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.

All people believe they are sane.
Sane people truthfully and insane ones falsely.
Therefore,A does not believe he is insane,but says it,so A is applied.
Also,C believes and says he is sane,so C must be pure.

Posted by Tim Axoy on 2003-04-13 04:13:09