This is Grant Maizels' pentominoes page.
Pentominoes are the twelve shapes that can be produced by joining five squares together continously.
Pentominoes can be arranged to form rectangles 6x10 (2339 solutions), 12x5, 15x4, and 3x20 (two solutions).
I first learnt about pentominoes from the Arthur C Clarke Novel Imperial Earth in the early 80s. After reading this It took 3 days to work out how to arange pentominoes in a 3 x 20 rectangle, with a pencil and paper. About 20 years later I finally got around to writing a brute force program to produce all solutions for a given rectangle.
The program, pent.c , takes one optional argument, (default is 10) the width of the recangle (10, 12, 15, or 20 though 3, 4, 5, and 6 are valid) and performs the following steps.
When run on my linux machine (Athlon XP-1600 with Red Hat 7.2) we get the following results (real from time) Note: Solutions Found is sometimes double the actual number of solutions because of mirrors:
|Compile Option||Width||Time (sec)||Solutions Found|
|gcc -O3 -DCHKVD||3||7.381||4|
|gcc -O3 -DCHKVD||4||94.253||402|
|gcc -O3 -DCHKVD||5||485.103||1308|
|gcc -O3 -DCHKVD||6||457.847||2339|
|gcc -O3 -DCHKVD||10||422.453||2339|
|gcc -O3 -DCHKVD||12||501.863||1308|
|gcc -O3 -DCHKVD||15||93.267||402|
|gcc -O3 -DCHKVD||20||5.861||4|
The program is designed and only tested on Unix/Linux. It can be compiled on Linux with the command:
gcc pent.c -o pent -O3 -DCHKVD
or if you want a slow version
using some optimisations and the -DCKVD option seem to help make it faster.
If the rectangle size selected has an odd number of rows, then mirror image solutions are reported.
This page, the linked programs and graphics are Copyright (C) 2003 Grant P. Maizels, Sydney, Australia