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)

Starting from who is not rich...

If A(nne) is not rich:

A:!R -> B:R and C:R (rule 1)

A:!R -> A:!I (rule 3)

A:!I -> B:I and C:I (rule 1)

C:R->C:A (rule 5) and C:!B (rule 2)

C:!B->A:B and B:B (rule 1)

B:B->B:A (rule 4) but that breaks rule 2

 

If B(eatrice) is not rich...

B:!R -> A:R and C:R (rule 2)

A:R and C:R -> A:A and C:A (rule 5) and B:!A (rule 1)

B:!A -> B:!B (rule 4) -> A:B and C:B (rule 1)

So now A and C are each R(ich), I(ntelligent) and B(eautiful) and rules 1 and 2 cannot be satisfied

 

Therefore C(laudia) must be the one to not be rich.

Posted by Bob Smith on 2005-06-22 19:51:47