# Constrained Intermarriages

The word problem below is the one that opens the new book by David Singmaster Problems for Metagrobologists (World Scientific, 2015, paperback, \$28):

Not far from the village of Much Puzzling is the village of Less Puzzling. As in all country villages, there are a butcher, a baker, and a brewer. However, their names were Smith, Jones and Robinson, and their occupations are not relevant here! Strangely, they ere all widowers of about the same age with daughters of about the same age. Last spring, there was a grand triple wedding when each of the men married one of the daughters. What is Mr Smith's father-in-law's father-in-law's wife's maiden name?

Solution

Not far from the village of Much Puzzling is the village of Less Puzzling. As in all country villages, there are a butcher, a baker, and a brewer. However, their names were Smith, Jones and Robinson, and their occupations are not relevant here! Strangely, they ere all widowers of about the same age with daughters of about the same age. Last spring, there was a grand triple wedding when each of the men married one of the daughters. What is Mr Smith's father-in-law's father-in-law's wife's maiden name?

### Solution

Suppose Mr. Smith married Miss Jones. Then if Mr Jones married Miss Smith,Miss Smith,Miss Robinson, Mr Robinson,Mr Jones,Mr Robinson,Mr Smith would have to marry his own daughter, which is not permitted. So Mr Jones married Miss Robinson,Miss Smith,Miss Jones,Miss Robinson and Mr Robinson married Miss Smith,Miss Smith,Miss Jones,Miss Robinson. So Mr Smith's father-in-law is Mr Jones,Mr Jones,Mr Robinson, whose father -in-law is Mr Robinson,Mr Jones,Mr Robinson, who married Miss Smith,Miss Smith,Miss Jones,Miss Robinson.

As another possibility, suppose Mr. Smith married Miss Robinson,Miss Jones,Miss Robinson. Then Mr Robinson must have married Miss Jones,Miss Smith,Miss Jones,Miss Robinson and Mr Jones married Miss Smith,Miss Smith,Miss Jones,Miss Robinson. So Mr Smith's father-in-law is Mr Robinson,Mr Jones,Mr Robinson, whose father-in-law is Mr Jones,Mr Jones,Mr Robinson, who married Miss Smith,Miss Smith,Miss Jones,Miss Robinson.

The information given does not determine which of the two cases actually occurred, but the question has the same answer - Miss Smith,Miss Smith,Miss Jones,Miss Robinson - in either case.