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)

Here's how I solved this..

1.  Since no woman can have more than 3 traits.  Two must have 3 and the third one 2.

2.  Ane must be Artistic.  If she is Intelligent or Rich, she is Artistic.  If she has neither of those two traits then she must have the other two traits, Beautiful & Artistic.
Anne: Artistic

3.  Since Anne is Artistic, only one other person can be Artistic.  Bernice and Claudia can't both be beautiful or they will both be Artistic.  So Anne must be Beautiful.
Anne: Artistic, Beautiful

4.  Claudia must be Artistic.  If she is Beautiful or Rich she is Artistic.  If she's neither of the two, then she has two be Intelligent and Artistic.
Anne: Artistic, Beautiful
Claudia: Artistic

5.  Since Bernice can no longer be Artistic, she can't be Beautiful.  So that leaves her two traits, Intelligent and Rich.  Also Anne & Claudia must each have three.
Anne:  Artistic, Beautiful
Claudia: Artistic
Bernice: Intelligent, Rich

6.  Since Bernice isn't Beautiful, Claudia must be.
Anne: Artistic, Beautiful
Claudia: Artistic, Beautiful
Bernice: Intelligent, Rich

7.  Two traits are left and they belong to either Anne or Claudia.  Neither can get both or that person will have 4 traits.  Anne can't be Intelligent or she will also be Rich.  So Claudia is Intelligent and Anne is Rich.
Anne: Artistic, Beautiful, Rich
Claudia: Artistic, Beautiful, Intelligent
Bernice: Intelligent, Rich

The answer is Claudia, but are any of them funny?

Posted by Albert on 2005-09-26 17:54:31