Brain Teasers
A Murder in Heather's Family
One of four people (Heather, her brother, her son, and her mother) was tragically murdered last night by one of the other three. Each of the three non-victims made one statement, of which exactly one was false. Here are the three statements:
1. "I am the mother of the murderer, but not the mother of the victim."
2. "I am the mother of the victim, but not the mother of the murderer."
3. "I am the same gender as the victim."
Who is the murderer?
1. "I am the mother of the murderer, but not the mother of the victim."
2. "I am the mother of the victim, but not the mother of the murderer."
3. "I am the same gender as the victim."
Who is the murderer?
Answer
Heather's mother was the murderer.Suppose statements 1 and 2 are both true. Then they would both be made by women, which means that statement 3 was made by a man, and the victim was a man. But this would mean that statement 3, and therefore all three statements, would be true.
This means that one of statements 1 and 2 must be false, and statement 3 is true. Suppose statement 3 was made by a woman. This means that the victim was a woman, and the other two statements were made by men. But then both statements 1 and 2 are false.
This means that statement 3 was made by a man, the victim was a man, and the other two statements were made by women. Suppose statement 2 is false. If Heather's brother is the victim, her mother could not have made a true statement 1, so she must have made statement 2, and the murderer could not have been Heather's brother, so it must have been Heather herself, but then she couldn't have made a true statement 1 either. On the other hand, if Heather's son is the victim, Heather herself must have made statement 2, which could only make her son the murderer.
This means that statement 1 is false. If Heather's brother is the victim, Heather herself could not have made a true statement 2, so she must have made statement 1, and the murderer could not have been her brother, so it must have been her mother. On the other hand, if Heather's son is the victim, her mother must have made statement 1, and the murderer must have been Heather's mother.
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Comments
Fantastic! Short and concise, clear deductive logic to solve, fun family relations confusion, great. WimpyKid, whether you create these or find them and bring them here, I'm in your debt.
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