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.
- If the killer and the victim were related, the killer was a man.
- If the killer and the victim were not related, the killer was a doctor.
- If the killer and the victim had the same occupation, the victim was a man.
- If the killer and the victim had different occupations, the victim was a woman.
- If the killer and the victim were of the same sex, the killer was a lawyer.
- If the killer and victim were different sexes, the victim was a doctor.
Who was the killer? Who was the victim?
Suppose the victim is a lawyer. Then, by 6, the killer and victim are of the same sex. Then, by 5, the killer is a lawyer. Then, by 3, the victim is a man. Since the killer and victim are of the same sex, the killer is a man. There is only one lawyer that is a man (Edwin), so Edwin killed himself. However, we know that one of the six killed one of the
other five. Therefore, the victim is a doctor.
Suppose the killer is a lawyer. Then, by 2, the killer and victim are related. Then, by 1, the killer is a man, so he is Edwin. Since the victim is a doctor, by 4, the victim is a woman. The only woman doctor is Betty, so the victim is Betty. However, Edwin and Betty are not related. Therefore, the killer is a doctor.
Now, we know that the killer and victim are both doctors. Therefore, by 3, the victim is a man. By 5, the killer and victim are of different sexes, so the killer is a woman. The only woman doctor is Betty, so she is the killer. Then, by 1, the killer and victim are not related. The victim is a man doctor, so he is either Aaron or Duane. Aaron is related to Betty, so the victim is Duane.
Betty killed Duane.
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Posted by Math Man
on 2012-09-01 15:11:54 |
Answer
