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	Pentomino - Wikipedia, the free encyclopedia
		A pentomino is a polyomino composed of five (Greek πέντε / pente) congruent squares, connected orthogonally.
		Pentominoes are a key part of the 2003 children's novel Chasing Vermeer by Blue Balliett.
		Pentominoes are prominently featured in a subplot of the novel Imperial Earth by Arthur C. Clarke.
	en.wikipedia.org /wiki/Pentomino (1142 words)

	3D pentomino solver program
		The kind with twelve pentomino shaped plastic pieces that you have to arrange in a 6x10 rectangle.
		The inside of the box is actually 1.5 milimeters bigger in each direction than what the sizes of the pentominos add up to, to allow for imprecisions and size changes in humidity.
		Also note that the 2d pentomino solver uses unaligned access, so it won't work on computers based on the Dec Alpah or ARM architecture, both of which are extremely rare for general purpose comuters.
	www.sentex.net /~mwandel/tech/pentomino.html (1087 words)

	Ivars Peterson's MathTrek - Pentomino Battleships
		Whereas a domino is simply two squares stuck together along one edge, a pentomino consists of five adjacent, or "simply connected," squares.
		Traditionally, each pentomino is identified by the letter of the alphabet that it roughly resembles.
		The goal of pentomino battleships is to locate the four unoccupied squares of an opponent's hidden grid.
	www.maa.org /mathland/mathtrek_11_24_03.html (703 words)

	John Greschak - Pentominoes for Flute, Trumpet and Cello - Program Notes (Site not responding. Last check: 2007-10-07)
		In this piece, melodic phrases are derived from the shape of the boundary of a pentomino.
		The pitch of the note is a function of the distance from the leading endpoint of the line segment to the centroid of the pentomino.
		When traveling along a (parent) path around a given pentomino in a pentomino puzzle, a child path (and thus a child melodic phrase) may be triggered whenever the parent path encounters a neighboring pentomino.
	www.greschak.com /m70pn.htm (220 words)

	George Huttlin's Pentomino Webpage
		A pentomino is the shape of five connected checkerboard squares.
		The object of the puzzle is to choose a shape made with 60 squares and then cover it using all 12 pentominoes.
		Puzzles based on pentominoes have been around for nearly a century and have been marketed under a variety of trade names.
	members.aol.com /huttlin/pentominoes.html (1440 words)

	Measurement Session 10, Grades 3-5: Classroom Case Studies
		A method for determining perimeter when combining two pentominoes is to add the perimeters of the two pentominoes and then subtract the number of sides touching when the pentominoes are combined.
		When tracing their combined shapes, however, if students do not also include the detail of all the squares in the pentomino, they will not be able to see the number of sides that are touching to make their new combined shape.
		Belber's homework assignment of repeating the task with three pentominoes provides additional generalizing opportunities and could ultimately lead to a rule for determining the maximum and minimum perimeters for any number of pentominoes.
	www.learner.org /channel/courses/learningmath/measurement/session10/35solutions_b.html (605 words)

	Mt. Baker Puzzle Books - Pentomino History
		Pentomino puzzles have been around since at least the early 1900's, when they were mentioned in The Canterbury Puzzles by Henry Dudeney (Dover Publications, 1986; first published in London, 1907).
		According to Dudeney, tradition has it that the chessboard broke into thirteen fragments - twelve unique pentomino shapes and one little piece of four squares only.
		The chessboard then had to be re-assembled, and thus the first pentomino puzzle was born.
	www.mtbakerpuzzlebooks.com /history.php (279 words)

	Pentominos Puzzle Solver
		This means that it simply tries the pentominos in all possible orders, trying to fill the available spaces from left to right and from top to bottom.
		When the Pentominos window first appears, it creates an 8-by-8 puzzle in which four squares have been selected at random to be left empty.
		The Symmetry Check command does not appear in the menu for a board that is too small to hold all 12 pentominos, since the method that is used for symmetry checking assumes that all the pieces are on the board.
	math.hws.edu /java/pent1.html (1801 words)

	Afterschool Training Toolkit \| Finding Pentominoes
		In this activity, students explore and build pentominoes, figures that are made up of five squares and can be arranged to form different geometrical shapes.
		Using the pentomino you created, turn it so that it is still the same arrangement of squares, but facing in a different direction.
		Explain that this is not a different pentomino because the combination of squares is the same.
	www.sedl.org /afterschool/toolkits/math/ex_pentominoes.html (438 words)

	More Pentomino Puzzle Solutions
		If pentominoes can't be flipped over, then there are 18 distinct shapes.
		Take a pentomino piece and increase its linear dimension by a factor of three.
		The problem is to fill in the shape using pentomino pieces.
	www.theory.csc.uvic.ca /~cos/inf/misc/MorePent.html (201 words)

	Enchanted Mind Java Puzzles - Pentominos
		The objective of this puzzle is to place all pentominos on the board after you have marked four squares to remain empty.
		Then click on the pentomino of your choice, hold the mouse-button and drag it on the board.
		To remove a pentomino you can drag it over the edge - any edge - of the board and release it.
	enchantedmind.com /puzzles/pentamino/pentamino.html (165 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		For example, the shape shown in Figure 1 a is a pentomino, whereas the one in figure 1b is not.
		My pentomino wood mosaics show a great many three-dimensional shapes in perspective which are constructed from pentominoes.
		The pentominoes, cut out of various veneers, are based on unit squares with 1 inch sides, because the length of 1 inch or integral multiples or fractions thereof seem to agree particularly well with our sense of proportions.
	www.basic.northwestern.edu /g-buehler/pentominoes/speech.htm (1423 words)

	Pentomino Constructions
		A large number of problems have been considered with pentominoes in the last 40 years and many of these are discussed on the sites listed above and here we shall just include a few which are not discussed elsewhere.
		Here the problem is to use 3 pentominoes to form a 15 square region and then add the remaining 9 pieces to complete a duplicated copy of the original area.
		This is not a particularly nice solution since the same pentomino is used more than once in some of the triplications (see the three I's, 2 T's and 2 Y's in the triplicated Y).
	clarkjag.idx.com.au /PolyPages/pentopatts.htm (660 words)

	Pentominos
		The main problem of the pentomino 'research' is to combine 12 pieces to rectangles.
		Pentomino pieces are mostly not two-dimensional, but are made of cubes and form pentacubes in the plain.
		The remaining pentominos appear as pairs of symmetric mirror solids.
	www.mathematische-basteleien.de /pentominos.htm (643 words)

	Equivalence Classes Among Pentomino Tilings of the 6x10 Rectangle
		Each pentomino is represented with a set of up to eight oriented pentomino data structures, one for each orientation.
		Two solutions have pentomino j in common if and only if they have the same values in the j'th element of their polar representations.
		Checking the pentominos that differ to see if they can be split in two congruent subsets {8} is the computationally most intensive task.
	www.cs.cmu.edu /~wjh/papers/hexclass.html (2831 words)

	Pentomino Puzzles
		One way is to start with the empty board, select the first pentomino, and try all possible ways of placing it on the board.
		Construct a matrix with 72 columns: 12 for the twelve pentominoes and 60 for the cells of the board.
		The row should contain a 1 in one of the first 12 columns, indicating the pentomino, and five 1's among the other 60 rows, indicating the five cells of the board the pentomino occupies; everywhere else the row should contain zeros.
	yucs.org /~gnivasch/pentomino (1340 words)

	Gerard's Pentomino Page
		The basic set of pentominoes consists of twelve different pieces (excluding the ones that are identical by rotating and flipping).
		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).
		As a pure symcom excerise: fit all 12 pentominoes together, forming any shape, so that each pentomino touches at least one other pentomino, and each pentomino forms a symmetrical combination with every pentomino it touches.
	www.xs4all.nl /~gp/pentomino.html (793 words)

	Problem Solving with Pentominoes - Instructional Units - Instruction - Technology Applications Center for Educator ...
		Skills: Students must recognize that when a pentomino is rotated or flipped, it is still the same pentomino.
		The students are given a LOGO Pentominoes Unit worksheet to monitor their progress.
		To create these shapes, they use the pentomino sets at their desks, draw the results, and then write Logo procedures and create the shape on their computer.
	www.tea.state.tx.us /technology/techapp/instruct/lp0005.htm (993 words)

	Begining Pentomino Problems
		These problems require two (or more) pentominoes to be put together to make one total shape, and then to find the same number of pentominoes that make the same total shape as the first one.
		Four pentominoes can be put together to make a copy of the P pentomino which is two times as wide and two times as high as the original piece.
		A pattern is given and you need to use some of the pentominoes to cover the pattern.
	www.rit.edu /~mecsma/Professional/Puzzles/Pentominoes/P-A.html (688 words)

	Pentomino hungarIQa. The Game
		) tilted the pentomino from the right and also from the left.
		The effect is astonishing: it gives more than a hundred times more challenges as known to pentomino-challenges, in all it doubles the number of step-pairs made by players and solves their sharing problems.
		The best known examples are: the 3x20, the 4x15, the 5x12, the 6x10, the "holed" 5x13 (when the hole in the middle is similar to a previously definite piece), the tripling (jigsaw puzzle of any tripled size piece), and the 8x8.
	www.pentomino.tvnet.hu /eng (805 words)

	Pentomino example
		Pentominos are the names of shapes created by 5 squares connected together.
		The objective of the puzzle is to place all pentominos inside the square after marking 4 boxes to remain empty.
		Drag over the pentominos, one at a time, and place them on the puzzle board.
	teams.lacoe.edu /documentation/classrooms/amy/geometry/6-8/activities/pentominos/pentominos.html (155 words)

	PentoMania Tutorial (Site not responding. Last check: 2007-10-07)
		Pentominoes are commonly found in many elementary classrooms.
		Pentominoes are puzzle pieces made from five equally sized squares, all touching at least one other square on a side.
		The traditional pentomino puzzle requires students to fit all twelve pentomino pieces into a rectangular shape.
	www.virtu-software.com /help/PentoMania/Home.htm (180 words)

	Info on Pentomino Puzzles
		A pentomino is an arrangement of 5 unit squares (or sometimes cubes) that are joined along their edges.
		Pentominoes as a Geometry Forum project of the month.
		Pento -- A program to solve the Pentomino problem (seems rather slow to me, but a nice feature is that it will show the backtracking as it is proceeding).
	www.theory.csc.uvic.ca /~cos/inf/misc/PentInfo.html (624 words)

	Puzzle - soma cube (Site not responding. Last check: 2007-10-07)
		This puzzle is a 3 dimensional counterpart of the pentomino (or if you wish the tangram).
		Likewise pentomino or tangram, the pieces of soma cube can be arranged into several different configurations.
		It is also possible to arrange all the pieces into a cube and put it into a box.
	www1.zetosa.com.pl /~burczyk/origami/g2-01-en.htm (199 words)

	F1 Source Code: Pentomino.f1
		The code below solves all rectangular problems, but it is trivial to modify it to solve pentomino layout for different shapes.
		There are two possible approaches to tackle the pentomino problem: calculate until all pieces are used or calculate until the whole board is covered.
		Instead of rotating and flipping the pentomino pieces // at run-time, we precalculate all possible orientation of a pentomino // piece, at the same time avoiding identical shapes due to rotational/mirror // symmetry.
	www.f1compiler.com /samples/Pentomino.f1.html (652 words)

	Pauli: a Game of Colorful Pentominoes
		On one side it should be grey to indicate that the pentomino is passive; on the other side the same pentomino should be a bright color to indicate that it is active.
		A set of pieces on the board is a panchromatic match of a pentomino if the squares they occupy form a copy of that pentomino, and exactly one piece of each color is present in that copy.
		If you control an active pentomino card and you make a move that forms a second match of that card, all of the pieces in the new match are immediately returned to their owners' stashes.
	www.xprt.net /~munizao/games/pauli.html (1997 words)

	Chasing Vermeer Webquest
		A pentomino puzzle is formed, and information fits on the piece.
		There is an attempt to form a pentomino puzzle.
		There is no attempt to form a pentomino puzzle with the information.
	www.oconee.k12.sc.us /teachers/lharrison/2004/vermeerwq.htm (1240 words)

	A Pentomino Exclusion Problem (ResearchIndex) (Site not responding. Last check: 2007-10-07)
		Abstract: Introduction A pentomino is a generalization of a domino that covers 5 squares.
		Many interesting problems involving pentominoes, and their further generalization polyominoes, are described in Solomon Golomb's classic book [2].
		One class of pentomino problems considers the possibility, or impossibility, of using pentominoes to construct a given figure in the plane.
	citeseer.ist.psu.edu /260012.html (266 words)

	Pentomino Puzzle Game with Geometric Puzzles
		Not only can students solve pre-existing pentomino puzzles (such as the one shown here), but they can use the 'edit mode' to design their own puzzles.
		From a quick examination of the puzzle (called rocket) displayed above, it is obvious that there is space for two of the purple pentominoes (one is already in place, the other fits in the empty space).
		PentoMania puzzles range from extremely simple to terrifically difficult, and for less advanced students, there is an easy mode, in which pentominoes are placed in the 'PentoBin' with the correct orientation, so they don't have to worry about rotating or flipping them.
	www.virtu-software.com /PentoMania (341 words)

	quine - The Pentomino Solving Quine in Perl (Site not responding. Last check: 2007-10-07)
		The set of pentominos, or pentominoes, are those pieces which can be constructed similarly of five squares.
		The most common puzzle which can be played with pentominos is to fill a given space with some or all of the pentomino pieces.
		In this program, the pentomino problem is solved Perl-style, thinking ``out of the box'' to organize a 2D problem into a series of 1D string elements that benefit from a regular expression engine.
	www.halley.cc /ed/linux/scripts/quine.html (1808 words)

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