What you will find here are computer versions of mathematical puzzles such as Rubic's cube, peg solitaire, tangram, 15-tile-puzzle ... etc. Puzzles whoes solution solely rely on logical analysis. If you like mathematical puzzles, you may find this book interesting Puzzles Old and New: How to make and solve them by Jerry Slocum and Jack Boterman. (amazon.com↗) The book includes photographs of many many puzzles. It gives you a panorama of all types of physical puzzles.
My favorite type of physical puzzles are the Rubik-type puzzles called Magic Polyhedrons. These puzzles screams: “group theory” and “combinatorics”!
mefferts.com↗ sells many magic polyhedrons. I bought a some 7 varieties from that store in 2001.
For a detailed account of Rubic's Cube and magic polyhedrons, see: Rubik's Cube↗, Magic Polyhedra↗.
This one is single-plane in 3 orthogonal direction onto the cube, face on. The simplest of the parallel-plane scheme.
This is a 5x5x5 magic polyhedron. It employes 4 parallel-plane cuts in 3 orthogonal directions onto a cube, in a direction that the cutting planes are parallel to the cube's faces.
Here are other orthogonal-parallel-plane cut varieties. They are isomorphic to each other puzzle-play-wise.
A magic polyhedron type of puzzle is essentially defined by the cuts and the solid it cuts into. The cuts defines the mathematical essence of the puzzle, while the solid shape gives the puzzle a flavor. Same cuts can be applied to different solids, yet still resulting the same puzzle mathematically. For example, a tic-tac-toe cut applied to a cube results the Rubic's Cube, and appling it to a sphere results a Rubic Ball. The same tic-tac-toe cut can be applied to octahedron for example.
There are abundant literatures on Rubik cube. Two books I've read are Handbook of Cubik Math↗ by D. Singmaster, A. H. J. Frey. And Rubik's Cubic Compendium↗ by E. Rubik et. al. I liked the first one better. Both are fairly popular.
★ Magic Polyhedron. David Byrden has wrote Java applets to play some 30 varieties magic polyherons! Super cool! http://byrden.com/puzzles/MainFrames.html Java
Puzzler (screenshot) is a Windows program by Noel Dilabough. Puzzler plays all types of magic polyhedrons. Puzzler plays some 20 non-trivial variations of magic polyhedrons, including the five platonic solids with different cuts. The program is great, unique, but the interface is very bad. Extremely frustrating to use. Puzzler is a shareware. http://www.mud.ca/puzzler/puzzler.html.(2003-07, 2006-09) Win
MagicCube4D by Don Hatch and Melinda Green. It plays 4-dimentional Magic Cube. It also maintains record of the world's first solvers and a solution database. The source code is also available. http://www.superliminal.com/cube/cube.htm. (2006-09) Win Linux Java
4DRubikCube by Ishihama Yoshiaki is a 2x2x2x2 magic cube simulator. http://www.asahi-net.or.jp/%7Ehq8y-ishm/hyper.html Mac Win Java
 Polyominoes by Kevin L Gong |
★ Polyominoes (2000 screenshot) is a polyominoes fitting game. Written by Kevin L Gong. In this program, you try to fit a set of polyominoes (connected squares) into a given shape. In another mode, two players take turns fitting polyominoes into a give shape. The first without a fitting piece losses. It's almost impossible to beat the computer. Mac, Windows and Java. polyominoes.com↗. Kevin's got a very informative and enjoyable home page http://kevingong.com/Personal/index.html (2003-09,2006-07) OSX Mac Java Win
Pentominos Puzzle Solver A pentominos solver, by David Eck. http://godel.hws.edu/java/pent1.html (2006-07) Java
For excellent introduction to polyominoes, see Martin Gardner's Hexaflexagons and Other Mathematical Diversions, Chapter 13. and Time Travel and other Mathematical Bewilderments. Chapter 14. (1988). If you are serious about this subject, there are classic math oriented texts: Polyominoes : Puzzles, Patterns, Problems and Packings by Solomon W. Golomb. (2nd ed., 1996)
There are lots of sites on polyforms. (polyform is the generic name for any shapes thare are formed by arranging similar shapes.) You may start browsing at these sites: http://alpha.ujep.cz/~vicher/puzzle/index.html; http://www.geocities.com/alclarke0/index.htm; A site in Chinese by Wen-Shan Kao: http://home.educities.edu.tw/proteon/index.html
For detailed info about tangram, see: Tangram↗
★ Tangram (4.1, 1999/07. v. 3.2 screenshot) Tangram is a popular tiling puzzle that's probably originated from China. The goal is to arrange a set of seven tiles to match a given shape. This software's interface is beautiful and well-designed. Author is S. T. Han (sth@kagi.com). Available for both Mac and Windows. URL: http://members.aol.com/sth777/defaul.html. (1999/11) Mac Win
Here is a Java version of Tangram http://www.diff.nl/internet/demos/tangram.php Java
A arresting introduction to tangrams can be found in Time Travel and other Mathematical Bewilderments↗ by Martin Gardner. (1988) It includes a short bibliography.
For detailed info about this game, see http://en.wikipedia.org/wiki/Peg_solitaire
S T Han's Poly-Peg and Cary Torkelson's Pegged, and a anonymous program. Jump and remove the piece jumped over. |
★ Poly-Peg 1.09 (screenshot) by S. T. Han. This puzzle is sometimes known as peg solitaire. You remove pieces on a board by "jumping" other pieces over it. The goal is to leave only one piece on the board. PolyPeg lets you edit your own shape of square or hexagonal board and set whether diagonal jump are allowed in square board. It also include a auto solve feature. Latest versions for Mac and Windows can be found in S.T.Han's web site at http://members.aol.com/sth777/defaul.html.Mac
Win
Pegged is a small mac program that plays Peg Solitare. It offers the traditional cross shaped board, but with 7 arrangement of end games. Written by Cary Torkelson in 1991, but still works great under Mac OS X Classic 2003. Local download: pegged.sit.hqx Here's a small anonymous program that plays peg solitare. It has a board different from pegged. pegSolitaire.sit.hqx Mac
For a complete mathematical analysis of Peg-Solitare, see The Ins and Outs of Peg solitaire by J. D. Beasley (1985)
★ Poly-Off 1.09 (screenshot) is another excellent shareware by S. T. Han. The game Poly-Off can be thought of as one type of cellular automata. In a square or hexagonal grid, you switch on or off a cell that will affect neighbor cells. The goal is to switch off all cells. I had lots of fun with this program. For Mac OS and Windows. URL: http://members.aol.com/sth777/defaul.html
Mac
Win
★ Poly-Dol v.1.01 (screenshot) by S. T. Han. The puzzle in this program is similar to a commercial program named Cogito. You shift pieces on a board until all the pieces are in certain order. You can only shift pieces in certain row, column, or array of the board. There are dozen boards to choose for play and you can make your own board shapes. I find this program to be much fun. For Mac and Windows. URL: http://members.aol.com/sth777/defaul.html
Mac
Win
★ Poly-Tile v.1.04 (screenshot) by S. T. Han. This puzzel is similar to a commercial program named Tesserae, published by In-Line designs Inc.
In this puzzle, Tiles of different design are layed over a board. You remove them one at a time by jumping (flipping) adjacent tiles of the same design. The goal is to leave only one tile on the board. I find this game too difficult. It's also hard to analyze because the random initial placement and designs. Like Poly-Peg and Poly-Dol, you can customize your board when you got bored with the given configurations. For Mac and Windows. URL: http://members.aol.com/sth777/defaul.html
Mac
Win
Sokoban (倉庫番=warehouse keeper) is a classic game invented by Hiroyuki Imabayashi in 1982. It is a puzzle where the player pushes boxes around a maze to designated locations. For more info, see: Sokoban↗
Here's a Sokoban game in Javascript: http://michbuze.club.fr/Boxworld/sokojs.htm.
★ MYHOUSE is a clever and fun logic puzzle in Flash software writen by M Aono. It is a variation of the classic Sokoban. Your goal is to move a bunch of shrimps home. The shrimps move in sync. When one bump into wall, it doesn't move but the rest moves. The red blocks are fire and if one shrimps runs into it you die. Your goal is to align all shrimps in such way to move them home. One flaw with this application is that it is too sensitive to keyboard input or mouse click on arrows. Often a tab results 2 or more moves thus bumping into the fire block and one has to start all over. This is frustrating. http://www.i-dac.com/game/myhouse/myhouse.html (2003-09,2006-09-01) Flash
above: The classic Parchessi or 15-puzzle of Sam Loyd. This screenshot is from a little program (a Desktop Accessory) from Apple Macintosh way back from 1988, but still runs fine under 2003 Mac OS X Classic. (pull menu Edit:Clear will switch the Apple logo to numbers.). Mac. 15Puzzle.sit.hqx
For more about 15-puzzle, see Wikipedia: 15-puzzle↗
above: Three tile-sliding puzzles. From left to right: 10-tile puzzle, Loyd's Lunacy, Dirty Dozen. |
The classic 10-tile puzzle. Your goal is to slide the red block all the way to the right side center. Yes, it can be done. This puzzle is dicussed in Scientific American, March 1995 (Volume 272 Number 3 Pages 108-110), Mathematical Recreations by Ian Steward. A beautiful wooden set of this puzzle has been marketed by various companies.). This screenshot shows a Mac program but i forgot its name or who wrote it.
Loyd's Lunacy is another block-sliding logic puzzle. The goal is to slide the large square from upper right corner to upper left. Author is Chip Moody. Written in 1990 but still works great under Mac OS X Classic in 2003. This program has a very funny “About” dialogue. loydsLunacy.sit.hqx Mac
Dirty Dozen is a block-sliding logic puzzle. Writen by Nick Triantos in 1993 but still works under Mac OS X Classic in 2003.dirtyDozen.sit.hqx Mac
 MineSweeper3D by Robert Webb |
★ MineSweeper3D by Robert Webb. It is similar to the puzzle Minesweeper that comes with Windows, but MineSweeper3D lets you play it on 3D solids. Very well done. Get it here: http://www.software3d.com/Mines3D/ (2003-09,2006-09-01) Win
Last Updated: 2005-10. © 1995-2005 by Xah Lee.
