Anne, Bernice and Claudia are three remarkable women, each having some remarkable characteristics.

(1) Just two are intelligent, just two are beautiful, just two are artistic and just two are rich.
(2) No one has more than three characteristics.
(3) Of Anne it is true that : if she is intelligent, she is rich.
(4) Of Bernice and Claudia it is true that: if she is beautiful, she is artistic.
(5) Of Anne and Claudia it is true that: if she is rich, she is artistic.

Who is not rich? (Show your reasoning)

If Anne is not artistic, she is not rich, and so she is not intelligent. (3,5) This would cause one of the other women to have 4 traits, and thus can't happen (1,2). So Anne is artistic.

Similarly, if Claudia is not artistic, she is not rich and she is not beautiful. (4,5) Again it would cause one of the other women to have 4 traits and can't happen. (1,2) So Claudia is artistic.

This means Bernice is not artistic and thus not beautiful (4), so Anne is beautiful (1). If Anne is intelligent, she is rich, and so she'd have all 4 traits, which can't happen (2). So Anne is not intelligent.

If Bernice or Anne were not rich, then Claudia would have all four traits, which can't happen (2). So Claudia is not rich (1).

Posted by Gamer on 2011-01-28 04:06:52