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Diversions



The pentomino problem consists of a set of twelve shapes, each consisting of five variously-arranged unit squares. For example, one shape is a rectangle of length five units and width one unit. The object is to arrange all twelve shapes into a rectangle. The pentomino program, "pentomin.exe", uses a brute force method to find every way in which the pentominos may be arranged to form a rectangle, being careful to avoid rotations and reflections of previously identified solutions.

Below is running a JavaScript and SVG2 version of the program.

This JavaScript version of the program runs slowly, intentionally, so as not to consume all your CPU power, but it should give you some idea of what it's about. Once it exhausts all solutions for the 3x20 configuration, it will advance, in turn (if you are sufficiently patient) to the 4x15, 5x12, and 6x10 configurations. If you are not sufficiently patient, you can advance, manually, to the other configurations by clicking on the rectangle. It should not take you long, watching it, to see improvements that can be made to the algorithm.

This JavaScript program employs SVG2 to present the arrangement of pentominoes.

The executable version of this program, which was written in "C" quite differently to the JavaScript version above, is available for you to download and save or run or to download the zip file that includes the Pentomino program (111.3kB), then extract and run “pentomin.exe”.

The file, “pentomin.exe”, is a Microsoft Windows Console application, so, if, after downloading the executable, you double-click on “pentomin.exe”, it will open an MS-DOS window and run. If you allow it to run to completion, which might takes days, depending upon your computer's speed, it will produce a listing of all solutions in the file “PENTOMIN.RTF”.

This was a problem set for my daughter (and her class mates) when she started high school. She attempted to find solutions using cut-out pieces of paper, which would never stay where they were placed, making the exercise rather frustrating. Instead of cutting new peices out of cardboard, as a sensible person would have done, I decided to write a program to do it instead.

The other diversion included in this ZIP file is the “Betagraph” demonstration.