Puzzles Game

[Gervie]

Game: Unmatch

Invented and implemented by Karl Scherer, August 2001


Object: Fill the tile frames. (6 randomized variants)

Essentially the game 'Unmatch' is the game 'Match' played in reverse.

Click anywhere on the 4x4 board to allow Zillions to randomize the board. Imagine this board consisting of nine overlapping 2x2 tiles. In order to fit all nine 2x2 tiles into the little 4x4 box, the tiles must overlap. The overlapping areas match.

Your task is to place each tile into one of the nine frames. One quarter of each frame is coloured already.

The 'sweet spot' for picking up and placing the tiles is always at the lower left quarter of a 2x2 tile.
Note that each tile must go to a different place.

Indicators at the lower left show which tiles have been placed already.

Variant 2: 3 colours
Variant 3: 2 colours
Variants 4, 5, 6 use a 5x5 board.

Background design: fractal R001100j by Karl Scherer.


More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz.

Updated 03/15/03
improved graphics

Download Unmatch Now!

 

[Gervie]

Game: Unplay Chess

Invented and implemented by Karl Scherer, July 2001


Object: Unplay the given situation back to the starting position.

This game plays chess moves backwards only. (Maybe a future version might play forwards and backwards.)

You are given a chess position. Play chessmoves backwards (e.g. Pawn e5-e4). You win when you reach the standard chess starting position.
To take a non-capture or en passant move back, move the piece concerned.
To take a capture move back, click the target square. Then select one move from the list of moves offered (if such a list is offered).

Typically you might play this game as a 'solitaire game', taking the part of both sides. However, it is equally possible to alternate between two players and play this game cooperatively. Of course only White can 'win' this game.
The challenge is in finding all the right moves to actually end up with the standard chess starting position.

First click one of the two buttons at the right border to tell the system whether you want to have warnings only or whether the system should declare a loss when you made a mistake.
You lose if after your move your opponent is in check.
You also lose if after your move your opponent has more than 16 pieces or more than 8 pawns.
You also lose when you move your king into an impossible double check (however, not all impossible double checks are detected by the system). The appropriate loss-message will be displayed at the top right border.

Variants:

Standard setup for your own retro problems. White starts.
Right click the mouse to set up you own starting positions.
Standard setup for your own retro problems. Black starts.
(Default) Retro problem 1 by Karl Scherer (forced: 6 last plies = 3 moves)
Retro problem 2 by Karl Scherer (forced: 11 last plies = 5 1/2 moves)
Retro problem 3 by Karl Scherer (forced: 19 last plies = 9 1/2 moves)
Retro problem 4 by Harry Nelson and Karl Scherer
Question: can White still castle? In other words: try to unplay the game without ever moving the white Rooks or the white King.

The idea for this game stems from the chess problemist area of retrograde analysis. For a full analysis of the retro problems given in this game see http://karl.kiwi.gen.nz/prchess2.html.


More freeware as well as real puzzles and games at http://karl.kiwi.gen.nz.

Download Unplay Chess Now!

 

[Gervie]

Game: Up And Down

Invented and implemented by Karl Scherer, July 2002


Object: Visit the four corner tiles. (two variants)

First click the board to randomize the setup.
The board consists of 64 diamond-shaped yellow and orange tiles which partially overlap. Corners of such a tile that are not visible are considered lying 'below' their visible counterparts.

Click a tile to drop your Token, then keep on clicking orthogonaly adjacent tiles while walking through the maze.
You have to alternate the type of overlap you cross (either going up, then down, up,... or the other way round: down, up, down, up,...).
Blue overlaps mean that the tiles are joined; no stepping up or down here.

You win if you have visited all four corner tiles of the board.
The corners you have visited will be marked. You are allowed to visit a tile twice.

Due to the randomness there might not be a solution in every case. However, I have not come across such a case.

Variant 2: You have to visit EACH of the 64 tiles at least once. The tiles you have visited will be marked.


Based on a classical maze where large sheets of material are laid out on the ground and you have to find a way from start to finish walking from sheet to sheet while following the alternating up/down rule at the overlaps.
As with 'A-mazes', the best solution might force you to step on the same tile twice, once with an 'up' step and once with a 'down' step'!

More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz.

Download Up And Down Now!

 

[Gervie]

Game: Vexed

Invented by James McCombe, 1999,
implemented by Ed van Zon, October 2001


Object: make all blocks disappear.

This is a blatant ripp-off of the Palm game Vexed, invented by James McCombe and further developed by the Vexed SourceForge Project.

You can move a block to the left or right, provided the space is free. Gravity will drop a block. If a block ends up directly next to another of the same kind, they both disappear. Once all the blocks are gone, you've solved the level.

To do well you should solve a level in no more moves than indicated as 'Par'. Some levels have solutions in less moves than the 'Par' count, but others do not.


Included are 9 level sets, for a total of 538 different puzzles:

Unless otherwise noted, the level sets were created by the Vexed Development Team.

The Classic levels pack was released with the original Vexed, created by James McCombe.
The Classic II pack is the challenging follow-on to the Classic levels, created by Steve Haynal.
The Variety Pack levels provide a full spectrum of difficulties from easy to hard.
The Variety II Pack levels is a continuation of the Variety Pack: from easy to hard.
The Children's Pack contains very easy levels meant for children.
The Twister levels are difficult. Many of these levels have twists that add challenge.
The Confusion Pack is hard! These levels are tricky and require careful planning to solve.
The Panic Pack levels are very hard! So hard you'll panic after the first one.
The Impossible Pack levels are, well, almost impossible. You need to be Einstein to make it through this game pack!

Solutions to all puzzles are included too, but don't take a peek too quick. It is not said that a given solution is the best possible.
Quite some solutions provided by Alfred Pfeiffer.

The zrf contains three piece sets.
Many thanks to Peter Postma who gave permission to include his 'stone block' piece set. (Due to a bug in Zillions v1.3.1 the background doesn't quite fit the stones, but it will after the next Zillions update.) Visit his Vexed pages, where you can play Vexed on the web.
The two other piece sets were copied from the Palm game.
Updated 02/16/02
bettered some solutions by Alfred Pfeiffer

Download Vexed Now!

 

[Gervie]

Game: Wazir Challenge

Created by W. D. Troyka, March 2002.


This is a collection of Turn Off variants in which the pattern of light changes correspond to the moves of various fairy chess pieces. In the standard Turn Off that comes with Zillions, when a light is selected, it and all orthogonally adjacent lights change state. This corresponds to the Wazir fairy piece, which can move to any orthogonally adjacent piece. Variants included in this file feature the Wazir, Fers, Dabbaba, Ferdaba, Alfil, Squirrel, Camel, and Zebra. A description of the moves of each piece is included in the "game description" section. Each game starts with all lights on, and the goal is to turn them all off.

Curiously, the Zillions version of Turn Off does not include a variant that starts with all the lights on. It turns out that this is a very difficult puzzle. In my experience Zillions has been unable to find the solution on the higher settings. Set to "stupid" it will sometimes find a solution by accident but usually after several hundred moves.

So the challenge is: Find the efficient solution to the Wazir 5x5 Turn Off puzzle. You can cheat all you want. The first person to send me the correct answer at [email protected] gets a certified smiley emoticon. :-)

Wazir Challenge is a companion game to Royal Turnoff.

UPDATE: Robert Gauss and Jeff Roy both solved this puzzle the week it came out. We all agree that the shortest solution is in 15 moves. This solution is now included with the game in a Solutions folder, which you can also access through the "Show Solution" option in the Help menu.

The order in which lights are selected is irrelevant because the state of a light -- off or on -- depends solely on how many times it or a neighboring light has been selected, not on the order of selection. A priori it is clear that the optimal solution cannot be over 25 turns. Selecting a light twice is the same as not selecting it at all (the second click undoes the first click), so an efficient solution cannot contain multiple selections of the same light.

Jeff Roy provided an interesting proof that the largest number of turns in the efficient solution to any solvable 5x5 Wazir puzzle is 17 turns. (By efficient I mean that all doublets have been subtracted out and that each light is selected either once or not at all.) He identified a "return pattern" of 16 distinct lights that, when selected, returns the board to the starting pattern so that no change in board state occurs. This pattern is a2, a3, a4, b1, b3, b5, c1, c2, c4, c5, d1, d3, d5, e2, e3, and e4. To summarize the proof: Suppose there is an efficient path of 18 moves from an initial state to a final state. A player could then add the 16 lights in the return pattern, which would create a list of 34 moves leading from the initial state to the final state. In this list of 34 moves there must be at least 9 doublets because there are nine more moves than there are lights on the board. (There can be no triplets because each pattern is composed of distinct selections.) If these doublets are subtracted out, you arrive at the same board state in 16 or fewer moves, which is a contradiction. Ergo, there is no such thing as an efficient path of 18 moves.

Updated 01/18/03
added 15-move solution

Download Wazir Challenge Now!

 

[Gervie]

Game: Wireworlds

Invented by Brian Silverman 1987,
implemented by Karl Scherer, August 2003.


(50 variants)

This Zillions game 'Wireworlds' is a collection of cellular automata, and a generalisation of the famous automaton 'Wireworld', which has extremely simple rules: The background colour (usually black) stays unchanged, Red ('electron head') turns Blue (electron tail), Blue turns Yellow (Wire), yellow turns Red if it is adjacent to one or two Reds.

It is easy to code the logical gates AND, OR, NOT, NAND, NOT in Wireworld. By combining such gates the workings of a computer can be simulated. The default variant shows the NOT gate, the next variant the OR gate and so on.
The 'electron' gun on the left emits one electron every 12 cycles, just to demopnstrate the NOT gate. The interval between data ('electron' or 'not electron') at the output is 6 cycles. Distance between electrons for this gate to operate properly: multiples of 6 cycles.

Click button '1' ('6', '30', '00') to run one, six, thirty cycles or forever. This will show how the 'electrons' move through the 'wires'. The 'hook' sign to the right is the sign for the logical 'NOT'.

Apart from showing the famous Wireworld setup, this game 'Wireworlds' also allows you to create a whole class of automatons (all closely related to the orginal Wireworld) by clicking the 'Y' buttons at the right border.
The number of Red neighbors determines whether a Yellow square turns Red,
the number of Blue neighbors determines whether a Red square turns Blue,
the number of Yellow neighbors determines whether a Blue square turns Yellow.

Clicking a Y-button on advances a cell's stage. E.g., the buttons in the column underneath the red square determine when Red turns to Blue.
A few additional buttons are for the convenience to trigger several buttons simultaneously: Row of coloured buttons: Click a colour to reset a whole column to 'Y' or blank. Numbers of neighbors: Click to reset a whole row to 'Y' or blank.

Click the left, right, up, down buttons to shift the pattern on the board.
You can click the board to edit it. Click the coloured button at the lower right to change the paint colour. Click 'Draw Line' to paint or clear(!) a line on the board; mark it by clicking the start and end positions. You can paint several lines in a row, and you can change the paint colour in between. Click 'Draw Line' again to switch this mode off.

The 'Border' option determines whether the area outside the board is treated as wrapping around (north and south border joined, east and west border joined) or as permanently black.


Apart from the the most basic logical gates and the 5-cycle flip-flop, I have created all other constructs by myself, so some variants may not show the most economic examples possible. However, I compared my designs to what I could find on the internet and all designs presented here seem to be the optimum. (I even managed to improve the size and the transit time of the humble AND gate). Please email me if you come up with some better ideas.

The classical Wireworld automaton was invented by Brian Silverman 1987. It can be run by the free program Mirek's Cellebration (www.mirekw.com), but Mirec's program contains only the most basic examples, and most of the gadgets given here in this Zillions program are missing in Mirec's program.
Also see Ed Peggs website (www.mathpuzzle.com, material from August 2002).
Other related Zillions games: 'Alive', Alive 2', 'Alive Auto', 'Game of Life', 'Rule110', 'Logic Gates'.

Please note: Wireworlds requires Zillions of Games version 2.0 (or higher)!

Updated 09/20/03
more variants added; some improvements

Download Wireworlds Now!

 

[Gervie]

Game: Y-Backtrack

Invented and implemented by Karl Scherer, December 2001


Object: Automatically fill any user-defined playing area with the given Y-pentomino. Watch the operation of a backtracking program in action and enjoy the solutions it comes up with! (30 variants, customizable)

To start, click the grey playing area. Zillions will AUTOMATICALLY tile the area without gaps or overlaps using copies of the polysquare shown in the top left corner.

Given a shape and a tile to fill it with, it is in general not known whether such a tiling problem has a solution. This game gives you the answers (if Zillions does not run out of memory) and lets you watch as the computer plays with the tiles.

YOU CAN GIVE THE COMPUTER ANY SHAPE MADE FROM SQUARES. (You can REDESIGN the fill-area very quickly and easily, either by deleting or adding new positions via selecting 'empty' or 'T0' with your right mouse button or by changing the board setup in the rules file.)

THE PROGRAM WILL DO EVERYTHING ELSE FULLY AUTOMATICALLY!

The system will stop (win) when it has found a tiling, and also stop (lose) if there is no tiling for the given shape.

This game presents a collection of
- all 23 Y-primes which fit onto a 32x32 board
- all 7 Y-primes which fit onto a 50x50 board

There exist only ten more primes for the Y-pentomino: 9x55, 12x55, 12x60, 12x65, 12x70, 12x75, 12x80, 12x85, 12x90, 12x95.

Please note that there are six alternative piece sets available.


See also Zillions games Ypento, Y-primes, G-Primes and Reptiles, Reptiles II and Backtrack for similar puzzles.

More freeware as well as real puzzles and games at my homepage http://karl.kiwi.gen.nz.

Updated 12/14/02
can run longer now; solves larger puzzles

Download Y-Backtrack Now!

 

[Gervie]

Game: Y-Primes

Implemented by Karl Scherer, November 2001


Object: Fill the playing area with Y-pentominoes. (30 variants)

If a shape tiles a rectangle, then this rectangle is called a 'prime rectangle' or a 'prime' for short, if it is minimal in the sense that it cannot be cut into smaller rectangles which also can be tiled by the given shape.

Hence for each shape that is 'rectifiable' (i.e. which can tile a rectangle), it is an interesting task to find all prime rectangles ('primes') for this tile. For any given tile there can only be a finite number of such rectangles. For the Y-pentomino we present here all known prime rectangles small enough to fit onto our board of size 32x32.

The Y-pentomino is represented by five square tokens. The system will automatically change the colour of the tokens after you have put down 5 tokens.

The system guides you through the placing of the five tokens per tile: Place two squares side by side, then a third orthogonally next to the second. The system will drop the remaining two squares automatically.

You can DELETE a placed pentomino by simply clicking the three squares which you placed on the board when you created the tile.

You win if you manage to fill the given rectangle. Solutions (zsg files) for most variants are attached.

Please note that there are three piece sets available.


The primes 10x16, 15x16 and 15x22 were first published by C.J. Bouwkamp and D.A. Klarner in JRM(3(1), which used a computer.
The 15x15 prime was found by Jennifer Hazelgrove with a computer (see JRM 7(3)).
All other primes were found by hand (!) by the author (9x20, 9x30, 10x14, 11x20, 14x15, 17x30, 21x25, 25x27), see Journal of Recreational Mathematics Vol 12(3), 1979-80. Astonishingly, my results found by hand bettered some of the earlier results found by computer.

Some of my results on prime rectangles (10x23, 11x30, 17x30, 18x25, 21x25) are published with this Zillions game for the first time. (I had these results to JRM in 1980, but they did not publish them because of the amount of matarial they had published on that topic already).

In the later years Torsten Sillke investigated a lot in the area of primes in two and three dimensions, using a computer (http://www.mathematik.uni-bielefeld.de/~sillke/).


See also the Zillions games 'Pento', 'Ypento' and 'Reptiles' for related puzzles.

Background design : fractal T011001l by Karl Scherer.

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 Y-Primes Now!

 

[Gervie]

Game: Ypento

Implemented by Karl Scherer, November 2000.


Object: Tile the given shapes with Y-Pentominoes. (6 variants)

The puzzles have an unlimited number of the Y-shaped pentomino. 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 Y-Pentominoes. Here you have no win condition.

Note that you can also redesign the fill-in area in all variants in order to create your own tiling problems.


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 T001100J by Karl Scherer


More related freeware, art, books, real puzzles and games see my home page http://karl.kiwi.gen.nz.

Download Ypento Now!