6.4. All inhabitants of the island are either knights who always 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?
Answer: The others answered: "Two".

Solution. The knight could not have answered "None," as this would have been a lie. Therefore, the first one is a liar. The other 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.

Thus, out of the five islanders, at least three are liars. Then the number of knights is either one, two, or none. If there were no knights at all, the first liar would have told the truth. There cannot be exactly one knight, as in this case, the second and third liars would have told the truth. Therefore, there are two knights on the island—both of the remaining islanders. Each of them will answer truthfully: "Two".

## Evaluation criteria:

+ the correct answer and solution with full justification are provided

$\pm$ it is justified that the first three islanders are liars and that the remaining two are knights, but it is not stated what they will answer

$\mp$ it is justified that the first three islanders are liars, but the solution is incomplete or incorrect

干 the correct answer is provided with the role of each islander specified and verified that it satisfies the condition, but the absence of other possibilities is not proven

- only the answer is provided