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, 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.

**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.

http://www.johnrausch.com/PuzzlingWorld/chap02d.htm
This takes you right to the section on pentominoes.

Has all solutions to the rectangles above (items 1,2,3,4).

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://www.wins.uva.nl/misc/pythagoras/polyominoes.html More great links. There is a lot out there.

http://godel.hws.edu/java/pent1.html Wonderful solver for the 8 x 8 square with four 1 x 1 holes.

http://www.pentomino.be.tf/ A nice student site with additional puzzle links.

**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.