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.

First, cobsider the statements about themselves. (Note that pure mathematicians are Knights and Applied mathemeticians are Liars)

No sane mathematician can claim to Applied. No insane mathematician can claim to be Pure. No Pure mathematician can claim to be insane. No Applied mathematician can claim to be sane.

Thus: A is Applied; B is sane; C is insane and D is Pure.

D's second statement is false. Since D is pure, he is telling the truth as he believes it, so D is insane.

B's second statement is true. Since B is sane, B is also pure.

C's second statement is false. Since C is insane, he believes it to be true, and so C is Pure

A's second statement is true. Since A is Applied, he believes he is lying, and so A is insane.

In Summary:
A is Applied and insane
B is Pure and sane
C is Pure and insane
D is Pure and insane

Posted by TomM on 2003-04-12 12:53:01