About site: Math/Recreations/Polyominoes - Arnab's Pentominos Puzzle
Return to Science also Science
  About site: http://www.geocities.com/hirak_99/goodies/pento.html

Title: Math/Recreations/Polyominoes - Arnab's Pentominos Puzzle Fast Pentominos puzzle solver, works on DOS/Windows platform. Free downloads.
Blocking_Polyominos Rodolfo Kurchan searchss the smallest polyomino such that a particular number of copies can form a blocked pattern. With solutions.

Canonical_Polygons Ronald Kyrmse investigates grid polygons in which all side lengths are one or sqrt(2).

Christopher_Monckton\'s_Eternity_Puzzle 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.

Counting_Horizontally_Convex_Polyominoes Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.8. Defines and counts horizontal convexity.

Cynthia_Lanius\'_Lesson__Polyominoes_Introduction From tetris to hexominoes, Cynthia explains them in color.

Dancing_Links Don Knuth discusses implementation details of polyomino search algorithms (compressed PostScript format).


  Alexa statistic for http://www.geocities.com/hirak_99/goodies/pento.html





Get your Google PageRank






Please visit: http://www.geocities.com/hirak_99/goodies/pento.html


  Related sites for http://www.geocities.com/hirak_99/goodies/pento.html
    A_Dissection_Puzzle T. Sillke asks for dissections of two heptominoes into squares.
    Equilateral_Pentagons Jorge Luis Mireles Jasso investigates these polygons and dissects various polyominos into them. Animations show cases of infinite solutions.
    Eternity_Page Alex Selby's page with a description of his solution method, with illustrations in .png and .pdf files.
    Flexagons Conrad and Hartline's 1962 article on Flexagons.
    Flexagons Folded paper polyiamonds which can be unfolded to show hidden faces. Make interesting school projects.
    Gamepuzzles Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc.
    The_Geometry_Junkyard__Polyominoes Numerous links, sorted alphabetically.
    George_Huttlin\'s_Puzzle_Page George Huttlin shares some ramblings in the world of polyominoes.
    Gerard\'s_Pentomino_Page Illustrates the 12 shapes. symmetrical combinations.
    Golygons Harry J. Smith's explains polyominoes with consecutive integer side lengths.
    Golygons_by_Mathworld What they are, and how to find them.
    Harold_McIntosh\'s_Flexagon_Papers Including copies of the original 1962 Conrad-Hartline papers. Abstract, html-pages, or .pdf documents.
    Henri_Picciotto\'s_Geometric_Puzzles_in_the_Classroom Polyform puzzle lessons for math educators to use with their students, including polyominoes, supertangrams, and polyarcs.
    Hepto Some packings of the 108 heptominoes (with unit thickness) into various blocks.
    Hexiamonds George Huttlin explains and illustrates these shapes composed of 6 equilateral triangles, which in turn tiles different forms.
    Hyperbolic_Planar_Tessellations Don Hatch's page on hyperbolic tesselations with numerous illustrations.
    Information_on_Pentomino_Puzzles At the Combinatorial Object Server.
    Isoperimetric_Polygons Livio Zucca tiles polygons of equal perimeter, or isoperiploes.
    Java_pentominoes Thery families web site with pentomino solver. (English/French)[Java].
    Knight\'s_Move_Tessellations Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves.
    Lego_Pentominos Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors.
    Livio_Zucca\'s_polyomino-covered_cube Colorful illustrations demonstrate how closed surfaces could be covered by polyominoes.
    Logical_Art_and_the_Art_of_Logic Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.
    The_Mathematics_of_Polyominoes Kevin Gong offers download of his polyominoes games shareware for Windows and Mac. 100 boards are included. A Java version is under development.
    Mathforum___a_Pentomino_Problem Geometry Forum: Lists the pentominoes; fold them to form a cube; play a pentomino game. (project of the month, 1995)
    Mathforum___Minimal_Domino_Tiling Tiling a square without cutting it into two.(Problem of the week 826, Spring 1997)
    Mathforum___Tiling_Rectangles_from_Ell Stan Wagon asks which rectangles can be tiled with an ell-tromino.
    Maximum_Convex_Hulls_of_Connected_Systems_of_Segments_and_of_Polyominoes 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.)
    Miroslav_Vicher\'s_Puzzles_Pages Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
    My_Polyomino_Page Michael Reid's numerous articles on polyominoes and tilnig, with references and links.
    Packing_Ferrers_Shapes 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).
    Packing_Polyominoes Mark Michell investigates packing pentominoes into rectangles of various non-integer aspect ratios in order to obtain the largest possible pieces using straight cuts.
    Packing_Shapes Erich Friedman's Introduction to a variety of packing and tiling problems.
    Pairwise_Touching_Hypercubes Erich Friedman's problem of the month asks how to partition the unit cubes of an a*b*c-unit rectangular box into as many connected polycubes as possible with a shared face between every pair of polycu
    Pentamini_Pentaminos_Pentominoes A container of mathematical games, gadgets and software. (English/Italian)
    Pento Amamas Software offers a pentomino solving software.
    Pento-Mania Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.
    Pentomino_Applet Rujith de Silva's applet puzzle offers games of four different sized rectangles. Source code available. [Java]
    Pentomino_Applet Fill up a given area using pentomino shapes, rotating and flipping them. Three levels of difficulty.[Java].
    Pentomino_Covers Problems on minimal covers.
This is sites2007.com cache of m/ as retrieved on 2009.01.08 sites2007.com's cache is the snapshot that we took of the page as we crawled the web. The page may have changed since that time.
var PUpage="76001067"; var PUprop="geocities"; var thGetOv="http://themis.geocities.yahoo.com/themis/h.php"; var thCanURL="http://us.geocities.com/hirak_99/goodies/pento.html"; var thSpaceId="76001067"; var thIP="68.178.254.29"; var thTs="1231438289"; var thCs="a86f2f3e99c1cb553c4864fff505677c"; Pentominoes

Pentominoes

Pentominoes ScreenshotClick 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 Dominoes, Triominoes, Terominoes, Pentominoes, etc. There are many interesting problems on Polynominoes. For example, one problem is to find out how many different Polynominoes exist of a specific type (Eg. How many Hexominoes are there?). The PentominoesThe 12 PentominoesThe Polynominoes make interesting objects to study for mathematicians. That's why there are numerous websites devoted on them - for example click here for a site with very good introduction to Polynominoes.

The Puzzle

The problem that we are interested in deals with Pentominoes (i.e. Polynominoes with 5 squares). It is known that ignoring all rotations and reflections, there are 12 Pentominoes in total. According to their look, they can be coded as C, F, I, L, N, P, T, V, W, X, Y, and Z (also this is the order they are shown in the program). Total 12 pieces each of area 5 squares each can cover up an area of 60 squares together. The puzzle is now to cover up any rectangle with area 60 (and sides measuring not less than 3 in length) using all these 12 different Pentominoes. To accomplish this you are allowed to rotate and/or reflect the pieces in any way you want. The program gives you the ability to experiment and solve the puzzle all by yourself. However, you will never end up solving the puzzle manually, since the enormous temptation of hitting Return and letting the program solving the puzzle is absolutely irresistable. Instead, perhaps, what you can actually try is to write your own program to solve it.

Number of Solutions

Although after experimenting manually for a while the game puts the existence of solutions into question (if you do still manage to keep yourself from hitting Return), the following numbers might prove otherwise. Grid size Number of solutions 6 x 10 2339 5 x 12 1010 4 x 15 368 3 x 20 2 to Goodies geovisit();setstats 1
 

Fast

Pentominos

puzzle

solver,

works

on

DOS/Windows

platform.

Free

downloads.

http://www.geocities.com/hirak_99/goodies/pento.html

Arnab's Pentominos Puzzle 2009 January

dvd rental

dvd


Fast Pentominos puzzle solver, works on DOS/Windows platform. Free downloads.

Rules




© 2005 Internet Explorer 5+ or Netscape 6+

Recommended Sites: 1. Arts - Business - Computers - Games - Health - Home - Kids and Teens - News - Recreation - Reference - Regional - Science - Shopping - Society - Sports - World Miss Gallery - Top Anime Hentai - DVD rental by mail - Calendrier 2007 - Credit Cards - Encyclopaedia - Mobile Phone - Bankruptcy
2009-01-08 11:11:30

Copyright 2005, 2006 by Webmaster
Websites is cool :)