Pentomino puzzle plan

A pentomino is a polyomino composed of five congruent squares, connected along their edges, which practically means that pentomino is consisting of 5 identical squares, which are arranged so that each square has at least one side common with other 4 squares. Pentominoes resemble the famous game Tetris – the only difference is that pentomino is composed of 5 squares, and the Tetris block of 4 squares.


Pentomino puzzle plan


There are 12 of these shapes, and each one is given a single letter name that resembles its shape.
 

Pentominoes letter names


If we make all 12 pentominoes, we can stack them into various 2D or 3D shapes and figures.

On the following image you can see a cutting diagram, by which you can make all the 12 pentominoes.
 

Pentominoes -  Cutting diagrams

 

The task is to assemble these 12 pentomino pieces into various shapes. The pentomino puzzle is usually tiled in the rectangle, and the various dimensions of the rectangle are: 6 squares x 10 squares, 5 squares x 12 squares, 4 squares x 15 squares and 3 squares x 20 squares.

There are thousands of ways to arrange them into these rectangles, and your task will be doing it in as many ways as you can. Finding all of the possibilities is very difficult, because:  6 squares x 10 squares rectangle has 2339 solutions, 5 squares x 12 squares rectangle has 1010 solutions, 4 squares x 15 squares rectangle has 368 solutions while 3 squares x 20 squares rectangle has only 2 solutions.

The solutions do not include rectangles obtained by rotation and reflection of whole rectangle, but it includes those obtained by rotation and reflection of a subset of pentominoes.

It is very interesting to tile rectangle with dimensions 8 squares x 8 squares, which is possible only if there are holes of 4 squares anywhere on a rectangle.  

The pentominoes puzzle seems to be simple, but the number of various tasks and variations of solving those tasks makes this puzzle very interesting. There is even a variation of game where you do not have to use all 12 pentominoes.   

A few 2D shapes, which you can make of all 12 pentominoes.

 

 

  Pentomino puzzle - 2D tasks
 

A few 3D forms, which you can make using all 12 pentominoes.

 

Pentomino puzzle - 3D tasks

 
A solution to tile block 5 squares x 4 squares x 3 squares by using all 12 pentominoes.

 

Pentomino puzzle - 3D example solution
 
 
Download plan for making Pentomino board game
Pentomino board game plan