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Polyominoes
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Looks at patterns that illustrate how the squares of polyominos are connected to each other.
http://web.idirect.com/~recmath/poly.html
Describes a numerical invariant that can be used to classify polyominoes.
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Polyominoes Instead squares we could use n equilateral triangles or n regular hexagons, and to obtain, respectively, polyiamonds or polyhexes. We will restrict our discussion to polyominoes (with polyiamonds and polyhexes the situation is absolutely the same For every polyomino we...A brief essay with some references.
http://www.cwi.nl/~jankok/etc/Polyomino.html
Numerous links, sorted alphabetically.
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The Geometry Junkyard: Polyominoes Connected subsets of the square lattice tiling of the plane are called polyominoes. These are often classified by their number of squares, so e.g. a tetromino has four squares and a pentomino has five; this nomenclature is by analogy to...Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.
http://student.cusu.cam.ac.uk/~jsm28/tiling/
Handmade wooden Pentomino and other puzzles; books.
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Puzzlecraft Crafter and seller of original mechanical puzzles and other puzzle items. Email: puzzles@puzzlecraft.com Phone 1-512-858-1415 All material on this website is copyright 1998-2003, Puzzlecraft. All rights reserved....Livio Zucca finds a set of markings for the edges of a square that lead to exactly 100 possible tiles, and asks how to fit them into a 10x10 grid.
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Xominoes Here is the complete ascii list or the picture of complete set. Don't think that the list is not complete. Remember S becomes Z and Z becomes S if you flip the piece. You can to place the pieces on...Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
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Vicher's puzzle page For more information about Eternity look at Ed Pegg's pages Mitre system Polyforms Polyominoes Polyomino variants Rounded polyominoes Diagonal polyominoes Polydominoes Polyares Polyhexes Polytans Polyiamonds Polydiamonds Tridrafters Pentadudes Heart-like Puzzle 1 Puzzle 2 Puzzle 3 3D Tridiamonds Expanded heptiamonds Polystrips...Computes from 1 to 3.38 billion solutions with graphic display to each of the 60+ problems of different sizes and shapes. Pieces vary from pentominoes to heptominoes, sometimes in combination. Table summarizes properties and example solution of each problem. [Java required].
http://www.xs4all.nl/~gp/PolyominoSolver/Polyomino.html
Every square can be dissected into L-ominoes. Can every Pythagorean square? Conjecture needs proof.
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A Puzzle I call the following visual proof that the sum of the first n consecutive odd numbers is n2, the L decomposition. Suppose we have two L decompositions, can the pieces of these two decompositions be reassembled into a single larger...Symmetries in the families of rectangular solutions.
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Pentomino Relationships There is something very nice about the way the twelve pieces of wood, each a different shape and each made of five cubes fit together into rectangles or cuboids, but if that was all there was to them, I would...At the Combinatorial Object Server.
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Info on Pentomino Puzzles A pentomino is an arrangement of 5 unit squares (or sometimes cubes) that are joined along their edges. Up to isomorphism (rotating and flipping there are 12 possible shapes, which are illustrated below. Each piece is labelled by the letter...A container of mathematical games, gadgets and software. (English/Italian)
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Pentamini pentaminos pentominoes scrolling auto...Problems on minimal covers.
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Pentomino Covers Although this site was designed with frames-capable browsers in mind, you can reach the important parts from here....Some packings of the 108 heptominoes (with unit thickness) into various blocks.
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Hepto This page contains some packings of the 108 heptominoes (with unit thickness) into various blocks. In fact, for all A×B×C blocks, where the product is 756, each dimension is at least 2 and two dimensions are at least 4. All...Undergraduate Research Project in Random Tilings.
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Tiling UROP Homepage Why we are so interested in random tilings of Aztec diamonds Papers relevant to our research project Other papers with more theoretical results Documentation to our software Links related to mathematics Our scrapbook of pictures Random tilings in motion This...Alex Selby's page with a description of his solution method, with illustrations in .png and .pdf files.
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Eternity page A solution to this puzzle was found on 15th May 2000 by Alex Selby and Oliver Riordan. Another solution was found independently by Gnter Stertenbrink on 1st July 2000. No other people are known to have solved it. Links to...Polyominoes, polycubes and polyspheres.
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Tiling and Packing results of Torsten Sillke News open problems and new solutions LEX notation scheme for polycubes. This can be used for polyspheres too. Pentacubes Ekkehard Knzell wrote a book (in German) on games played with pentacubes. There he explains his pentacube numbering system. The book...Home Page of the inventor of polyominoes. Includes biography, black and white picture, research interests and publications list.
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Solomon W. Golomb's Home Page He became a foreign member of the Russian Academy of Natural Science in 1994. He has received numerous awards and medals, as well as two honorary doctorate degrees. He was appointed the first holder of the Viterbi Chair in Communications...Enumeration on regular tilings of the Euclidean and Hyperbolic planes.
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Animal enumerations (main page) Animal enumerations on regular tilings inSpherical, Euclidean, and Hyperbolic2-dimensional spaces Introduction Results Links Contact [Up] Introduction Let S be a 2-dimensional space (i.e a surface and let {p} be a regular polygon with p sides defined onS. This means that...Fast Pentominos puzzle solver, works on DOS/Windows platform. Free downloads.
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Pentominoes Click here to download pento.zip (22 kb Polynominoes A Polynomino is a geometric shape that you can create by joining a few number of squares of same size, side by side. According to the number of squares they are named...Rules, the solution by Alex Selby and Oliver Riordan, other resources and links. The puzzle is made up of 209 pieces of polydrafters, each one is a combination of 12-30/60/90 triangles.
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eternity This header plots the critical line of the Riemann Zeta Function. A complete understanding wins a $1,000,000 prize Main Links Orders Post Next Page Next 10 THE ETERNITY PUZZLE Christopher Monckton's Eternity Puzzle (different image, larger image William Waite's Batman...Lorente Philippe's site describes the building blocks, nomenclature, solutions, and numerous games. (French/English)
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Pentomino, Homepage Seite ist nur mit den neueren Netscape-Versionen, die Frames verarbeiten knnen in ihrer vollen Schnheit zu sehen. Fr alle, die keinen Frames-tauglichen Browser haben hier die alte Version. For the new design of this page you need a WWW-Browser which...SOMA puzzle site with graphics, newsletter and software.
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Thorleif's SOMA page This new job as a teacher requires a huge effort in reading the stuff, making homework for the kids, etc. so right now, the SOMA page comes second. BUT du be assured, I keep all the notes and stuff you...English words that can be written using the pentomino name letters FILNPTUVWXYZ and other related curiosities, including a homage to Georges Perec. (English/French).
http://www.iap.fr/users/esposito/pento.html
A paper on their enumeration by Elisa Pergola and Robert A. Sulanke.
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Schröder Triangles, Paths, and Parallelogram Polyominoes This paper considers combinatorial interpretations for two triangular recurrence arrays containing the Schröder numbers, sn 1, 1, 3, 11, 45, 197 and rn 1, 2, 6, 22, 90, 394 for n 0, 1, 2 These interpretations involve the enumeration of...Graphics problems, solutions (including animated GIF) and links. (English/German through main page)
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Pentominos You must arrange the squares, so that they must have in common at least one side. The shapes are similar to capital letters, so they have letters as names. Building Rectangles top The main problem of the pentomino research is...Solves given Pentominoes 3D puzzles. Solution is displayed in 3-D with disassembly and rotations. General information and data. [requires Java]
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Eithan´s Pentominoes-3D Solver Use drag left click to rotate, drag right click to zoom. Back to my HomePage. General Information: I wrote this Java applet after I searched the whole web for a solver to the 3D pentominoes puzzle problem and didn´t find...Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.
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Guenter Albrecht-Buehler, Ph.D. Fellow, European Academy of Sciences, Brussels Fellow, Institute for Advanced Studies, Berlin Robert Laughlin Rea Professor of Cell Biology Northwestern University Medical School, Chicago To enter the site, click here and for future reference, please, bookmark the...Soma-solving program in QBASIC by Courtney McFarren.
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The Soma Cube The puzzle did not become popular in the States until 1969 when Parker Bros. packed and shipped it as the 3-D answer to Tan-Grams Sadly, the disco-erazoic Soma Cube was smothered away into extinction by another puzzle during the pre-rappazoic...Windows software to solve polyiamond and sliding block puzzles.
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Taniguchi's Programs This home page will show you my original programs. Opening 16 May 1997 Revised 3 Dec. 2000 Pan-Iamond Solver Ver 2.1 FreeSoft 1999.07.10 83KB WIN95 Download iamond21.lzh Readme(English) Any polyiamond puzzle can be solved by this program. Sliding Block Puzzle...Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.
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Pentomino Puzzle Game with Geometric Puzzles Elementary school students love to play with pentominoes. Not only do they enjoy fitting the shapes into pre-defined figures, they loved to simply sit and create shapes and pictures of their own. In the elementary classroom, pentominos games are as...From tetris to hexominoes, Cynthia explains them in color.
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Cynthia Lanius Lesson: Polyominoes Introduction Have you ever played dominoes? How about TetrisTM? If you are on a fast connection, you can play TetrisTM here. What do those two games have in common? Well, maybe a lot, but one thing that I thought of is...Fill up a given area using pentomino shapes, rotating and flipping them. Three levels of difficulty.[Java].
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Fwend.com: pentomino Pentomino how to play licensing feedback tell a friend game menu Download the plug-in....Thery families web site with pentomino solver. (English/French)[Java].
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Pentominoes are shapes compound of five square blocks joined by one edge. There are only twelve different shapes, each shape is named regarding a lettre f, I, L, n, p, T, U, V, W, X, Y and Z. b I...A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available.
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Somatic Somatic is a solver for arbitrary polyomino and polycube puzzles, like the soma puzzle. The soma puzzle is made from a set of 7 pieces, each build from 3 or 4 small cubes. With these pieces one can build a...Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.8. Defines and counts horizontal convexity.
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Counting horizontally convex polyominoes We present a new proof that the number, a(n of horizontally convex n-ominoes satisfies the recurrence a(n 5a(n-1)-7a(n-2)+4a(n-3 0. Introduction A finite union of closed unit squares whose vertices have integer coordinates is called a polyomino if its interior is...Harry Smith describes Dr. Dewdney's article in the July 1990 Scientific American's Mathematical Recreations column.
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What is a Golygon from Harry J. Smith Recreations column in the July 1990 issue of Scientific American. Here is what he wrote Allow me to start you on a journey in Golygon City. You can take a similar trip in New York, Kyoto or almost any large...Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.
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PUZZLE FUN Web Page Here is the non-frame based version of the document....Rodolfo Kurchan asks, for each k, what is the smallest polyomino such that k copies can form a blocked pattern. With solutions.
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Blocking Polyominoes I asked which is the smallest polyomino that can block itself using 2 replicas, and then the same for 3,4,5 and N replicas. The only condition is that if we take out 1 piece there could not be part of...Ronald Kyrmse investigates grid polygons in which all side lengths are one or sqrt(2).
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Canonical Polygons The idea which gave birth to the Canonical Polygons (CPs) arose informally while drawing figures on graph paper. Especially interesting to me was a certain class of polygons whose sides followed the grid lines or diagonals. Adopting the restriction that...David Eck's graphical solver applet uses recursive technique. Source code available. [Java]
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Pentominos Puzzle Solver A pentomino consists of five equal-sized squares attached edge-to-edge to form some shape. There are twelve possible pentominos that can be formed in this way (plus their reflections and rotations In this applet, each piece is represented by a different...Eric Laroche presents computer programs for generating polyominoes and polyomino tilings. Includes source codes in C, and binaries.
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sqfig figure construction patterns for figures constructed from squares [polyominoes] Figure construction patterns for figures constructed from squares [polyominoes and tiling construction patterns. This is an exercise in optimizing data access algorithms (patterns domain specific data representations, and code microarchitecture. Optimization results are obvious, considering the calculation efforts needed for...Puzzles using pentominoes and hexominoes. Fuzion, game that designs and (semi-)automatically finds solutions. Links.
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Pentomino Fuzion Puzzles Fuzion puzzles using pentominoes and hexominoes with colorful pentomino shareware game Fuzion that designs puzzles and automatically finds solutions. By Ken Zeltner of ZeezRealm. Your frames don't work! Install a newer browser...T. Sillke asks for dissections of two heptominoes into squares.
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How many pieces are necessary? H This is an old question of Wolfgang Schneider (Kubi-Games, NKC 215 A similar question appeard in: Puzzletopia No 101 (15th Aug. 1995).CONTEST Seven puzzle from Junk Kato. This is the same question as above...Kevin Gong's home page includes articles, programs for Mac, Win and Java.
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The Mathematics of Polyominoes Includes an explanation of what it is that we're actually counting. Applying Parallel Programming to the Polyomino Problem Kevin Gong, 1991. Using parallel programming to enumerate 2-d and 3-d polyominoes. Includes a detailed description of the rooted translation method of...T.Sillke discusses the dissection problem.
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How many ways can a square be dissected into six similar triangles Bob Wainwright Hess comunicated this problem to Nob. Nob publishes it in his puzzletopia 101 Aug. 1995 Nob listed 97 dissections. Only dissections with right angled triangles have...Michael Reid's numerous articles on polyominoes and tilnig, with references and links.
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Michael Reid's polyomino page An odd rectangle tiled by L4m+2 by Philippe Rosselet More planned Links Andrew Clarke's Poly Pages Karl Dahlke's polyomino page Polyominoes at David Eppstein's Geometry Junkyard Peter Esser's polyform page Jorge Luis Mireles Polypolyomino pages George Sicherman's polyform curiosities Tiling...Jorge Luis Mireles Jasso investigates these polygons and dissects various polyominos into them. Animations show cases of infinite solutions.
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Equilateral Pentagons There are an infinite number of distinct E5 since the internal angles can take practically any real value. Next java applet shows some familiar geometric shapes disected into E5s. Where the disection is not unique, an animation shows some possibilities....Expository paper by R. Bhat and A. Fletcher. Covers pre-Golomb discoveries. the triplication problem and other aspects.
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PENTOMINOES Pentominoes are said to have been invented by Solomon W. Golomb in 1953 at a talk he gave to the Harvard Mathematics Club. Although he coined the name, pentominoes have been around since a much earlier time. The first pentomino...Karl Dahlke explains and demonstrates tiling. Includes C-program source.
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A polyomino is a shape that consists of unit squares pasted together. This is an extension of the word domino, two squares placed side by side. But the word poly means meny, hence we may have many squares arranged to...Folded paper polyiamonds which can be unfolded to show hidden faces. Make interesting school projects.
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Magnus Enarsson A flexagon is a polygon folded from paper with a very remarkable quality; you can turn it inside out to make it reveal hidden surfaces. History It all started in 1939 when Arthur H. Stone, a twenty-three-year-old student, was cutting...Centre for Innovation in Mathematics Teaching presents colourful examples of many tiling problems, duplication, triplication, etc.
http://www.ex.ac.uk/cimt/puzzles/pentoes/pentoint.htm
Including copies of the original 1962 Conrad-Hartline papers. Abstract, html-pages, or .pdf documents.
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Flexagons The theory of the flexagon, by Anthony S. Conrad [html pdf (1 MB Return....This Geometry Forum problem of the week asks for the number of different hexominoes, and for how many of them can be folded into a cube.
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Geometry Forum Problems and Lists How many ways can you arrange six squares in the plane so that they all share an edge with at least one other square? Two such arrangements are shown below: _ _ _ _ _ _ _ |_|_|_ _ |_|_|_|_|_...Conrad and Hartline's 1962 article on Flexagons.
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$FILE Next: Contents Contents Contents Introduction: The story of the Flexagon Building and Operating the Flexagon The Covering Space Representation of Flexagon Operation Maps and Plans The Pat Structure New Angles G-Flexagons Construction of a -Flexagon of General Order Proper...Illustrates the 12 shapes. symmetrical combinations.
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Gerard's Pentomino Page The basic set of pentominoes consists of twelve different pieces (excluding the ones that are identical by rotating and flipping To make it easier to talk about the pieces, they are given names, as indicated. These names were first proposed...Harry J. Smith's explains polyominoes with consecutive integer side lengths.
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Golygons from Harry J. Smith This page accessed times since June 7, 1997. Page created by: hjsmithh@sbcglobal.net Changes last made on Friday, 13-May-05 13:43:59 PDT...What they are, and how to find them.
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Golygon From MathWorld A plane path on a set of equally spaced lattice points, starting at the origin, where the first step is one unit to the north or south, the second step is two units to the east or west, the third...About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes. (Companion sites available in French/German/Italian, look up the respective languages under TOP:WORLD:...)
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The Poly Pages ...Christian Eggermont's link page.
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Links Polyforms and dissection Puzzle consists of at least three rods intersecting each other at right angles. This site lets you explore the six piece burrs. Immensly interesting Sidney Some puzzles he solved including the Bedlam Cube. Includes programs and source. Cube puzzles Soma.... Ed Pegg Jr.'s site has pages on tiling, packing, and related problems involving polyominos, polyiamonds, polyspheres, and related shapes.
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polyom Zucca is now selling the sexehexes at his site. He has a contest on his page on polyforms. William Waite has many interesting polyform puzzles he cuts from wood, in particular the Interlace Circle and Mixed Angle puzzles. Mira Vicher...Jorge Luis Mireles explains finite and infinite spirals made up of polyforms.
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10 The easiest way to define what a polyform spiral is, is with next figure. Here we have geometric art with simple rules. Use two distinct geometric forms and tile the plane totally forming two spirals with each form. Apply colors...Colonel Sicherman asks what fraction of the triangles need to be removed from a regular triangular tiling of the plane, in order to make sure that the remaining triangles contain no copy of a given polyiamond.
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Polyiamond Exclusion Golomb investigated the question: how few cells can you remove from the plane to exclude the shape of a given polyomino? Here I investigate the related question: how few cells can you remove from the plane to exclude the shape...Mathforum. This Geometry problem of the week asks whether a six-point star can be dissected to form eight distinct hexiamonds.
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Geometry Forum Problems and Lists Bernice were riding the bus home after school when Boutros pulled out a piece of paper Check out this puzzle our teacher gave us today he said It's from some book by a guy named Martin Gardner. It seems sort...Peter Turney lists the 261 polycubes that can be folded in four dimensions to form the surface of a hypercube, and provides animations of the unfolding process.
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Unfolding the Tesseract How many ways can a tesseract be unfolded? A tesseract is a four-dimensional hypercube. See a movie of the folding of an unfolded tesseract: MPEG Movie (520KB) QuickTime Movie (504KB) Animated GIF (789KB) The above movies are from a presentation...Java applet demonstres that this tetromino-packing game is a forced win for the side dealing the tetrominoes. Complete with mathematical proof. [Java]
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Java Gallery: Tetris Tetris game that has been modified to play the same pieces over and over. This game must end (in a loss) before 70,000 pieces have been played. The current high score is 400. How many pieces can you place? This...Joseph Myers and John Berglund found a polyhex that must be placed in two different ways in a tiling of a plane, such that one placement occurs twice as often as the other.
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An Unbalanced Tile A tile that is unbalanced with different sized transitivity classes There are many tiles that are 2-anisohedral. The two transitivity classes required for these tiles will usually be the same size OK, OK, that's not precise. Look at ratios of...Anna Gardberg makes pentominoes out of sculpey and agate.
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Anna's Pentomino Page I discovered pentominoes in Arthur C. Clarke's book Imperial Earth. The GIF that you see above is one of the more than 2000 ways to fit the set of twelve pentominoes into a 6 by 10 rectangle. One can also...George Huttlin explains and illustrates these shapes composed of 6 equilateral triangles, which in turn tiles different forms.
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Hexiamonds Hexiamonds are puzzle pieces similar in concept to pentominoes but they are not based on the standard checkerboard. Instead, hexiamonds are based on a pattern of equilateral triangles as seen in Chinese checkers. Each hexiamond is formed by joining six...George Huttlin shares some ramblings in the world of polyominoes.
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George Huttlin's Pentomino Webpage Each of the letters above is formed from the puzzle pieces known as pentominoes. A pentomino is the shape of five connected checkerboard squares. There are only twelve different pentomino shapes. Since each of these shapes covers an area of...Livio Zucca tiles polygons of equal perimeter, or isoperiploes.
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PolyEdges I was child the square was the polygon with four equal edges. I define a series of polygons by their edges, on a squared grid. For example below there are the 5 possible polygons with perimeter 2+2SQR(5 Here there are...Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves.
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Knight Tour Tessellations By putting each pattern on a separate chess board, closing the open pattern to make a geometric shape, and filling in the pattern with the same color as the line path's color, there now exists four pieces that can be...Kevin Gong offers download of his polyominoes games shareware for Windows and Mac. 100 boards are included. A Java version is in the works.
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Welcome to Polyominoes Polyominoes is a challenging game and puzzle. Included are 100 different boards to choose from. You can play the polyomino game against the computer, or use a board as a solitaire jigsaw puzzle. Polyominoes 7.0 is available now for Mac...Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors.
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Pentominoes LEGO Besides my fascination with LEGO bricks, I have many other hobbies and interests. One such pasttime has been crafting puzzles, games, and brainteasers of various sorts. Often I craft the necessary pieces out of wood, but other times I make...Open source polyomino and polyform placement solitaire game.
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freshmeat.net: Project details for Polygon Puzzle Search for in projects articles comments web results by YAHOO! search Section Main Unix Handhelds Mac OS X Themes login register recover password [Project] add release add branch add screenshot broken links change owner email subscribers update project update branch...R & A Media presents its puzzles including a chessboard cut into twelve interlocking polyominos.
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MindBlock wooden cube and checkerboard puzzle Plex puzzle is a put together puzzle that makes an 8x8 chessboard, a 4x4x4 cube and over 50 other shapes.This puzzle's simplicity belies its innate complexity!Complete details are listed on the next few pages including the puzzle's history, versions produced,...Rujith de Silva's applet puzzle offers games of four different sized rectangles. [Java]
http://www-2.cs.cmu.edu/~desilva/pento/pento.html
Wil Laan's applet searches for solution of packing hexominoes into more than 45 different shapes.[Java]
http://home.quicknet.nl/mw/prive/wil.laan/puzzle/cornucopia.html
Bezdek, Brass, and Harborth. Abstract to an article which places bounds on the convex area needed to contain a polyomino. (Contributions to Algebra and Geometry Volume 35 (1994), No. 1, 37-43.)
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In this note we prove the following two isoperimetric-type theorems. The $d$-dimensional volume of the convex hull of any connected system of finitely many segments in bbf R}^d$ with total length 1 which are parallel to the standard co-ordinate axes...Tiling a square without cutting it into two.(Problem of the week 826, Spring 1997)
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Math Forum: MacPOW 826: A Minimal Domino Tiling N such that you can tile the board without it being possible to draw a line parallel to any side of the board that does not slice any domino into two? Source: This problem was found by John Guilford on...Joe Fields suggests that L-decomposition of squares of Pythagorean triplets could always be tiled.
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A Puzzle I call the following visual proof that the sum of the first n consecutive odd numbers is n2, the L decomposition. Suppose we have two L decompositions, can the pieces of these two decompositions be reassembled into a single larger...Mehta & Ward Alberg explains the soma cube and provides an applet for practice. Source codes included. [Java]
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Soma Applet Problems worthy of attack prove their worth by hitting back The Soma puzzle was a game marketed by Parker Brothers, Co. around 1970 that was based, in turn, upon an idea attributed to the mathematician Piet Hein. Its basis is...Bob Newman examines the history of the subject and presents his minimal solutions.
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Tessellations What is the smallest polyomino that tessellates and locks? The published solution was this, in which the polyomino has 25 squares. It didn't look very minimal to me. I soon found one with 18 squares. There's an easy simplification of...L. Alonso and R. Cert's abstract of a paper published in vol. 3 of the Elect. J. Combinatorics. Full paper available in different formats (.pdf, postscript, tex etc).
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R27 of Volume 3 (27) The Electronic Journal of Combinatorics Abstract for R27 of Volume 3(1 1996 Download the full paper: PDF version PostScript version gz) dvi version tex version Next abstract Table of Contents for Volume 3 (1) Up to the E-JC/WCE home page...Alexandre Owen Muñiz presents the Icehouse set which lends itself to different polyomino coloring games.
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Some Nice Pentomino Coloring Problems The first tiling problem using the 12 pentominoes was designed by Henry Dudeney and published in 1907, and in the years since much has been done to expand the realm of polyform puzzles, by finding new shapes to tile and...Stan Wagon asks which rectangles can be tiled with an ell-tromino.
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Math Forum: MacPOW 856: A Tiling from Ell This problem is live and if you solve it you can submit your solution to the AMM. Thus I will not post a solution, give hints, or comment on submissions (and request the same for any of you who solve...B. Berchtold's applet helps tile a 6x10 rectangle. [German]
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Pentominos Browser versteht zwar das APPLET tag, startet aber das applet aus irgendwelchen Gründen nicht Ihr Browser ignoriert leider das APPLET tag! Klick auf Step lässt den Computer das Puzzle schrittweise lösen. Klick auf Go lässt den Computer das Puzzle lösen....Matthew Blum demonstrates the properties of random domino tiling of an Aztec diamond. Interactive graphics display.
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Tiling UROP Homepage Why we are so interested in random tilings of Aztec diamonds Papers relevant to our research project Other papers with more theoretical results Documentation to our software Links related to mathematics Our scrapbook of pictures Random tilings in motion This...Jay Jenicek's page hosted by Puzzlecraft. Includes software for a game described on the page (2-3 players).
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The Pentominoes Page Jay is no longer hosting it but it was so nicely done we decided to re-host it in its entirety. Puzzlecraft April 14, 2003. Pentominoes are shapes that use five square blocks joined edge to edge to form various combinations....Alon, Bóna, and Spencer show that one can't cover very much of an n by p(n) rectangle with staircase polyominoes (where p(n) is the number of these shapes).
http://arxiv.org/PS_cache/math/pdf/9812/9812075.pdf
Rujith de Silva's applet puzzle offers games of four different sized rectangles. [Java]
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Pentominoes Pentominoes is a jigsaw puzzle involving twelve rectilinear pieces. These pieces constitute all the ways in which five squares may be arranged with their edges matching. Their total area is 5 x 12 60 squares. The challenge is to fit...Mark Michell investigates packing pentominoes into rectangles of various non-integer aspect ratios in order to obtain the largest possible pieces using straight cuts.
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Mark's Packing Pentominoes page Karmel kibbutz in central Israel. I enjoy recreational mathematics but, as you might imagine, it was not everyone’s favourite pastime, so I had to literally make my own amusements. I had a Martin Gardner book on Mathematical Games, in which...Don Knuth discusses implementation details of polyomino search algorithms.
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9dancing-color.ps ms q«&TU m Hà¶bîU L j’e b¦c Y.f k WoÖw o³ðO m _ V O»ÕWw g v VE 8 _2 UÓvj w Z k»O wï_ûw 1ÒˆVo 7çw7w÷o qwoC Ou n X½ÿxcG®y C76Y n>>t V z w¸OlÙþr~w hÇp n ní1 KC 1 Åw.... Joseph Myers classifies the n-ominoes up to n=15 according to how symmetrically they can tile the plane.
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Polyomino, polyhex and polyiamond tiling Some authors require also that a polyomino be simply connected, i.e. that it have no enclosed holes, but that is not the definition used here See below for a very limited selection of references to the literature on polyominoes. Polyominoes...From Scott Kim's Inversions Gallery.
http://www.scottkim.com/inversions/gallery/golomb.html