AT, BAT, and CAT

Here is another puzzle posted on Facebook by Konstantin Knop. Puzzle. One day, three inhabitants of the Island of Knights and Liars invited a foreign correspondent to visit so that they could tell him about their island. Knights always tell the truth, while liars always lie. The first inhabitant said, “The island has at most AT inhabitants. All the islanders are liars.” The second added, “The island has at most BAT inhabitants. Not all the islanders are liars.” The third disagreed, “The island has exactly CAT inhabitants. At least two islanders are knights.” Unfortunately for the correspondent—and for us—he did not know the local number words very well. He knew only that AT, BAT, and CAT stood for three consecutive positive integers in increasing order. How many knights and how many liars live on the island? Share: