Two men are brothers-in-law if one is married to the other’s sister. What is the largest possible group of men in which each is brother-in-law to each of the others?
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Three. Three men can be mutual brothers-in-law if A marries B’s sister, B marries C’s sister, and C marries A’s sister. But D has no way to join this group. He cannot ask his sister to marry A, B, or C, because they are already spoken for. And if he himself marries the sister of, say, A, then he cannot be a brother-in-law to C unless C or D is A’s brother, which implies a violation of the law against consanguinity. (If a man may marry his own sister, then there’s no limit to the number of mutual brothers-in-law.)
(David L. Silverman, “A Problem of Relations,” Journal of Recreational Mathematics 3:3, July 1970)
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