Problem Description

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 47 cabbages.

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  will be helpful in solving the equation represented by the problem:

Thisyear² - Lastyear² = 47

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 

• Browse source extract
• Download source
• Download  executable

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 with theory.