On an island there are two types of inhabitants: knights, who always tell the truth, and knaves, who always lie. We met on this island a group of four inhabitants who, when asked about their identity, answered as follows:
A: "There is at least one knave among us."
B: "There are at most two knights among us."
C: "There are at least three knaves among us."
D: "There are no knights among us."
How many knights are there in this set of four inhabitants?
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Solution
The answer is . The four statements are equivalent to:
A: "There is at least one knave among us."
B: "There are at least two knaves among us."
C: "There are at least three knaves among us."
D: "There are at least four knaves among us."
If there are knaves, exactly the first statements are true, so there are knights. Since knaves and knights are equal in number and together there must be four in total, we will have two knights and two knaves.
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