$[$ Mathematical logic (other) $)]$

All inhabitants of the island are either knights who only tell the truth, or liars who always lie. A traveler met five islanders. In response to his question: "How many of you are knights?" the first answered: "None!", and two others answered: "One". What did the others answer?
The knight could not answer "None," as that would be a lie. Therefore, the first one is a liar. The next two answered the same, so they are either both knights or both liars. But if they were knights, there would be at least two knights on the island, and the answer "One" would be false. Therefore, both the second and third are liars. This means that out of the five islanders, at least three are liars, and there are no more than two knights. But since the first three lied, there are neither 0 nor 1 knights. Therefore, the remaining two islanders are knights. Each of them will answer truthfully: "Two."

## Answer

"Two."

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