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The Relative Riddle

The Relative Riddle

This week’s Puzzle Corner is a classic riddle requiring reasoning to reconcile. (Please forgive the crude alliteration.) While many of you have encountered this riddle before and already know the answer, the riddle probably caused curious consternation (I beg your pardon once more) the first time you saw it. Riddles like the one presented here automatically appeal to a wide variety of people and it’s quite likely your students will enjoy puzzling over The Relative Riddle. Although not many riddles are mathematical in nature, this one is, and solving it involves a key concept in the area of mathematics known as set theory.

Before introducing this puzzle to your class, please caution students not to blurt out the answer if they already know it or figure it out before the rest of this class. Doing this will rob other students of the opportunity to think the riddle through and solve it for themselves.

To help your students become better puzzle solvers and mathematical thinkers, it is imperative that you try to build a classroom puzzle and problem-solving ethos that encourages students to work on the problems before being shown any solutions. Doing this builds persistence, one of the most important problem-solving traits. In our current educational climate where getting the correct answer quickly and efficiently often seems more important than developing students’ thinking skills, building persistence is often neglected.

FishingThe Riddle

Two fathers and two sons went fishing. Each of them caught a fish and none of them caught the same fish. However, they only caught a total of three fish. How is this possible?

Solution

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The Relative Riddle stated: Two fathers and two sons went fishing. Each of them caught a fish and none of them caught the same fish. However, they only caught a total of three fish. How is this possible?

The only way this riddle makes sense is if there are three fishermen. Therefore, one of the fathers in the riddle must also be a son. This works if the three fishermen are a father, his son, and his son’s son (grandson). The apparent discrepancy occurs because the second person above fits into two categories – father and son. However, just because he fits into both categories doesn’t mean he should be counted twice.

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