Question

В классе 75 детей. Они встали в круг и договорились, что некоторые из них на любой вопрос будут отвечать только правду, а остальные – только неправду. Каждому из них задали два вопроса: «Кто стоит слева от тебя – мальчик или девочка» и «Кто стоит справа от тебя – мальчик или девочка». Какое наибольшее количество из этих 150 ответов могло быть «Мальчик», если известно, что среди ответов был хотя бы один ответ «Девочка»?

Answer 1

150-2=148 потому что 1 девушка а возле нее 2 мальчика ети мальчики а эти мальчики ответили вопросы

Answer 2

Problem Analysis

In this problem, there are 75 children standing in a circle. Some of them always tell the truth, while others always lie. Each child is asked two questions: "Who is standing to your left, a boy or a girl?" and "Who is standing to your right, a boy or a girl?" We need to determine the maximum number of answers that could have been "Boy" if we know that at least one answer was "Girl".

Solution

Let's consider the possible scenarios:

1. If all the children who always tell the truth are standing next to each other in the circle, then the maximum number of "Boy" answers would be the number of truth-telling children. In this case, the maximum number of "Boy" answers would be 3.

2. If the truth-telling children are not standing next to each other, then the maximum number of "Boy" answers would be 2. This is because if there are more than 2 truth-telling children, they would have to lie about the gender of at least one child standing next to them, which contradicts the given condition that at least one answer was "Girl".

Therefore, the maximum number of "Boy" answers that could have been given, given that at least one answer was "Girl", is 2.

Conclusion

In a class of 75 children standing in a circle, where some always tell the truth and others always lie, the maximum number of "Boy" answers that could have been given, given that at least one answer was "Girl", is 2.