 troublemakers. The top students always tell the truth, while the troublemakers always lie. One day, all the students sat around a round table and each of them made a statement to the rest of the class: "At least a third of you are troublemakers!" We need to determine the possible values of N.

Solution

Let's consider the possible scenarios based on the number of troublemakers in the class.

1. If there is only 1 troublemaker in the class: - In this case, the statement made by the troublemaker is false, as there are not enough troublemakers to fulfill the statement. - However, since the top students always tell the truth, they will also say that at least a third of the class are troublemakers. - This creates a contradiction, as both the troublemaker and the top students cannot be telling the truth at the same time. - Therefore, it is not possible for there to be only 1 troublemaker in the class.

2. If there are 2 troublemakers in the class: - In this case, the statement made by the troublemakers is true, as there are exactly 2 troublemakers in the class. - The top students will also say that at least a third of the class are troublemakers, which is true in this case. - Therefore, it is possible for there to be 2 troublemakers in the class.

3. If there are 3 or more troublemakers in the class: - In this case, the statement made by the troublemakers is true, as there are at least 3 troublemakers in the class. - The top students will say that at least a third of the class are troublemakers, which is also true in this case. - Therefore, it is possible for there to be 3 or more troublemakers in the class.

Based on the above analysis, the possible values of N are: - N = 2 (if there are 2 troublemakers in the class) - N ≥ 3 (if there are 3 or more troublemakers in the class).

Note: It is not possible to determine the exact value of N based on the given information. We can only determine the lower bound (N = 2) and the fact that N must be greater than or equal to 3.