Four islanders argue over the knight count

Question

On the usual island, knights always tell the truth and knaves always lie. Four residents make these claims: - Wen: "All four of us are knaves." - Xia: "Exactly one of us is a knight." - Yuki: "Exactly two of us are knights." - Zane: "Exactly three of us are knights." How many knights are there, and who are they?

Accepted Answer

Start with Wen. Could Wen be a knight? Then his statement "all four of us are knaves" would be true, but that would make Wen himself a knave, a contradiction. So Wen is a knave, and his claim is a lie. The lie being false means it is not true that all four are knaves, so at least one knight exists somewhere among the four. Since Wen is a knave, any knight must be one of Xia, Yuki, or Zane. Now notice their three statements name different knight-counts (one, two, three). Only one of those counts can be the real number, so at most one of the three statements is true, meaning at most one of Xia,…

Four islanders argue over the knight count

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