Pentominoes

A pentomino is a geometric shape formed by adjoining five squares with one another edge to edge. There are twelve unique ways to do this (not counting rotations and reflections). Those twelve pieces are pictured here and make up the "classic" set of pentominoes. Traditionally each piece is named using the letter of the alphabet which most closely resembles its shape:

F

I

L

N

P

T

U

V

W

X

Y

Z

The concept of pentominoes (and their more general cousins: polyominoes -- made from any number of squares joined) have been a part of recreational mathematics for over a hundred years, but it was the 1965 book Polyominoes by American Professor Solomon W. Golomb which formally defined the shapes and made a rigorous, documented study of them.

I received my first set of pentominoes when I was about 9 years old (it was sold by the company Gabriel under the named Hexed -- pictured, right). The lid of the box proclaimed that there were 2339 ways to fit the pieces in the box (a 6x10 rectangle). Boy, was I determined to find all of them. Even at that young age, I was pretty focused. I played with those pentominoes often, and each time I found a solution, I would record it on a sheet of graph paper using colored pens (after having checked against the previous solutions).

This, of course, was all before the "computer age". At some point I found other things to do with my time, but I had, by then, discovered 59 of the answers (I still have the graph paper with my answers, over 20 years later). Since that time I have drifted back to the 12 wonderful geometric shapes, and they have always caught my eye in toy and games stores.

These days I have a number of different sets. Several basic plastic sets, a set of wooden, "solid" ones (meaning they have a thickness dimension as if made from cubes, not flat squares -- so they may be assembled into 3D figures), many sets that I have made from LEGO bricks, and a set of solid steel pieces.

I expect that I will augment my collection in the future... I'd certainly like sets made of brass, crystal, and even a large stone-carved set to stand in my backyard.

With the prominence of computers and the internet these days, information about these objects is readily available. A search on Google turns up quite a bit.

My most recent pentomino project has been the creation of the Pentomino Daily Calendar (year 2006).

I will also include links to various articles about pentominoes that I write. While most of the fun with pentominoes revolves around filling or building certain configurations, there are many other fascinating questions that can be asked about the pieces. As I get time, I will write webpages about some of the questions I have thought about, and provide answers when I know them. Here is a current list of articles:

1. Enclosing Extra Pieces
2. Landlocked Pentominoes
3. Numerous Solutions
4. Transmuting Pentominoes
5. Pentominoes As Letters
6. Pentominic Surfaces
7. Neighborly Pentominoes
8. Longest Narrow Path
9. Counting Rounded Pentominoes
10. Enclosing Unique Pentominoes
11. Elemental Pentominoes
12. Pentominic Shelves
13. Office Nameplate
14. About Those 2339 Solutions...