Just like a domino which is constructed from 2 squares juxtaposed along the sides, a pentomino is constructed from 5 such squares, each having atleast one of its sides along that of another. While there is a unique domino, pentominos come in 12 different flavors. And that is what makes them interesting. I have reproduced here the 12 forms. But before peeping in, try to construct them yourself. To give you an idea, here are the tetrominos on which the game tetris is based.

The challenge is to arrange the 12 different forms together so that they fit in a rectangle of 10 x 6. If you get frustrated, just peep into the famous illustration provided by Clarke in the Imperial Earth.

Believe me, there are thousands of such unique combinations possible (2339 to be precise). The hidden challenge is to write a program which will generate all these solutions. I have a recursive program that uses brute force to do that. The c program fits into 45 lines (besides the datafile) but it is obviously too slow. A lot of fast programs are available on the net. Some of these use the truncated tree approach. Can YOU do it? A graphical interface would be best.

Before I leave the topic of ...minos, can you fill the chessboard with linear triminos? Obviously not! 1 square will be left over. Can you prove that there are only four specific squares on the board which can be left vacant (one at a time ofcourse) by covering the rest of the board by 21 linear triminos? What squares are these?

Few pentomino solutions obtained by my brute force C program.

If you do write the program, do let me know. I am willing to pass on the code that I have scripted to people interested. Free ofcourse!!

Java version of a program that gives you all the possible solutions if you wait long enough.

Have fun.

Recently I came across another pentomino page. Guenter Buehler has a fast DOS program that gives you all the solutions to the problem. He also has some other intersting stuff on art and logic.
Philippe Lorente is trying his hand at 3D pentominos!

Feedback appreciated at aam@astro.caltech.edu

Last outdated Jan 13 2000