Pentominoes

Pentominoes is the set of shapes created by combining 5 squares or cubes, with faces touching each other, in every possible combination. Mirror images and rotations do not count as additional combinations.

With this, we achieve 12 unique shapes, totaling 60 cubes, as seen below:

They tend to resemble the following letters, respectively:

F I L N P T U V W X Y Z

**What can you do with these 12 puzzle pieces? You would be
amazed!**

(Remember, each piece contains 5 squares, so there are 60 cubes total.)

Using all 12 pieces, you can make:

- A 6 x 10 rectangle (see photo below)
- A 5 x 12 rectangle
- A 4 x 15 rectangle
- A 3 x 20 rectangle
- An 8 x 8 square with 4 pieces missing in the middle (see photo below)
- An 8 x 8 square with 4 pieces missing in the corners
- An 8 x 8 square with 4 pieces missing almost anywhere
- A 3 x 4 x 5 cube (see photo below)
- A 2 x 5 x 6 cube
- A 2 x 3 x 10 cube
- A 2D replica of each piece, only three times larger
- A 5 x 13 rectangle with the shape of 1 pentomino piece missing in the middle
- Shapes with jagged edges
- Tessellations using a pentomino
- Hundreds of other shapes!

**You can make your own set of pentominoes!**

Run, don't walk, to the nearest craft shop and buy 60 wooden cubes, each measuring about 3/4" on a side. Glue sets of 5 together into each of the 12 pieces shown above. (Make sure the U isn't too tight for the others to fit into it!) Then, have hours of fun trying to create each of the above shapes.

The photo on the right is a pentominoes set I purchased in Shanghai, China. Each cube measures about 15mm on a side. It's a very nice set, great size, clever box with lid, and only cost about 120RMB ($15). The manufacturer is Dr. Br@in.

**3-D Pentomino Puzzle**

This is made by Learning Resources, with blue and yellow plastic pieces, each cube measuring 20mm on a side. A great set to work with, but does not seem to be available on their web site. Item # LER 2240

**Rainbow� Premier Pentominoes**

This is also made by Learning Resources, with six sets of pentomino pieces in
various colors of plastic tiles. This does seem to be available on their
web site. Item # LER 0286-6 for about $20.

**Shapes Puzzle**

From OfficePlayground. Measures 0.75" x 4.8" x 6.9" Only $4.

**KATAMINO**

https://www.youtube.com/watch?v=W0luMnybKB4&feature=youtu.be

https://www.youtube.com/watch?v=w9mQQn62nIo&feature=youtu.be

https://www.youtube.com/watch?v=_fb0DBSVOX8

https://www.youtube.com/watch?v=C_StVEJNv4I

This is my favorite set, made by Gigamic in France. A very nicely constructed set of colored wooden pieces, where the cubes are 20mm on a side. It also comes in a pocket version and a deluxe version. A great set of instructions for different ways to play this. It was a gift, so I don't know how much it cost.

**If you'd like to check out some other useful
links on Pentominoes, try these:**

http://www.johnrausch.com/PuzzlingWorld/ A fantastic site on several types of puzzles. Just do a site search for pentominoes. There are a lot of other kinds of puzzles out there, too!

http://www.xs4all.nl/~gp/pentomino.html Nice review.

http://www.xs4all.nl/~gp/PolyominoSolver/Polyomino.html Provides solvers for several configurations.

http://www.cut-the-knot.com/ This doesn't have any pentominoes that I could find, but has lots of great info on math!

http://math.hws.edu/xJava/PentominosSolver/ This works if you have Java working on your browser, or you can download an executable to keep for yourself!

There's more out there - just search for "pentominoes".

**For books on pentominoes, I highly recommend the
following:**

**Mathematical
Puzzles & Diversions**

Martin Gardner

LCCN 59-9501

Simon and Schuster

NY 1959

**Creative Puzzles of the World**

Pieter van Delft and Jack Botermans

LCCN 77-80234

ISBN 0-8109-2152-9 (pbk)

ISBN 0-8109-0765-8

Harry N. Abrams, Inc.

NY 1978

**Polyominoes**

Solomon W. Golomb

ISBN 0-691-02444-8 (pbk)

ISBN 0-691-08573-0

Princeton University Press

Princeton, NJ 1994

**Pentominoes**

Jon Millington

ISBN 0-906212-57-X (pbk)

Tarquin Publications

Norfolk, England 1995

**Tilings
and Patterns**

B. Brunbaum and G.C. Shephard

ISBN 0-7167-1193-1

W.H. Freeman and Co.

NY 1987

For more selections, check out amazon.com for other books by Martin Gardner, pentominoes, puzzles, etc.