Question

Петя задумал число от 1 до 16. Вася задаёт ему вопросы с ответом "да" или "нет". Отвечая, Петя может один раз соврать (неизвестно, когда; а может и не соврать). Отгадает ли Петя число, задав не более 7 вопросов? Пожалуйста, помогите!

Answer 1

Да может с такими вопросами

оно четное?

оно двухзначное?

и спрашивай оставшиеся числа

Answer 2

Can Petya guess the number with no more than 7 questions?

Petya has chosen a number between 1 and 16, and Vasya will ask him questions with "yes" or "no" answers. Petya can either tell the truth or lie once during the game. The question is whether Petya can guess the number with no more than 7 questions.

To determine if Petya can guess the number within 7 questions, let's analyze the possibilities:

1. If Petya tells the truth all the time, he can guess the number with certainty within 4 questions. This is because there are 16 possible numbers, and each question can eliminate half of the remaining options. After 4 questions, there will be only one possible number left.

2. If Petya lies all the time, he can still guess the number within 7 questions. This is because even though he can lie once, the number of possible lies is limited. For example, if Petya lies on the first question, Vasya can ask the same question again to get the truth. Therefore, Petya's lie can only affect one question. With 7 questions, Petya can still narrow down the possibilities and guess the number.

3. If Petya mixes telling the truth and lying, it becomes more complicated. In this case, the number of possible outcomes increases, and it becomes harder to determine if Petya can guess the number within 7 questions.

Based on the analysis above, it is possible for Petya to guess the number within 7 questions, regardless of whether he tells the truth all the time, lies all the time, or mixes telling the truth and lying.

Please note that the above analysis assumes that Petya and Vasya play the game optimally, and there are no additional rules or constraints mentioned in the question.