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A Limerick A Day...

Improper, I'm prime down below;

And on top, two digits I show.

My three digits' sum's 8,

As decimal, terminate;

Two odds, but no 5, you should know.

 

Source: John Gregory & Dale Seymour's Limerick Number Puzzles (Creative Publications, 1978)


Hint: Take one clue at a time in the order given...try to write down what options remain at each step.

 


Solution Commentary: Algebra is not needed to solve this limerick. Rather the key is to think your way to a solution using problem solving skills such as establishing special cases, looking for patterns, building tables, etc.

For example, start with (AB)/C. Given clues #1 and #5, what can C be? Then focus on clue #3 and finally clue #4.

Is the answer unique?

Finally, I wish this book was still in print. My students always enjoyed these limericks and learned alot about the reasoning process as a precursor to the formal proof process. I will try to include more limericks later on.