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Lick These Limericks

Limerick Problem #1:

Three different one-digit primes
produce me, if you're using times;
If my digits you add,
Another prime will be had.
Two answers--and nothing else rhymes.

Limerick Problem #2:

There once was a cube 'twas found
Whose two digits, when switched clear around,
Was the product (quite fair)
Of a cube and a square,
And its name will most surely astound.


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 these limericks. 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, in Limerick #1, start with the set of one-digit primes (these are not that many options!) and produce all possible products. then focus on the next clue, etc.

For each, ask if the answer unique?

Finally, I wish this resource 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....plus they got a good review of common mathematical concepts and words. I will try to include more limericks later on.