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.