35. 

We are again faced with three islanders A, B, and C. A makes the statement: "B and C are of the same type." Someone asks C: "Are A and B of the same type?"

What will the islander C answer?
35. To solve this problem, we need to consider two cases separately.

First case: A is a knight. Then B and C are of the same type. If C is a knight, then B is also a knight and, therefore, of the same type as A. Therefore, C, being a truthful person, should answer "Yes." If C is a liar, then B is also a liar (since B is of the same type as C) and, therefore, belongs to a different type of islander than A. Therefore, C, being a liar, should lie and answer "yes."

Second case: A is a liar. Then B and C are not of the same type. If C is a knight, then B is a liar and, therefore, of the same type as A. Therefore, C, being a knight, should answer "yes." If C is a liar, then B, being of a different type than C, is a knight and belongs to a different type of islander than A. But then C, being a liar and claiming that A and C are not of the same type, should lie, so he would answer "yes" to the question.

Thus, in both cases, C will answer "yes."