Mr. MacGregor always planted his cabbage
patch in a square
configuration. This summer he decided to plant extra for his rabbit friends and ended up planting an extra
How big was his patch last year and this year?
Background & Techniques
A computer is not really required to solve this puzzle, but it only
takes a few lines of code to do so.
Try it with pencil and paper before clicking on the
"Solve" button. A little knowledge of factoring and prime numbers
be helpful in solving the equation represented by the problem:
Thisyear2 - Lastyear2 =
I added a hint as a comment
over in the Browse source extract
link if you get stuck.
The problem, by the way, is adapted from
the book Recreations in the Theory of Numbers, by Albert Beiler,
Dover Publications. Equations in number theory, such as
this one, where solutions are restricted to integers are known
as Diophantine equations (after Diophantus of Alexandria,
apparently the guy considered to be the father of algebra).
Running/Exploring the Program
Suggestions for Further Explorations
Recreations in the Theory of Numbers is a gem of a book if you
like numbers. The final chapter has 100 short puzzles like this one,
all with solutions! And the preceding 292 pages
provide a good background, balancing the "recreational" part
|Original Date: November 18,
Modified: February 18, 2016