# PENTAMINOS LÍNEA

### 42,00€

What makes the Pentaminos fascinating is its initial simplicity, so different from the ennigmas and problems described below. Unlike a 1000-piece puzzle, which has a single solution, the Pentaminos, while consisting of only 12 pieces, has thousands of possible solutions.

Altogether there are twelve different Pentaminos, each designated by a different letter of the alphabet: (F, I, L, N, P, T, U, V, W, X, Y, Z). Pentaminos obtained by joining others at their axis or by rotation are not considered to be ‘different’ Pentaminos.

A Pentaminos is a polinimo, a term coined in 1953 by the North American mathematician and engineer Solomon W. Golomb to describe geometric figures made up of identical square sides joined by their edges.

Polinimos fall into different categories: minós, which are made up of a single square, dominós, consisting of two squares, triminós, having three squares, tetraminós, made up of four squares, and pentaminós, with five squares.

Altogether there are twelve different Pentaminos, each designated by a different letter of the alphabet: (F, I, L, N, P, T, U, V, W, X, Y, Z). Pentaminos obtained by joining others at their axis or by rotation are not considered to be ‘different’ Pentaminos.

THE TRADITIONAL GAME

The object of the traditional Pentaminos game varies, and with time and practice, a variety of problems and enigmas can be created, some of which are described here:

The Square

This consists of forming a square with 8 x 8 minós, using all of the pieces and leaving four of the squares open in different positions. The resulting structure can be stored in the box.

The Rectangle

Each of the Pentaminos’ 12 figures is made up of 4 squares, giving us a total of 60 squares. Another Pentaminos enigma is to build rectangles (with a surface of 60 squares) using all of the pieces. There are a number of possible dimensions for the rectangle:

– The 6 x 10 rectangle was first solved by John Fletcher in 1965. There are exactly 2339 solutions.

– The 5 x 12 rectangle has 1010 solutions.

– The 4 x 15 rectangle has 338 solutions.

– For the 3 x 20 rectangle there are only 2 solutions.

THREE TIMES GREATER

Each Pentaminos figure can be created at a scale three times larger, using 9 of the 12 Pentaminos.

THE CUBES

Because the Pentaminos3D has volume, the units forming each figure are cubes instead of simple squares. This allows us to work in three dimensions, expanding and increasing the complexity of the problems and enigmas we wish to resolve.

In the same way that the rectangle enigma required the use of 60 squares, the three-dimensional Pentaminos enigmas involve the use of 60 cubes and require the use of the 12 pieces.

The possible sizes of the figures vary:

The 2 x 5 x 6 version has 528 solutions, excluding those obtained by rotation or symmetry. The 3 x 4 x 5 version is more complex and all of the possible solutions are not known. A high-speed computer processor was used to analyze one fifth of the possible combinations (some 3.5 billion). 9,317 solutions were obtained, of which 2775 were mirror images or reflections of others, leaving us with a total of 6542 real solutions. It is estimated that an analysis of the remaining 80% would contain many that would be reflections or mirror images, leaving us with somewhere around 10,000 different solutions.

OUR CONTRIBUTION

The Pentaminos that you have before you is three-dimensional, meaning that the figures that you build can stand freely and be seen from different angles. You can choose to follow the Pentaminos rules or to freely create figures, structures that are balanced or not, or figures that contravene in some way the strict mathematical precepts governing some of the proposed enigmas and problems. The pieces comprising this Pentaminos3D contain space; their emptiness allows us to gaze through them, seeing nothing but their outlines. All of these features provide practically limitless possibilities for the construction of fascinating visual worlds. We hope that in using it you take a step beyond the suggested enigmas and find your own language.

Author: Javier Bermejo. Made by: PICO PAO

## Additional Information

Weight | 0.5 kg |
---|---|

Dimensions | 24 x 23 x 3 cm |

Materials | MDF wood |