Planarity: why not multi-touch?

In 2005 a mathematics student called Mary Radcliffe developed the concept of a puzzle she called Planarity. It was implemented as a computer game on the internet by John Tantalo. The idea is to take an undirected graph, and the puzzle is to place the vertices (‘nodes’) in such a way that the graph is planar, i.e. the the edges (‘lines’) do not cross. A graph (drawn in 2D) without crossing edges is called a planar graph in mathematics, and this suggested name Planarity. It is an old problem in mathematics how to quickly determine whether a graph is planer or not.

The game became somewhat of a craze among the flash-based gaming community under the name Untangle (just google for “untangle game” and you will find dozens of implementations). Unexpectedly, the game is also available on the iPhone.

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Chip’s Challenge reloaded

Things are moving ridiculously fast in the app store—I hardly can keep up with all the new puzzles becoming available every day! You might have noted that I keep adding updates to previous post when new apps arrive that simply replicate other puzzles (see for example my post on Rush Hour or Lights Out), or when previously criticized omission are added in updates (see for example my posts on Mouse House or Blocked). However, sometimes I will write a new post, when there is too much significantly new that has become available.  

In this post I will revisit the topic of puzzles games that are similar in gameplay to one of those dinosaurs of computer games: Chip’s Challenge (for background, see my previous post on such games).

TurtleFlip & Adiro: alienated peg jump

With this post, I will finally finish off the sequential removal puzzles, as far as I have found them in the app store (see all posts in this category). In a sequential removal puzzle, objects have to be removed according to some rules. By taking the wrong order of actions, you might end up in a dead end, so sequential removal puzzles can be seen as an abstract kind of maze (see my earlier primer on maze puzzles explaining this in more depth).  

In real-life physical puzzles, sequential removal puzzles are not so widespread, because it is difficult to find interesting rules for removal that are transparently executable while manipulating objects on a board. Peg jump is possibly the only physical sequential removal puzzle. In contrast, for computer games the principle of sequential removal is very widespread, because even rather unwieldily rules of removal can be easily implemented for a computer to consistently perform. No cheating or accidental errors can occur. Because the goal of removing things, viz. clearing the board, is so intuitively simple, many computer games use this principle (just look at the dozens of Bejeweled-like games in the app store). The differentiation between such games lies in the details of the rules of removal. Enter the twisted rules of TurtleFlip!

FLIP: nice try, but not yet ready

The app FLIP is a combination of a Bejeweled-like match-three game, a tilt maze and a match-and-vanish puzzle. So in principle, there are many very interesting puzzle concepts combined into one neat little package. However, the execution leaves much to be desired, and the level-design is not very challenging. So, I really cannot recommend this app just now, but I will keep an eye on any updates.

Hiqup: peg jump on steroids

Finally somebody reconsidered Peg Jump. The app Hiqup [link redirects to iTunes] is a sequential removal puzzle in which pieces are basically removed by jumping over them. So far nothing new. However, developer Moopf introduced various new twists into this classic puzzle principle, which make it an interesting puzzle-app, well worth the (low) price.

Lights Out: not straighforwardly sequential removal

In a sequential removal puzzle pieces have to be removed in a sequence. Doing it in the wrong order will lead to a dead end. Lights Out is also a puzzle in which something has to be removed (all lights have to be turned off), and as a user you will perform actions sequentially. However, it turns out after some more pondering over the solutions that the order of actions is not important. So, strictly speaking this is not a sequential removal puzzle, but it definitively feels like one.

Match-and-vanish puzzles with limited moves

The 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).

Vexed: the original match-and-vanish puzzle

Continuing 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.

Cubes: the SameGame with a twist

There 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.

Chain Shot! – the SameGame over and over again

The 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?