Solution to Webster and the Missing Link

This is the solution to the whodunnit problem raised in "Webster and the Case of the Missing Link" .

Webster’s Solution:

In the lecture, "Webster and the Case of the Missing Link"  Webster and Gupta are convinced that Mr. Wright took Ms. Beerdham’s Homo Erectus skull. Here is how Webster knows who did it and why he knows it’s a prank. Let’s first review the notes:

         -Rushholm’s lie detector malfunctioned
         -Five students are accused
         -Each student made three statements
         -Of the three statements made by each student, the lie detector has correctly identified two of each of the three statements to be true, and one false, but the detector is unable to identify which statements are true and which is false

         The statements:

         -Mr. Luften: I did not take the head. I have never stolen anything in my life. Sutherland did it.

         -Mr. Wright: I did not take the head. I have never stolen anything in my life. Don’t believe everything the others tell you.

         -Mr. Dunstan: I am innocent. I never saw Brady before. Sutherland is guilty.

         -Mr. Sutherland: I am innocent. Brady did it. Luften lied when he said I did it.

         -Mr. Brady: I did not take the head. Wright is the guilty one. Dunstan and I are old pals.

Now the Solution:

Since Luften said Sutherland did it, Sutherland’s first and last statement are equivalent, both indicating his innocence. Since we know that each person has only one false statement, these statements cannot both be false, and therefore must both be true. So Sutherland did not do it.

Also, Sutherland’s statement that Brady did it must be false, since his other two statements have been determined to be true. Brady, therefore, did not do it.

We know Sutherland did not do it, so Dunstan’s third statement is false, which means his first two statements are true, indicating that Dunstan is innocent.

Also, since Sutherland did not do it, we know Luften’s last statement is false, which means his first two are true, and he too is innocent.

Therefore, if Luften, Dunstan, Sutherland and Brady are innocent, Wright must be guilty.

We can further confirm this as follows; We know that Sutherland is innocent, therefore Dunstan’s claim that he is guilty is false, making Dunstan’s other two statements true, so in-fact Dunstan never saw Brady before. We already know that Brady is innocent, therefore his first statement is true. We also now know that he does not know Dunstan, therefore Brady’s last statement is false. His second statement must be true, therefore Wright did it.

Now, why does he know it’s a prank:

Wright’s first statement, “I did not take the head,” is obviously false, since it has been proven he took it. Therefore, his two other statements are true, which means it is true that he has never stolen anything in his life. If he took it, but it is true that he did not steel it, it holds true that he intended to return it, making it a prank.

This logic problem is adapted from a problem presented in, Irving M. Copi, Introduction to Logic, Sixth Edition.