Get Adobe Flash player

Pentominoes


Like many others I learned about pentominoes from Martin Gardner’s column in the Scientific American. I was fascinated by them at once and the first thing I did when I was back home was to cut a set out of carton and try to solve the puzzles he has been giving in his article. Later on I always tried to read about pentominoes, collect some material about them. Besides that I have also devised some games and puzzles (with their solutions) myself.

Even as a student of architecture I thought about the similarity between pentomino puzzles and design problems. Architects arrange volumes, each with different shapes after their specific functions, when working on plans and they try to find the best suitable arrangement by trial and error as if they were working on a pentomino puzzle. Or sometimes they would do exactly the opposite, that is, they put different surfaces, shaped differently after specific functions, together in order to create a meaningful whole. Even if they create irregular shapes, good examples have always a clear geometry. Apart from this, architecture generally uses symmetrical arrangements. Like in architecture it is possible to create an almost infinite number of shapes with limited elements with pentominoes. All of these are valid for urban arrangements too.

Because of these I always saw pentominoes as a very suitable toy or game for architects and I still think like that. I even think that they can be a very useful tool in the education of architecture. In his book about the geometry of building plans J. P. Steadman mentions polyminoes and polycubes as an analytical design tool and gives some examples. (J. P. Steadman, Architectural Morphology, London, 1983) I have also mentioned pentominoes and its derivatives in my book published as lecture notes. (Üstün Alsaç, Theoretical Observations on Architecture, Gazimağusa, 1997) I have also published an article about pentominoes in a children’s magazine when I was maintaining a column about mathematical games. (“Can Sıkıcı Bir Gün ve Beşkareler” (A boring day and pentominoes), Doğan Kardeş, issue 55, p. 44-49, 1993)

What are pentominoes?

Since this web page is prepared to address mainly Turkish readers I do not want to repeat anything which can be found on many other Internet sites and pages. All I want to say here is that these pages contain some puzzle-like compositions I have created with pentominoes, and hope to attract the attention and interest of especially young readers and beginners. If you are one, do not hesitate to work on them by using squared paper and pencil. Better, you can build pentomino pieces out of carton and create your own figures. Of course it is also possible to use two or more sets to increase the possibilities and the number of variations.

Games with pentominoes

Solomon W. Golomb, inventor of pentominoes, has also devised a strategic board game for two players with pentomino figures. This game has two variants in which players place their pentomino figures on a 8×8 checker board.

I thought of an extension for it. Here there are two sets of pentomino figures (one set for each player) and the board has 11×11 squares. This creates some kind of balance between the players because each of them has the equal number of figures with similar shapes. The game becomes more exciting and requires a slightly different strategy.

If you would make the sets and the board and try these games you may enjoy them too. Especially children and young adults are quite successful in them. My brother Engin, who has learned about pentominoes and these games from me when he was a child, was very fond of playing them with me and enjoyed them very much because he was generally beating me.

After the pentominoes

If you liked pentominoes similar other puzzles and games may also interest you. There are numerous variations using equal triangles, more than five squares, hexagons, etc. There are also some that use irregular shapes such as right angle triangles or parallelograms. There are also various combinations of them. If you tackle them mathematically or use them just to create interesting forms there will be some under them you may enjoy.

There are also similar arrangements in three dimensions. They use combinations of regular solids such as cubes or triangular pyramids. Most popular of them is the so called SOMA cubes, an invention of the Danish thinker and artist Piet Hein. There is also three dimensional pentominoes as a special category. All of them can be tackled mathematically or they can be used to create interesting three dimensional figures. Many Internet sites and pages are dedicated to them.


Leave a Reply