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)

Claudia is not rich.

If Anne is intelligent then she is rich (3) and also artistic (5) and therefore can't be beautiful (2). Benice & Claudia must then both be beautiful (1) which means they are both artistic (4) but then all 3 are artistic which cant be true (1) therefore Anne is not intelligent.

As Anne is not intelligent the other two must be (1) Bernice and Claudia are intelligent.

If both Bernice and Claudia are beautiful then they are both artistic (4) which means they both have three characteristics and so neither of them can be rich but at least one of them has to be rich (1) so therefore only one of Bernice and Claudia must be beautiful therefore Anne must be beautiful.

As stated above only one of Bernice and Claudia are beautiful that same person must be artistic (4) and she then has three characteristics so therefore can't be rich (2) so Anne must be rich.

Anne is rich therfore Anne must be artistic (5).

One of Bernice and Claudia is beautiful and artistic and the other is rich.

If Claudia is rich then Bernice is beautiful and artistic. Claudia must also be artistic (5) but this means all three women are artistic which can't be true (1) therfore Claudia is not rich which means Bernice is rich and Claudia is beautiful and artistic.

In summary:
Anna is beautiful, artistic and rich.
Claudia is intellegent, beautiful and artistic.
Bernice is intellegent and rich.

Posted by Lisa on 2005-06-22 13:40:04