Question

В классе 91 ребёнок. 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 182 ответов могло быть «Мальчик», если известно, что среди ответов был хотя бы один ответ «Девочка»? Помогите пожалуйста!!!

Answer 1

91 ответов девочек и 91 ответов мальчиков

Answer 2

Problem Analysis

In this problem, there are 91 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 be "Boy" if we know that at least one answer was "Girl".

Solution

To solve this problem, we need to consider the different scenarios that could occur based on the number of children who always tell the truth and the number of children who always lie. Let's analyze these scenarios:

1. If all 91 children always tell the truth, then all 91 answers will be "Boy". This scenario is not possible because we know that at least one answer was "Girl".

2. If all 91 children always lie, then all 91 answers will be "Girl". This scenario is also not possible because we know that at least one answer was "Girl".

3. If there is at least one child who always tells the truth and the rest always lie, then the maximum number of answers that could be "Boy" is 90. This is because the child who tells the truth will always answer truthfully, and since we know that at least one answer was "Girl", the remaining 90 answers can be "Boy".

4. If there is more than one child who always tells the truth, then the maximum number of answers that could be "Boy" is less than 90. This is because if there are multiple children who always tell the truth, they will contradict each other's answers. Therefore, the maximum number of answers that could be "Boy" in this scenario is less than 90.

Based on the above analysis, the maximum number of answers that could be "Boy" is 90.

Conclusion

The maximum number of answers that could be "Boy" is 90, given that at least one answer was "Girl".