All Relative

A problem from Dick Hess’ All-Star Mathlete Puzzles (2009):

A man points to a woman and says, “That woman’s mother-in-law and my mother-in-law are mother and daughter (in some order).” Name three ways in which the two can be related.

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The woman can be the man’s daughter-in-law, because his wife is the daughter of his mother-in-law. The woman can be the man’s wife’s aunt (his mother-in-law’s brother’s wife), because his mother-in-law is the daughter of her own brother’s wife’s mother-in-law. The woman can be the wife of the man’s nephew (the wife of his wife’s sister’s son), because his wife is the daughter of his mother-in-law. Equivalently, the man can be the woman’s father-in-law, her niece’s husband (her husband’s sister’s daughter’s husband), or her aunt’s husband (her husband’s mother’s sister’s husband).

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October 12, 2013October 18, 2013 | Puzzles