| Source:
http://mathnexus.wwu.edu/Archive/problem/detail.asp?ID=182
Limerick Problem #1:
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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:
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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)
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Drawing
from tom on 8/21/2009 |
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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 |
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..
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.
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Drawing
from tom on 8/21/2009 |
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My Solutions:
Limerick Problem #1:
The one-digit 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. |
