27. 

When I first encountered the previous problem, it immediately struck me that C essentially does nothing, playing the role of a kind of "free accessory." Indeed, when B spoke, the falsity of his statement could have been established without C's involvement (see the solution to the previous problem). The following version of the problem allows us to get rid of the "excess" in the conditions.

Suppose the stranger asked A a different question: "How many knights are there among you?" And to this question, A answered inaudibly. So the stranger had to ask B: "What did A say?" B replied: "A said that there is one knight among us." And then C shouted: "Don't believe B! He is lying!"

Who among B and C is the knight and who is the liar?
27. The answer in this problem is the same as in the previous one, but the reasoning is somewhat different.

First of all, note that B and C cannot both be knights or both be liars, since B contradicts C. Therefore, B and C cannot both be knights or both be liars: one of them is a knight, and the other is a liar. If A were a knight, there would be two knights in total. Therefore, A did not lie and said that among the three individuals, there is only one knight. On the other hand, if A were a liar, the statement that among the three islanders A, B, and C, there is only one knight, would be true. But then A, being a liar, could not have made this true statement. Therefore, A could not have answered the stranger's question: "Among us, there is one knight." Consequently, B incorrectly reported A's statement, from which we conclude that B is a liar, and C is a knight.