8.1 On the Island of Truth, only knights, who always tell the truth, and liars, who always lie, live. A tourist met four residents of the island A, B, C, D. Resident A told the tourist: "Exactly one of us four is a liar." B said: "All of us are liars." Then the tourist asked C: "Is it true that A is a liar?". When the tourist heard C's answer ("yes" or "no"), he was able to accurately determine whether A was a liar or not. Who among the residents can be a liar?

Only A, B, and D

Only B and C

Only A and B

Definitely A and B, and possibly D, but possibly not

Definitely B and C, and possibly D, but possibly not
Answer: definitely A and B, and possibly D, but possibly not

Solution. Let's consider the first two questions. B is definitely a liar. If A is a knight, then the only option is KLLK. If A is a liar, then the remaining options are LLLK, LLLL, and LLKL (the option where all are liars is impossible due to B's answer). In the first and fourth, C answers "no," and the tourist would not have been able to determine who A is (since in the first he is a knight, and in the second he is a liar). Therefore, C answered "yes," leaving the second and third options, in which A and B are liars, C is a knight, and D may or may not be a liar.