Source:
http://mathnexus.wwu.edu/Archive/problem/detail.asp?ID=182
Limerick Problem #1:

Three
different onedigit primes
produce me, if you're
using times;
If my digits you add,
Another
prime will be had.
Two answersand
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
and Dale Seymour's Limerick Number Puzzles (Creative Publications, 1978)
.


Drawing
from tom on 8/21/2009 
.
Hint: Take one
clue at a time in the order given...try
to write down what options remain at each step.
.
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Finger pointing down
from darrell94590 on 1/2/2006 
.
..
THE SOLUTION
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.
.
.


Drawing
from tom on 8/21/2009 
.
.
My Solutions:
Limerick Problem #1:
The onedigit primes
are 2, 3, 5, and 7. There are four ways
to multiply three
of these numbers.
2 x 3 x 5 = 30 and 3 + 0 = 3 which is a prime.
2 x 3 x 7 = 42 but 4 + 2 = 6 which is not a prime.
2 x 5 x 7 = 70 and 7 + 0 = 7 which is a prime.
3 x 5 x 7 = 105 but 1 + 0 + 5 = 6 which is not a prime.
The two answers for
the limerick are 30 and 70.
Limerick Problem #2:
The two digits cubic
numbers are 27 and 64.
27 switched around is 72 which equals 8 x 9, a cube and a square.
64 switched around is 46 which equals 2 x 23 or 1 x 46.
Both don't work.
The cube the limerick
seeks is 27. 