MHB The Island of 10: Identifying the Knaves

[castor28]

On a fictional island there are 10 inhabitants, who all know each other, of which 5 are knights, who always tell the truth and the rest of them are knaves, who always lie.

A visitor to the island wants to determine the 5 knaves. What is the minimum number of yes-no questions he must ask the inhabitants in order to find the 5 knaves? (each question is asked to one person only).

 

[castor28]

Here is the proposed solution.
[sp]
As there are $\binom{10}{5}=252>2^7$ possible answers, we need at least 8 questions.

There is an easy solution with 9 questions: ask 9 villagers something like "Are you a bird ?". The challenge is to find the answer in 8 questions.

There is a classical "double negation" trick that allows you to get the true answer to any yes/no question: if you ask "If I asked you <your question here>, what would you answer?", a liar will have to lie twice, and he will give you the correct answer.

The important clue here is that all the villagers know each other, and therefore each of them knows the answer.

You can make a list of the 252 possible answers, show that list to any villager, and ask "If I asked you if the correct answer is in the first half of the list, what would you answer?"

This will allow you to eliminate half of the list. You can then repeat the process with the other half. Since $252<2^8$, you will get the answer with at most 8 questions.
[/sp]