Brain Teasers
Four Men and Four Women at a Wedding
Four men, Al, Ben, Carl, and Dan, and four women, Edith, Fran, Gertrude, and Heather, attended a wedding. One of the four men married one of the four women. Here are some facts:
1. If neither Al nor Edith got married, then Gertrude got married.
2. If neither Al nor Fran got married, then Ben got married.
3. If neither Ben nor Gertrude got married, then Carl got married.
4. If neither Carl nor Fran got married, then Edith got married.
Who got married?
1. If neither Al nor Edith got married, then Gertrude got married.
2. If neither Al nor Fran got married, then Ben got married.
3. If neither Ben nor Gertrude got married, then Carl got married.
4. If neither Carl nor Fran got married, then Edith got married.
Who got married?
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
Ben married Edith.Suppose Al got married. Fact 3 tells us that he married Gertrude, contradicting fact 4. So Al could not have gotten married.
Suppose Carl got married. Fact 2 tells us that he married Fran, contradicting fact 1. So Carl could not have gotten married.
Suppose Dan got married. Fact 2 tells us that he married Fran, while fact 3 tells us that he married Gertrude, contradicting each other. So Dan could not have gotten married.
Therefore, Ben got married.
From fact 1, Ben could not have married Fran or Heather. From fact 5, he could not have married Gertrude, leaving only Edith.
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