17) The census employee on the Island of Knights and Knaves must determine the type (Knight or Knave) and the educational level of the residents (Knights always tell the truth, while Knaves always lie). In an apartment inhabited by a married couple, he only gets these responses:

Husband: We are both graduates.

Wife: We are both of the same type.

How many boxes can the employee fill in with certainty?

![](https://cdn.mathpix.com/cropped/2024_04_17_4c97eba1baa5e71bd15fg-2.jpg?height=54&width=603&top_left_y=1558&top_left_x=206)
17) The answer is (D). Given the wife's statement, the husband is certainly a knight (if he is a knave, he must have lied about the husband, if he is a knight, he told the truth), and therefore both spouses are graduates. Thus, the statements are consistent with any type of wife, and therefore only three cells can be filled.