Lick These Limericks
Three different one-digit primes
Limerick Problem #1:
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.