Question

В классе учатся 25 школьников, каждый из которых либо отличник, либо хулиган. Отличники всегда говорят правду, а хулиганы всегда врут. Однажды 4 ученика этого класса сказали: «Если я перейду в другой класс, то среди оставшихся учеников будет больше половины хулиганов». Каждый из оставшихся 21 сказал: «Если я перейду в другой класс, то среди оставшихся учеников хулиганов будет в три раза больше, чем отличников». Сколько отличников учится в классе? Укажите все возможные варианты. Если ответом являются несколько чисел, то они вводятся все — каждое число в отдельное поле ввода в произвольном порядке.

Answer 1

4.

....................................

Answer 2

Ответ:

25 учеников

Пошаговое объяснение:

потому что 21+4=25

Answer 3

Problem Analysis

We are given a class with 25 students, each of whom is either an excellent student or a troublemaker. Excellent students always tell the truth, while troublemakers always lie. Four students from this class made the following statements: 1. "If I transfer to another class, there will be more than half troublemakers among the remaining students." 2. Each of the remaining 21 students said, "If I transfer to another class, the number of troublemakers among the remaining students will be three times greater than the number of excellent students."

We need to determine the number of excellent students in the class.

Solution

Let's assume that the number of excellent students in the class is x. Since there are 25 students in total, the number of troublemakers will be 25 - x.

According to the first statement, if one of the four students transfers to another class, there will be more than half troublemakers among the remaining students. This means that the number of troublemakers among the remaining 24 students will be greater than 12. Mathematically, we can express this as:

25 - x - 1 > 12

Simplifying the inequality, we get:

x < 12

According to the second statement, each of the remaining 21 students said that if they transfer to another class, the number of troublemakers among the remaining students will be three times greater than the number of excellent students. Mathematically, we can express this as:

25 - x - 1 = 3x

Simplifying the equation, we get:

4x = 24

Solving this equation, we find that:

x = 6

Therefore, there are 6 excellent students in the class.

Answer

The number of excellent students in the class is 6.