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:
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.
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:
Puzzles & Diversions
Simon and Schuster
Creative Puzzles of the World
Pieter van Delft and Jack Botermans
ISBN 0-8109-2152-9 (pbk)
Harry N. Abrams, Inc.
Solomon W. Golomb
ISBN 0-691-02444-8 (pbk)
Princeton University Press
Princeton, NJ 1994
ISBN 0-906212-57-X (pbk)
Norfolk, England 1995
B. Brunbaum and G.C. Shephard
W.H. Freeman and Co.
For more selections, check out amazon.com for other books by Martin Gardner, pentominoes, puzzles, etc.