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# Relative Reckonings

This week’s Puzzle Corner activity comes from the field of recreational mathematics where people do math just for the fun of it. One of the areas of recreational mathematics is logic. Logic puzzles are usually challenging and are normally resistant to quick and easy solutions.The puzzle presented here, Relative Reckonings, is no exception.

This puzzle challenges you to find out how 23 roles—one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, two brothers, one sister, three sons, one daughter, one father-in-law, one mother-in-law, and one daughter-in-law—can be represented by only seven people. It is—or should be—obvious that some of the people have to play multiple roles (e.g., a father is also a son). This answers the first question in the puzzle. The challenge comes in making sense of just who is who, a task that is not as easy as it might first seem.

How is this possible?

Who are the seven people and what are their relationships to each other?

I hope that you and your class find this Puzzle Corner activity both challenging and enjoyable.

Solution

Click the arrow below to view the solution.

The family relationships described in this puzzle are possible because each person plays more than one role. The son is also a father, the grandson is also a brother, etc. The people present are three grandchildren—a girl and two boys, their mother and father, and their paternal grandparents.