Four mathematicians have the following conversation:

A: I am insane.
B: I am pure.
C: I am applied.
D: I am sane.
A: C is pure.
B: D is insane.
C: B is applied.
D: C is sane.

You are also given that:

Pure mathematicians tell the truth about their beliefs.
Applied mathematicians lie about their beliefs.
Sane mathematicians beliefs are correct.
Insane mathematicians beliefs are incorrect.

Describe the four mathematicians.

A says the is insane. He could either be insane and applied, or sane and applied.
B says he is pure. He could be Pure and Sane or Applied and Sane.
C says he is applied. He could be Pure and Insane, or Applied and Insane.
D says he is sane. He could be Sane and Pure or Insane and Pure.

So far we know:
A = Applied
B = Sane
C = Insane
D = Pure

D says C is sane, which we know is incorrect. Since we know D is pure, he must be insane.
B correctly says D is insane. He is sane so he must also be pure.
C says B is applied, which is also incorrect. C is insane, so he must be pure.
A says C is pure - which is correct. Seeing as A is applied he must be insane.

So we get:

A = Applied & Insane
B = Sane & Pure
C = Insane & Pure
D = Pure & Insane

Posted by Lewis on 2003-07-13 00:13:27