Match-and-vanish puzzles with limited moves

15 January 2009

IMG_0001.PNGThe match-and-vanish principle of sequential removal puzzles has taken off in the numerous Bejeweled variants, also en masse found in the app store. As a side-effect, as few of such arcade games have developed separate puzzle modes alike to Vexed. Different from Vexed, these puzzles all take the Bejeweled cue that you have to get three identical tiles together before they disappear (in Vexed also groups of two tiles disappear). Also different from Vexed is that these puzzles do not have any walls that block the movement of the blocks. The only constraint are blocks of other color that are in the way. This does not allow for difficult puzzles, so all these puzzles have to add an extra constraint, and that is that the number of allowed moves is limited. So, these puzzles are not so much about removing all blocks (which is easy), but to do so within a pre-set number of movements (which can become pretty difficult).

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Vexed: the original match-and-vanish puzzle

14 January 2009

vexed.pngContinuing the series about sequential removal puzzles, this post introduces Vexed, which is probably the first puzzle to use the principle of automatic and immediate removal of tiles when identical tiles come into contact. This principle has become enormously popular in the wake of Bejeweled and its masses of clones and variants. Bejeweled turns this principle into an arcade-style game because removed tiles are replaced by new ones. Vexed has a clearer puzzle logic: remove all movable objects by bringing identical objects together.

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Cubes: the SameGame with a twist

12 January 2009

IMG_0004.PNGThere is one more SameGame implementation (besides the numerous ones discussed in my previous post) that I think deserves a separate posting: Cubes. There is also a lite version with only four levels to try it out, and a free ad-supported full version – though this free version does not (yet) seem to be available in all iTunes stores. As one might figure out from the illustration, Cubes is a 3 dimensional SameGame implementation. Although this seems to be just a little step further, this turns out to be a really capturing puzzle with good clarity.

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Chain Shot! – the SameGame over and over again

8 January 2009

reMovem.pngThe first kind of sequential removal puzzles that I will discuss is the computer game Chain Shot! and its derivatives. Chain Shot! was developed originally by Kuniaki Moribe in 1985 for the Fujitsu FM-8/7 series, and ported to UNIX under the name of Same Game in 1992 by Eiji Fukumoto. This puzzle is probably one of the most ported/cloned puzzle programs available for computers, known under many different names (see a list of pre-2000 ports on wikipedia). Later, it got ported to Windows Mobile where the same game is known as either Jawbreaker, Bubble Breaker, Bubblet or Bubblets. And now it has come to the iPhone, and again the same game is popping up over and over again. The basic principle is actually really nice (Biedl et al. 2001 is an analysis of its complexity is, showing that it is NP complete), but do we really need dozens of versions of this?

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Peg Jump: a primer on sequential removal puzzles

26 December 2008

pegjump.pngContinuing my survey of sequential movement puzzles in the app store, I will take up sequential removal puzzles in the next few posts. In a sequential removal puzzle, pieces are removed one after another until a particular goal is met, typically the removal of all pieces, or all but one. All sequential movement puzzles, including sequential removal puzzles, can be considered to be mazes, including classic sliding block puzzles and more fancy “hidden” multi-state mazes.

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Set: another copyright problem

23 December 2008

3_Tuple.jpgThe game Set (designed by Marsha Falko in 1991) is a very enjoyable and innovative card game, in which the object is to find matching sets of three cards as quickly as possible. The deck of cards consists of 81 cards that are all unique combinations of four characteristics with three different options (3 to the power 4 = 81). For example, in the picture shown to the right, the characteristics are color, shape, shadings, and number of objects. The company Mustang Mobile (run by the Falko family) has the exclusive license for development of mobile versions of this game, but this company has (not yet) released a version for the iPhone. However, their exclusive license does not withhold others to do this (a recurrent problem). The following apps are straightforward implementations of Set for the iPhone (links redirect to iTunes):

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Please acknowledge the designer!

18 December 2008

IMG_0003.PNGThe point of copyright and intellectual property for puzzle designs already came up in passing in my posts about to Rush Hour and Lunar Lockout. However, today an even more obvious problem arose in the app store: Blockade (link redirects to iTunes). This gives me the possibility to very clearly and forcefully explain to all developers out there:  

  • Puzzle-designs are intellectual property of the designer.
  • Even if they are available online, please ask the designer when you want to use the puzzle.
  • Don’t be afraid: most will be thrilled and extremely cooperative.
  • And most importantly: mention the name of the designer clearly alongside each individual puzzle!

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Knight’s jump mazes: nothing really there yet

14 December 2008


By using special rules for movement, simple mazes can become complex multi-state maze-puzzles. A well-known special kind of movement that can be used for such puzzles is the knight’s jump from chess. There are two puzzles available in the app store that use this kind of movement, but neither of them offers really nice puzzles yet. However, this could easily be changed for the better.

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Tilt mazes: replacing dexterity with logic

13 December 2008


One of the fascinating possibilities of the iPhone is to use the accelerometer to guide objects through mazes. This can be done with mazes in a literal sense, like in Labyrinth, or in a somewhat less maze-like setting, as in Super Monkey Ball. In these apps, the problems have to be solved through dexterity: a steady hand and smooth movements are necessary reach the goal.

In contrast, the principle of tilt mazes is to only use logic to reach the goal. The basic idea of such mazes is that the maze can be tilted, but the movements of all objects in the maze continue in the direction of the tilt until a wall (or hole) blocks the movement. As far as I know, Andrea Gilbert was the first to propose such puzzles in 1999.

There are three implementations available in the app store that use this principle (links redirect to iTunes):

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Riddle racing until blocked

11 December 2008

IMG_0001.PNGIn my previous post I discussed various puzzles that used the principle of “movement-until-blocked” to transform a simple grid into a more or less complex maze. In a comment to that post, Bob Hearn drew my attention to another such puzzle in the app store that I had missed (iTunes link): Riddle Racer (a free version to try it out is also available). The goal of this puzzle is to move the car to the centre of the board with the help of the orange pylons. Both the car and the pylons can be moved, but only if they are blocked at some point by the car or another pylon.

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Movement-until-blocked mazes

10 December 2008

IMG_0002.PNGA regular maze is good, but a concealed maze is better. By allowing only particular kinds of movements, a simple grid suddenly can become a twisted virtual maze. A recurrent trick is to only allow straight movement that continues until blocked. Various puzzles in the app store use this approach. And to give away my conclusion, I find Q Touch (shown here to the right) currently the most interesting of them.

The following five apps all are this kind of “movement-until-blocked” mazes:

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KinWits: more multi-state by paired movement

9 December 2008

IMG_0002.PNGOne of the ways to make ‘virtual’ multi-state mazes is by using multiple moving figures. You will be in different parts of the maze depending on the combined position of all moving figures. I discussed a particularly nice example of such mazes in my previous post on Theseus. However, there is another puzzle of this kind in the app store: KinWits (there is also a free version of this puzzle to try it out). And if you wonder why this puzzle is a maze in the first place (it sure doesn’t look like one on face value), then read my primer on maze puzzles before you read the rest of this post.

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Theseus: a multi-state maze by paired movement

8 December 2008

IMG_0001.PNGIf you can get hold of a copy of Robert Abbott’s books Mad Mazes and Super Mazes you should immediately buy them. Unfortunately, they are out of print now. These books really redefine what mazes are all about. They contain various ingenious variations on the multi-state theme: your position in the maze is actually different depending on how you got there. Although there are many ways to make such mazes (see for example my previous posts), Robert Abbott’s designs are as good as it can get. Now one of his multi-state maze designs (or ‘mazes with rules’ as he likes to call them) has hit the app store: Theseus (iTunes link).

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How to get multi-state: a maze with funky doors

7 December 2008

IMG_0001.PNG The basic idea of a multi-state maze is that a visually perceived position in the maze can have different ‘states’. This means that being in a particular position in (the visual presentation of) the maze does not mean that you are in the same position of the state-diagram of the maze. In other words: although it might seem that you are on the same position, you can be in different parts of the ‘real’ maze. This abstract principle needs to a good mechanism to work as a puzzle. One approach is to use doors that selectively block a particular part of the maze, and which can only be moved in certain positions. As always with multi-state maze-design, this approach was pioneered by Robert Abbott in his Sliding Door Mazes. A variation on this theme (though I think completely independently developed) is the iPhone game Space Trap, shown here to the left (iTunes link).

[Update 6 February 2009] Space Trap seems to have disappeared from the app store, but today another version of the same puzzling principle became available: Open Doors. Different developers, but there seems to be a direct connection between Alcomi (the company behind Space Trap) and Armor Games (from Open Doors). All a bit confusing though… [end update]

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Thing that roll: Rolling Block puzzles

2 December 2008

IMG_0006.PNGAs argued in my previous post, maze puzzles get more interesting when the actual maze is concealed. A really nice concealment of a maze puzzle are rolling block puzzles. In such puzzles a block (larger than 1x1x1, typically 1x1x2) is rolled around a grid of squares. What is so special about that, you might ask? Well, the effect is a multi-state maze, which can result in really nice puzzles.

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A primer on maze puzzles

30 November 2008

labyrinth72.jpgMazes are a favorite kind of puzzles for many. Actually, I will argue below that all sequential movement puzzles are actually concealed mazes. However, one important distinction to be made first is that between a maze and a labyrinth. A labyrinth (like the famous one shown to the left here) is only a single twisted path without junctions. There is no possibility to get lost here, and consequently it cannot really considered to be a puzzle. Only when junctures and dead ends are introduced, the puzzling aspect becomes worthwhile, and then the puzzle is called a maze.

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Chip’s Challenge: a Sokoban Laboratory

30 November 2008

IMG_0001.PNGFor those of you who like the idea of Sokoban, but find it a bit abstract, Chip’s Challenge is probably a good alternative. The original game was designed in 1989 by Chuck Sommerville for the Atari Lynx (in a sense an iPhone predecessor). In Chip’s Challenge, you guide around Chip McCallahan through a series of increasingly difficult puzzles. Many of the puzzles have Sokoban parts in them, but there are many other additions, like ice for sliding, conveyor belts, floors that only be passed once, and bouncing balls that ask for precise timing.

There are various games in the app store that take more or less direct cues from Chip’s Challenge, although I have no idea whether there are any direct links. None of the games even mention Chip’s Challenge. Only one of the games (Loopy Laboratory) cites Chip’s Challenge so directly that it is clearly inspired by it.

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Sokoban: not just sliding, but pushing blocks

28 November 2008

200811281037.jpgIn his classic definition of Sliding Block puzzles, Edward Horden explicitly noted that “there must be no requirement that they be pushed or pulled by other pieces.” So, let’s change the topic from sliding blocks (as discussed in the last few posts) to pushing blocks.

The most well-known instantiation of a pushing block puzzle is Sokoban (Japanese for ‘warehouse keeper’), created in 1980 by Hiroyuki Imabayashi. In this puzzle, various blocks must be pushed to their destination in a twisted warehouse. The blocks cannot be pulled, so when a block is pushed into a corner it is stuck, and eventually the puzzle will have to be restarted.

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Rubik’s Cube: great apps, but wasted efforts…

26 November 2008

cube.PNGErnö Rubik’s Cube is possible one of the most well-known puzzles of recent years. Almost exactly a century after the 15-puzzle craze of 1880, Rubik’s Cube set off its own craze from 1980 onwards. It’s a fantastically great puzzle (it actually was the puzzle that got me into the hobby of collection, solving and designing puzzles), and now it has come to the iPhone as well. However, it might just as well have passed this opportunity. The iPhone is not the right place for a Rubik’s Cube.

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Re-Shuffling Rush Hour

25 November 2008

subwayshuffle.PNGA sliding block puzzle is normally played inside a tray, in which the block can move around orthogonally. How about other possibilities of moving block around? Enter Subway Shuffle: Rush Hour on a graph. Or, as the developer Bob Hearn explains it:

Imagine playing Rush Hour, but make all the cars 1×1 instead of 1×2 or 1×3. But still some can only move vertically, others horizontally. Replace the cars by tokens, red for horizontal, blue for vertical, and put the tokens on nodes of a graph with colored edges: red tokens can only move on red edges, blue on blue. If you use a grid graph, with horizontal edges red and vertical edges blue, then you have 1×1 Rush Hour. If you relax the grid graph constraint, and also allow more colors, then you get Subway Shuffle. These relaxations allow for lots of interesting possibilities in puzzle configuration. It’s also possible to have extremely complicated puzzles in a very small space: I’ve generated some puzzles on small graphs that require over 1,000 moves.

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