Question

Один из пяти братьев испек маме пирог. Андрей сказал: Это Витя или Толя. Витя сказал: Это сделал не я и не Юра. Толя сказал: Вы оба шутите. Дима сказал: Нет, один из них сказал правду, а другой обманул. Юра сказал: Нет, Дима, ты не прав. Мама знает, что трое из ее сыновей всегда говорят правду. Кто испек пирог?

Answer 1

толя 

если бы пирог испек Андрей то были бы не верны утверждения 1,3 ,5  и т д, если нужно подробное обьяснение напишите мне

Answer 2

Problem Analysis

We are given a scenario where one of five brothers baked a pie for their mother. Each brother makes a statement about who baked the pie, and we need to determine which brother is telling the truth.

Solution

Let's analyze each brother's statement and use logical reasoning to determine who baked the pie.

1. Andrey's statement: "It was either Vitya or Tolya." - This statement doesn't provide any conclusive information.

2. Vitya's statement: "It wasn't me or Yura." - This statement implies that either Andrey or Tolya baked the pie.

3. Tolya's statement: "You both are joking." - This statement doesn't provide any conclusive information.

4. Dima's statement: "No, one of them told the truth, and the other lied." - This statement implies that one brother is telling the truth, and the other is lying.

5. Yura's statement: "No, Dima, you're wrong. Mom knows that three of her sons always tell the truth." - This statement implies that three brothers always tell the truth.

Based on the information provided, we can deduce the following:

- Vitya's statement implies that either Andrey or Tolya baked the pie. - Dima's statement implies that one brother is telling the truth, and the other is lying. - Yura's statement implies that three brothers always tell the truth.

Since three brothers always tell the truth, and Dima's statement confirms that one brother is telling the truth, we can conclude that Andrey is telling the truth, and Tolya is lying. Therefore, Andrey baked the pie for their mother.

Answer

Andrey is the brother who baked the pie for their mother.

Note: The solution is based on logical reasoning and does not require external sources.