Game: Pancakes Based on the 'Pancake Sorting Problem' published on Edd Pegg's Math Puzzles web pages in January 2002. Implemented by Karl Scherer, July 2002 Object: Sort the Pancakes by size. Click the board to get a stack of Pancakes of mutually different sizes. Click a Pancake to flip upside down the stack on top of and including the clicked Pancake. You win when the Pancakes are sorted by size, the smallest at the top. Try to use as few moves as possible. The game 'Pancakes' is somewhat related to the game 'Towers of Hanoi'. More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz. Updated 03/15/03 improved graphics (by Keith Carter) and sounds Download Pancakes Now!
Game: Pearl Puzzle Invented and implemented by Karl Scherer, January 2001 Object: Separate the colours. (6 variants) First click anywhere on the board to create a random setup. Twelve Pearls will appear, 3 blue ones, 3 red, 3 green, 3 yellow. Click the board on various places. You will find that this triggers random movement of the Pearls only in certain areas and into certain directions (!). For example, tapping the far left of the box triggers random movements (in a certain area) towards the top, right or bottom, but never to the left. Use this selective shaking to separate the colours, so that the three green Pearls are in one compartment, the three red ones are in another compartment and so on. In variant 2 the movements are a bit more random. Variants 3, 4, 5 and 6 use more Pearls. As additional challenges you may try to move all Pearls into one compartment. These are not separate variants in this game because of technical limitations. This game simulates the real 'Pearl Puzzle' game of 12 coloured pearls in a closed plastic container with four compartments which I invented in 1999 and have for sale on my web page. For more freeware as well as real puzzles and games see my home page http://karl.kiwi.gen.nz. Updated 03/10/01 Win-message bug fixed. Download Pearl Puzzle Now!
Game: Pearl Puzzle II Invented and implemented by Karl Scherer, April 2001 Object: Separate the colours. (6 variants) First click anywhere on the board to create a random setup. Twelve Pearls will appear, 3 blue ones, 3 red, 3 green, 3 yellow. Click the board on various places. You will find that this triggers random movement of the Pearls only in certain areas and into certain directions (!). For example, tapping the far left of the box triggers random movements (in a certain area) towards the top, right or bottom, but never to the left. Use this selective shaking to separate the colours, so that the three green Pearls are in one compartment, the three red ones are in another compartment and so on. In variant 2 the movements are a bit more random. Variants 3, 4, 5 and 6 use more Pearls. As additional challenges you may try to move all Pearls into one compartment. These are not separate variants in this game because of technical limitations. This game simulates the real 'Pearl Puzzle II' game of 12 coloured pearls in a closed plastic container with four compartments which I invented in 1999 and have for sale on my web page. For more freeware as well as real puzzles and games see my home page http://karl.kiwi.gen.nz. Updated 04/15/01 Corrected board image. Download Pearl Puzzle II Now!
Game: Pento Implemented by Karl Scherer, November 2000. Object: Tile the given shapes with the 12 Pentominoes tiles. (25 variants) The twelve Pentomino tiles consist of all polysquares with 5 squares. These can be used to exactly cover the given fill-in area. See the description in the downloaded package for instructions on how to handle the tiles. One of the game variants allows you to play freely with the Pentominoes. Here you have an unlimited number of each tile available. Note that you can also redesign the fill-in area in all variants in order to create your own tiling problems. You can even create two separate areas side by side (also see variant 6). Much material has been published on polysquares. See for example: the book 'Polyominoes' by Solomon Golomb 1994 the book 'A Puzzling Journey to the Reptiles and Related Animals' by Karl Scherer 1987, privately published many articles in the Journal of Recreational Mathematics etc Background image: Fractal ZTAQ112W by Karl Scherer More related freeware, art, books, real puzzles and games see my home page http://karl.kiwi.gen.nz. Updated 12/14/02 minor code improvement Download Pento Now!
Game: Pento-Solver Implemented by Karl Scherer, December 2001 Automatically fill any user-defined playing area with any combination of the 12 Pentominoes. (22 variants with customizable playing area) For each pentomino type, you can determine whether the computer should use no tile, one tile or many (unlimited) tiles. Just click '0', '1' or 'M' for any of the twelve types displayed at the top. Given a shape and a set of tiles to fill it with, it is in general not known whether such a tiling problem has a solution. (For example, which pentominoes or pairs of pentominoes tile the doughnut shape given in the default variant?) Pento-Solver allows you to try any combination of pentominoes for any given shape, and there are many discoveries still waiting to be made! You can give the computer any shape made from squares. Select 'T0' with the right mouse button to add a square to the board. Finally, click one of the two text bars to let the computer tile the given playing area automatically. The left button saying 'Fixed Colours' means that each pentomino type has its own, fixed colour. The right button saying 'Sequential Colours' means that the colour will change with each tile placed, the colours being from a series of 16 colours. This is especially useful when you use only very few types of tiles. NOTE: YOU CAN SPEED UP PENTO-SOLVER THREEFOLD by switching off the sound (menu option VIEW/OPTIONS/SOUND). Please note that there are six alternative piece sets available, producing three types of coloured tiles and two types of Blanks. Version 1.3: 50% faster, 30% less moves necessary per solution. Sources for pentomino-related problems: - Solomon Golomb's book 'Polyominoes'. - Michael Reid's Web pages - Torsten Sillke's Web pages - Many articles in the 'Journal of Recreational Mathematics' and many others. The following Zillions games also deal with polysquare tilings: Backtrack, Reptiles, Reptiles II, Pento, Ypento, MAX-Solver, G-Backtrack, G-Primes, P-Backtrack, P-Primes, Y-Backtrack, Y-Primes. 'Pentomino' and 'polyomino' is a trademark by Solomon Golomb. More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz. Updated 01/05/02 code improvements Download Pento-Solver Now!
Game: Picador Created by W. D. Troyka, March 2001. Picador is an illustration of a famous logical paradox. The paradox can be described as follows: You are a contestant on a game show. You are asked to select one of three doors. There is a fruitcake behind one of the doors. You really want the fruitcake. You select door no. 2. The host now turns to you and says: "I know where that fruitcake is and I can tell you it's not behind door no. 1." He opens door no. 1 to reveal nothing behind it. "But," he continues, "I'm going to give you the opportunity to change your pick to door no. 3." The question is, should you change your pick to door no. 3? There is a right answer to this question and a wrong answer. If you make the right choice, your odds of finding the fruitcake are two in three. If you make the wrong choice, your odds are one in three. Many people find this result baffling. There are two doors remaining, so the odds must be fifty-fifty that the fruitcake is behind each. But this reasoning is flawed. Picador gives you an opportunity to figure out the correct answer through experiment. You play the game by first selecting the door you think the fruitcake is behind. Zillions will then automatically open one of the other doors, which will always be a door with no fruitcake behind it. You can then keep your original choice or change your pick to the other unopened door. If you find the fruitcake, you score a hit. If you do not, you score a miss. Zillions will tally your hits and misses as you repeat the experiment. The object of the game is to achieve twenty hits before you suffer fifteen misses. If you follow the correct logic, you should normally accomplish this. If you follow the wrong logic, or choose randomly, you will normally lose. A brief history of this paradox is provided in the "History" section that comes with the game. An explanation of the riddle (including the answer) is provided in the "Strategy" section. Download Picador Now!
Game: Planes Invented and implemented by Karl Scherer, July 2001 Object: Avoid any collision of planes. (3 randomized variants) You are an air traffic controller at Frankfurt Airport. First click the board several times. Each time you click, a new plane will appear at the border and start to fly across the screen. Clicking an empty square allows all planes to move one step into the direction they are pointing to. Click a plane to steer it ninety degrees to the right. Watch out for the moment you need it! The goal is to avoid collision at all times. Two planes will collide when they end up in exactly the same place on the screen. Hence two planes on adjacent squares will not collide! Two counters on the right border count your moves and your collisions. I am pretty sure that after playing this game you will appreciate the stressful work even more which these air traffic controllers have to do... Variant 2: Horizontally and vertically flying stealth planes. They are black and twice as fast. Variant 3: Stealth planes flying into all directions. Invented and implemented by Karl Scherer 13 July 2001, exactly one day before a long flight from New Zealand to Germany. Graphics & sounds: Imagine It! clickart collection. More freeware as well as real puzzles and games at http://karl.kiwi.gen.nz. Updated 08/04/01 2 variants added. Download Planes Now!
Game: Plinko Implemented by Ken Franklin, December 2002. Description: Based on the well known Plinko game commonly seen as part of CBS's Price is Right gameshow (30 years - USA). Object: Drop the plinko chips at the top of the board. The chips fall diagonally (as they hit the posts) until they reach the bottom prize/noprize zones. The Goal is to earn > $X,000 in X attempts. Alternate Plinko: Coverage The Goal is to cover Row 1 entirely before any chip rests in the 3rd Row. NOTE: This zillions rules file is designed for a minimum screen resolution of 1024x768. Download Plinko Now!
Game: Quad City Air Created by W. D. Troyka, December 2001. Summary: Starting in Des Moines, use the lines to visit all other cities exactly once, and then return to Des Moines. Story: You have saved up some frequent flier miles with Quad City Air. You now wish to cash in your miles for a dream vacation. Unfortunately the use of your miles is restricted. You must visit each and every city serviced by the airline exactly once. There are fifteen such cities, all located in Iowa, including your home town of Des Moines. Starting in Des Moines, you must visit each of the other fourteen cities exactly once using existing routes, and then return to Des Moines. If you are unable to complete the circuit, you will be stranded in a distant airport, forced to hitchhike home, and charged the full face value of your tickets (equal to two followed by nineteen zeros). Good luck and bon voyage! Download Quad City Air Now!
Game: Quadrilles Implemented by Karl Scherer, May 2003. Classic Puzzles, invented by the French mathematician Edouard Lucas (1842-1891). Source: Creative Puzzles of the World, 1980, Plenary Publ. Int. Domino puzzles of 'Quadrille' type. (5 variants) You have to solve a so-called 'Quadrille' puzzle, which means that you have to use the given dominoes and the given area they cover and make the dominoes 'fit' in the following sense: The given area is divided into coloured 2x2 squares. You have to rearrange the dominoes such that each square carries four half-dominoes of same value (e.g. all showing the number 5). (The coloured 2x2 squares become more obvious once you move the dominoes; the squares are painted onto the playing board). You can place the dominoes temporarily outside the given area. Note that in contrast to the two-player domino game rules, adjacent domino halves do not necessary have to show the same numbers! You win when you manage to rearrange the dominoes according to these rules. Remember: the final covered area has to be of the same shape as the one given at the start, and all 2x2 squares must show four times the same number. The default variant is very easy and only meant as a warm-up for the other variants, which use the full set of 28 tiles. More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz. Please note: Quadrilles requires Zillions of Games version 2.0 (or higher)! Download Quadrilles Now!
Game: Quantum Maze Invented and implemented by Robert A. Kraus, December 2002. This puzzle consists of a number of pieces called quanta (plural of quantum) which are represented by white diamond shields with a blue cross and border. They can move freely over the empty spaces (light purple) but are (usually) blocked by the walls. The walls come in 5 colors: red, blue, yellow, green, and brown. The quanta cannot be moved individually, but can only by moved simultaneously in a synchronized manner. The object of the puzzle is to make all of the quanta disappear. (Note: the squares of the board are adjacent orthogonally only. There is no diagonal movement.) At the bottom of the board is a row of 14 buttons. You play the puzzle by clicking on the buttons, not by moving the pieces. Click on one of the 4 light blue buttons with arrows at the right end of the row to move all unblocked quanta in the direction of the arrow. Quanta are blocked by walls and any other blocked quanta, but not by moving quanta. This means that if one quantum in a row of adjacent quanta can move, then all of the others will move with it in sequence. Next in the button row (moving to the left) are 4 orange buttons with arrows. Clicking on one of these will cause all of the quanta which are blocked by a wall (only) to make a quantum jump over the wall, provided there is an empty space on the other side, or another jumping quantum (but not a stationary one). Again, this allows an entire sequence of quanta, separated by walls, to jump together. Next are 2 purple buttons with double arrows. Clicking on one of these causes every quantum which is adjacent to another quantum in the given orientation (horizontal or vertical) to disappear. Finally, at the left end of the row are 4 colored buttons (blue, red, yellow, green) with black X's. Clicking on one of these causes all quanta which are adjacent to a wall of the corresponding color to disappear. (The brown walls are inert.) The most important rule of the puzzle is that each of the 10 leftmost buttons can be clicked only once, after which it is blacked-out. The 4 rightmost buttons (ordinary movement) may be clicked as often as needed. You win when there are no quanta remaining. Download Quantum Maze Now!
Game: Quilt Invented and implemented by Karl Scherer, April 2001. Object: Uncover the picture. (39 variants) Click the board to randomize the setup. Click one of the square tiles. The square and some other squares will change, each from red to blue to transparent. Now we list which positions will be changed with each mouse click. We write 'ortho 3' short for 'position at a distance orthogonally of up to 3 steps', and 'diag 2' short for 'position at a distance diagonally of up to 2 steps'. Variant 1: ortho 1 Variant 2: diag 1 Variant 3: ortho 2 Variant 4: diag 2 Variant 5: ortho 1 diag 1 Variant 6: ortho 2 diag 1 Variant 7: ortho 1 diag 2 Variant 8: ortho 2 diag 2 Variant 9: ortho 8 Variant 10: diag 8 Variant 11: ortho 8 diag 1 Variant 12: ortho 1 diag 8 Variant 13: ortho 8 diag 8 Variants 14 - 26: as above, but on a 6x6 board. Variants 27 - 39: as above, but on a 8x8 board. You win when you see all of the picture again. All these puzzles are solvable! You can switch the piece set (menu item 'View/Switch Piece Set'). Background design: fractal R001100e by Karl Scherer. Button design: by Morgan Owens. More related freeware as well as real puzzles and games see my home page http://karl.kiwi.gen.nz. Download Quilt Now!
Game: Rabbit Invented and implemented by Karl Scherer, January 2001. Object: Make your rabbit race all tunnels, then eat the carrots. (2 variants) First, click anywhere on the board to drop your rabbit and to allow a randomized set of undergound rabbit tunnels to be established. The twelve tunnels are numbered. Each tunnel has two exits. Move your Rabbit one step into any direction towards an entrance of a tunnel. The easiest way to do this is to enable SMART MOVES in the OPTIONS MENU and click the target square for your rabbit. The rabbit will race through the tunnel and reappear at the other end. Each tunnel can be travelled only once. The used tunnels will be marked. Once the rabbits has raced through all the tunnels, it is hungry and ready to eat the carrots. However, the rabbit can only access the carrots when it exits a tunnel adjacent to the carrots. In variant 2 there are twentyfour tunnels. Due to the randomization not all setups may be solvable. However, unsolvable setups seem to be rare. I have never seen one. More freeware as well as real puzzles and games at my home page http://karl.kiwi.gen.nz. Download Rabbit Now!
Game: Rabbits Invented and implemented by Karl Scherer, June 2001 Object: Recreate the original setup. (3 variants) Click any rabbit at the bottom or left border to let Zillions randomize the board. These border Rabbits are the buttons in this game. Now click one of the border Rabbits to flip a row or column. The flipped images will cycle between Rabbit, Carrots and Hole. The Rabbit in the bottom left flips the diagonal. Variants 2 and 3: In these variations clicking a button shifts a row, column or diagonal by one step. There are no flips in these variations. More freeware as well as real puzzles and games at http://karl.kiwi.gen.nz. Download Rabbits Now!
Game: Reptiles Invented and implemented by Karl Scherer, November 2001 Object: A shape which tiles a larger version of itself is called a rep-tile (from 'repetition tiling'). The selection screen offers you a choice of polysquares. Select a polysquare to start the corresponding game. The puzzle will show you that the polysquare is a rep-tile. You have to fill the given area with copies of this tile. Mirror images are allowed. The given area is an enlarged version of the given polysquare or a rectangle. You paint a polysquare by dropping a set of monochrome squares. The system will automatically change the colour of the tokens after you have completed painting one tile. You can also easily delete a placed tile; see game descriptions. You win if you manage to tile the given area. For further details please consult the game descriptions and the history texts of the various games. (Note each polysquare game has more than one variant associated with it. Especially there is a 'freeplay' variant on a big 32x32 board for each tile.) Also try to find 'faultfree' solutions: Once you have solved a puzzle, try to solve it with the additional condition that the tiling shall be 'faultfree', i.e. it has no breaking line from one side of the border to the other. There are also six 'Freeplay' options available from the main screen. In those games you may place the squares anywhere on the board. The colour of the squares will change automatically, e.g. in 'Freeplay 4' the colour of the dropped squares will change every 4 drops. This allows you to invent your own polysquares and to mix several types of polysquares. Please note that there are three alternative piece sets available. Several of the puzzles presented here have been taken from my book 'A Puzzling Journey To The Reptiles And Related Animals', 1986, one of three books on geometrical problems and puzzles I have privately published. For details see my web page. Another good source for related problems is Solomon Golomb's book 'Polyominoes'. More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz. Updated 08/09/03 made solutions available via Help/Show Solution Download Reptiles Now!
Game: Reptiles II Invented and implemented by Karl Scherer, December 2001 Object: A shape which tiles a larger version of itself is called a rep-tile (from 'repetition tiling'). The selection screen offers you a choice of polysquares. Select a polysquare to start the corresponding game. The puzzle will show you that the polysquare is a rep-tile. You have to fill the given area with copies of this tile. Mirror images are allowed. The given area is an enlarged version of the given polysquare or a rectangle. You easily paint a polysquare by dropping only three squares, details see game text. The system will automatically drop all other squares. Details see game text. You can also easily delete a placed tile; see game descriptions. You win if you manage to tile the given area. For further details please consult the game descriptions and the history texts of the various games. Some solutions (zsg files) are included. (Note that each polysquare game has more than one variant associated with it. Especially there is a 'freeplay' variant on a big 32x32 board for each tile.) There are also six 'Freeplay' options available on the main screen. In those games you may place the squares anywhere on the board. The colour of the squares will change automatically, e.g. in 'Freeplay 4' the colour of the dropped squares will change every 4 drops. This allows you to invent your own polysquares and to mix several types of polysquares. Please note that there are three alternative piece sets available. Good sources for related puzzles and problems are the following books: Solomon Golomb's : 'Polyominoes', 1965 and 1994. Karl Scherer : 'A Puzzling Journey To The Reptiles And Related Animals', privately published 1986. Many people have worked on polyominoes in recent years, but of limitations of publishing space not very many solutions have been published (see my comments in game 'Y-primes'). Outstanding is the work of Torsten Sillke, who investigated a lot in the area of polysquares in two and three dimensions. He found hundreds of new rectangular packings using a computer. The condensed information on these results are available on his web pages. (http://www.mathematik.uni-bielefeld.de/~sillke/). The actual images of solutions, however, are still mostly unpublished... More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz. Updated 08/09/03 made solutions available via Help/Show Solution Download Reptiles II Now!
Game: Reptiles III Invented and implemented by Karl Scherer, February 2002 Object: A shape which tiles a larger version of itself is called a rep-tile (from 'repetition tiling'). The selection screen offers you a choice of polysquares. Select a polysquare to start the corresponding game. The puzzle will show you that the polysquare is a rep-tile. You have to fill the given area with copies of this tile. Mirror images are allowed. The given area is an enlarged version of the given polysquare or a rectangle. You easily paint a polysquare by dropping only three squares, the system will automatically drop all other squares. (If the polysquare has more than eight squares, then you have to drop four squares.) Details see game text. You can also easily delete a placed tile. You win if you manage to tile the given area. For further details please consult the game descriptions and the history texts of the various games. Some solutions (zsg files) are included. (Note that each polysquare game has more than one variant associated with it. Especially there is a 'freeplay' variant on a big 32x32 board for each tile.) There are also six 'Freeplay' options available on the main screen. In those games you may place the squares anywhere on the board. The colour of the squares will change automatically, e.g. in 'Freeplay 4' the colour of the dropped squares will change every 4 drops. This allows you to invent your own polysquares and to mix several types of polysquares. Please note that there are three alternative piece sets available. Several of the puzzles presented here have been taken from - Solomon Golomb's book 'Polyominoes'. - my book 'A Puzzling Journey To The Reptiles And Related Animals', privately published. - Torsten Sillke's Web pages. The actual images of most solutions, however, are still mostly unpublished... More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz. Updated 08/09/03 made solutions available via Help/Show Solution Download Reptiles III Now!
Game: Rhamses Invented and implemented by Karl Scherer, March 2002 Object: Eliminate all Rhamses figures apart from one. (8 variants) The Rhamses figures can be moved in one direction only, namely either to the North, South, East or West. Starting with East, the direction changes with every move (E,S,W,N,..), as indicated by a small arrow at the border. You win if you have eliminated all Rhamses statues apart from one. Some of the variants have randomized setups. More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz. Download Rhamses Now!
Game: Rhamses II Invented and implemented by Karl Scherer, March 2002 Object: Eliminate all Rhamses figures apart from one. (8 variants) In this solitaire game a Rhamses figure jumps over any consecutive row of tokens and lands on an empty square immediately after it. All tokens that have been jumped are captured. You win if you have eliminated all Rhamses statues apart from one. Some of the variants have randomized setups. Please note that the Rhamses II file contains no sound directory, the game rather refers to the sounds of the original Rhamses game. Hence you need the original Rhamses game installed to hear the sound. Alternatively, you can copy the Audio directory from the Rhamses package into the Rhamses II directory or merge all Rhamses packages into one directory structure. More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz. Download Rhamses II Now!
Game: Rhamses III Invented and implemented by Karl Scherer, March 2002 Object: Eliminate all Rhamses figures apart from one. (9 variants) The Rhamses figures can be moved in one direction only, namely either to the North, South, East or West. Starting with East, the direction changes with every move (E,S,W,N,..), as indicated by a small arrow at the border. The Rhamses figure jumps over any consecutive row of tokens and lands on an empty square immediately after it. All tokens that have been jumped are captured. You win if you have eliminated all Rhamses statues apart from one. Some of the variants have randomized setups. Please note that the Rhamses III file contains no sound directory, the game rather refers to the sounds of the original Rhamses game. Hence you need the original Rhamses game installed to hear the sound. Alternatively, you can copy the Audio directory from the Rhamses package into the Rhamses III directory or merge all Rhamses packages into one directory structure. More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz. Download Rhamses III Now!
