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 cannot say he is insane unless he is either a liar, or very confused. If he beleived he was insane and was pure, he would be sane, but then be wrong about his guess which doesn't work. If If he believed he was sane and pure, he would be sane and would say so. If he was Applied and beleived he was insane, he would say sane, and actually be insane which he is so that is also a contradiction. So A is an Applied Sane person.
A says C is pure. This is a lie so A believes C is applied. A is always right about his beliefs so C is Applied. C says he is applied so he beleives he is pure. this isn't true so C is insane. C says B is applied. This is a lie so C believes B is pure. C is insane so this is incorrect. B is also applied. B says he is pure. Since we know he is a liar, he believes he is applied. Being correct about his belief, B is sane.B says D is insane which is a lie so B believes D is sane. B is right always so D is sane.D says C is sane. This is wrong so either D is lying or he doesn't actually know. We know D is always correct so he has to be lying. D is Applied.

A is applied sane.
B is applied sane.
C is applied insane.
D is applied sane.

Posted by Jon on 2003-04-14 07:27:10