Brain Teasers
The Butcher and the Baker
One of Mr. Johnson, his wife, their son, and their daughter is a butcher, and another is a baker. Here are some facts:
1. If the butcher and the baker are the same gender, then the baker is older than the butcher.
2. If neither the butcher nor the baker is the parent of the other, then the butcher is older than the baker.
3. If the butcher is a man, then he and the baker are the same age.
4. If the butcher and the baker are of the opposite gender, then the man is older than the woman.
Whose occupation can be determined?
1. If the butcher and the baker are the same gender, then the baker is older than the butcher.
2. If neither the butcher nor the baker is the parent of the other, then the butcher is older than the baker.
3. If the butcher is a man, then he and the baker are the same age.
4. If the butcher and the baker are of the opposite gender, then the man is older than the woman.
Whose occupation can be determined?
Hint
All four facts are in the form of "hypothesis and conclusion" statements, which can only be true if the hypothesis is false or if the conclusion is true.Answer
Mr. Johnson's daughter can be determined. She is the butcher.Suppose the butcher is a man. This means that hypothesis 3 is true, making conclusion 3 true, making the butcher and the baker the same age, making conclusion 2 false, making hypothesis 2 false, making one the parent of the other. But since they are the same age, this cannot be right. So the butcher must be a woman.
Suppose the baker is a man. This means that hypothesis 4 is true, making conclusion 4 true, making the baker older than the butcher, making conclusion 2 false, making hypothesis 2 false, making one the parent of the other. Since the baker is older, he must be the parent. Therefore, Mr. Johnson is the baker and his daughter is the butcher.
Suppose the baker is a woman. This means that hypothesis 1 is true, making conclusion 1 true, making the baker older than the butcher. Therefore, Mr. Johnson's wife is the baker and his daughter is the butcher.
Either way, the daughter can be determined as the butcher.
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