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:

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

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. https://youtu.be/W0luMnybKB4

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.