The sisters of Aaron Green were Betty and Clara; the name of Aaron's girlfriend was Flora Brown and, Duane and Edwin were Flora’s brothers. Their occupations were as follows:

• Aaron was a doctor.
• Betty was a doctor.
• Clara was a lawyer.
• Duane was a doctor.
• Edwin was a lawyer.
• Flora was a lawyer.

One of the six killed one of the other five. Here are some clues to the murder.

1. If the killer and the victim were related, the killer was a man.
2. If the killer and the victim were not related, the killer was a doctor.
3. If the killer and the victim had the same occupation, the victim was a man.
4. If the killer and the victim had different occupations, the victim was a woman.
5. If the killer and the victim were of the same sex, the killer was a lawyer.
6. If the killer and victim were different sexes, the victim was a doctor.

Who was the killer? Who was the victim?

Suppose the killer is a lawyer.  Then, by the contrapositive of #2, the killer and victim are related.  Then, by #1, the killer is a man.  The only male lawyer is Edwin, so he is the killer.  Since the victim is related to the killer, the victim is either Duane or Flora.  Suppose Duane is the victim.  Then by #4, since Edwin and Duane have differing occupations, the victim is a woman; but Duane is not a woman, so that is a contradiction.  Then the victim must be Flora.  But then by #3, since Edwin and Flora have the same occupation, the victim is a man.  But Flora is not a man!  So this is a contradiction as well, which leads us back to our very first supposition being incorrect.

Thus, the killer must be a doctor -- either Aaron, Betty, or Duane.  By the contrapositive of #5, we also know that the killer and victim are of opposite sex.  Then by #6, we also know that the victim is a doctor as well.  Thus the killer and victim have the same occupation (doctor), and by #3, the victim is a man, which makes the killer a woman.  The only female doctor is Betty, so Betty is the killer.  By the contrapositive of #1, the killer and victim are not related.  The only doctor not related to Betty is Duane, so the victim is Duane.

Betty killed Duane.

Posted by Caleb on 2012-08-26 17:26:07