Whaaat are Pentominoes?

The word Pentomino comes from the Greek word for the number five (pente) and also from the -omino of dominos.

The creator, Solomon W. Golomb gave them this term with the interpretation that domino stands for the Greek prefix of di- meaning the number two. There are twelve pentomino pieces. He gave each of the different shapes a name based on the letters of the Latin alphabet. (F, I, L, N, P, T, U, V, W, X, Y, Z)

The pentominoes are a simple-looking set of objects through which some powerful mathematical ideas can be introduced, investigated, and applied. ... The pentominoes are a puzzle that has been used by teachers to introduce students to important math concepts such as symmetry, area, and perimeter.

Pentominoes play a pretty big part in things in our story. Calder has them constantly rattling around in his pocket. He thinks about them a great deal, uses them to solve puzzles and also refers to them in terms of sussing out the larger puzzle at work here. He tells Petra that the pentominoes "help him to figure things out.." and they "kind of talk to" him. He gets "a feeling that they want to tell (him) something" and he'll grab one and a "word will just pop into his head." (p. 84)

Pentomino problems are usually a rectangle of various sizes that you have to fill with the blocks. No overlapping or sections hanging off the edge allowed!

With each of these different shapes combined there are exactly 2339 solutions. You could play with it for hours!

You can make this into a math puzzle game on an 8×8 grid with 2 or three players. Players take turns in placing pentominoes on the board so that they do not overlap with existing tiles and no tile is used more than once. The objective is to be the last player to place a tile on the board. This version of the Pentominoes game is called “Golomb’s Game” after the creator. The first pentomino problem, written by the great English inventor of puzzles, Henry Ernest Dudeny, was published in 1907 in the Canterbury Puzzles.

Each of the twelve pentominoes can be modeled two-dimensionally with nine of the remaining pentominoes. To do this, first pick up a piece to model and put it aside as this piece will not be necessary for the scaled model. Second, try to construct a duplicate on a 3/1 scale. The new model will only need nine pieces.

Try to fit your pentominoes together to make one of the following shapes. Notice that your set of pentominoes has 60 squares in all, so we can try to tile rectangles of dimensions 1x60, 2x30, 3x20, 4x15, 5x12 and 6x10. Of these, the formats 1x60 and 2x30 can not be covered with the 12 pentominoes, for obvious reasons (consider the 'X, piece, for example, which is 3 units wide in every direction). The number of solutions for each of the rectangles is:

3 x 20..........................2

4 x 15..........................368

5 x 12..........................1010

6 x 10..........................2339

Besides its intrigue as a puzzle, the placement of pentominoes on a checkerboard also makes it an exiting competitive game of skill. Played by two or three players, the object of the game is to be the last player to place a pentomino piece on the checkerboard. Players take turns choosing a piece and placing it on the board. The pieces must not overlap or extend beyond the boundary of the board, but they do not have to be adjacent. The game will last at least five, and at the most twelve moves and it has more opening moves than chess. Can you demonstrate a game that only lasts five moves? (assuming both players are doing their best of course.)

A pentomino (also known as a pentimino is a plyomino of five squares. The ancient pentomino puzzle uses free pentominoes. It was the inspiration behind Tetris. Aleksey Pazhitnov found pentominoes to be too complex, so he simplified it to teriminoes. Tetris was inspired by pentomino puzzles!!

The figures shown are known as pentomino checkerboards and are constructed two dimensionally (lying the pieces flat). Note that one of them forms a Yin Yang symbol when you put the two equal halves together. Here, you can make your own puzzle by selecting any four squares on the checkerboard to leave blank.

This is another interesting problem played with the 12 pentominoes. In the previous problems, we are fitting pentominoes to a region, avoiding holes. Now, we try to make as many holes as possible. Two holes may not touch each other in their perimeters. Furthermore, each hole has to be surrounded by eight squares. It has been proved that the number of holes cannot be greater or equal to 14. There are only 2 solutions for 13 holes. Here is one solution.

The following is different from the previous tiling problem. We try to form a fence with the 12 pentominoes encompassing a empty field. The pentominoes along the fence must be connected along a side. There are four shapes, in each of them we try to maximize the area of the field.

Form a rectangular fence around a rectangular field

Form a rectangular fence around a field of any shape

Form a fence of any shape around a rectangular field

Form a fence of any shape around a field of any shape

A solution of problem 1 is presented below. It has been proved maximum

SO fun! What can you make with your pentominoes?

Besides the rectangle configurations and animals you can use your pentominoes to make all sorts of things

This is another way pentominoes can be used. Artists use the repeating shapes to make cool designs and things. They remind me of M.C. Esher with their interlocking parts.

Maurits Cornelis Escher (Dutch pronunciation: [ˈmʌurɪt͡s kɔrˈneːlɪs ˈɛʃər]; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. He has tons of other amazing work you can check out.

By making a set of pentominoes out of cubes instead of squares, you can try to solve many more puzzles. (Wooden cubes are sold at most craft stores, but try to make sure that they are of uniform sizes.) The first puzzle with these solid pentominoes is to be able to put them into a 3x4x5 box. Ten of the twelve pentominoes can be modeled three-dimensionally with all twelve pieces. Construct the pentomino figures on a 2/1 scale, but this time around a new dimension is added -- they must be three stories tall! This technique is fiendishly difficult as the pentominoes can be used any which way that works. Keep in mind that there are two pentominoes that cannot be constructed in this manner -- the W and the X.

Here is a link : Some other interesting shape things to try