Review: WrapSlide for iPhone and iPad

The Rubik's Cube turned 40 recently, and there's little doubt that it has been one of the most influential puzzles ever invented. Many puzzle games on the App Store compare themselves to the Cube, but in most cases that's just marketing fluff. WrapSlide, however, is a different story.

Developed by Alewyn Burger, a researcher at Stellenbosch University (South Africa), it might look like just another toroidal sliding block puzzle. But looks, in this case, are very deceiving. The movement mechanics are different from the usual ones, and produce a very challenging puzzle.

Review: Einstein™ Enigma for iPhone and iPad

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Einstein™ Enigma (yes, "Einstein" is a trademark) by the German BBG Entertainment is an old style sliding puzzle with a couple of new twists.

The App Store blurb boasts that the game was inspired by the Enigma machine, but don't believe that marketing fluff: it has nothing to do with that.

Review: Circles: Rotate the Rings, Slide the Sectors, Combine the Colors for iPhone and iPad

The first release of Circles was quite boring. From the screenshots it seemed something different, but in reality it was just another impersonation of the ubiquitous toroidal sliding block puzzle. The only difference was that instead of the usual square grid, in this game the tiles are warped to form a circle.

Luckily, version 1.1 fixed this by adding several new configurations that are guaranteed to make even experts of sliding block puzzles scratch their head.

Review: Senkai Puzzle for iPhone and iPad

Senkai Puzzle is a well presented puzzle game for iPhone and iPad which was originally released a couple of months ago. The first version left me a bit cold because after solving the puzzle for the first time, which isn't too difficult, it lacked a clear objective to motivate playing again. An update has just been released, and the game is now a lot more interesting, in a Spinpossible sort of way.

At its core, Senkai is another group theory, sequential movement puzzle. It is played on a 2x2 arrangement of cubes, and this is the start position:

A move consists in turning a pair of cubes around their common axis, like this:

Of course the goal is to return to the start position after shuffling.
The user interface is very well done and uses swipes to turn the cubes. An excellent detail is that you can move the cubes just a little, to see what's on the side faces, without actually making a move. You can do that also to see what's on the back face, but that's not needed because the back face is the same as the front face, except that one is white and the other is red. The solved state uses only the white faces.

The update which has just been released adds an introductory 2x1 puzzle, which is much simpler to solve:

As I said at the beginning of the review, the initial version of the game lacked a purpose: it just showed a counter of the number of moves made, without any objective to meet.
This is fixed now because a "belt" grading system has been added:

after shuffling the cubes, you are shown not only the number of moves you made, but also the optimal number of moves needed. As the table above (for the 2x1 puzzle) shows, you need to solve the puzzle with no more than 5 extra moves to earn an orange belt, and so on; solve it 30 times with the optimal number of moves, and you'll earn the black belt. The requirements for the 2x2 puzzle are more relaxed to account for the higher difficulty.

I don't know what the theoretical maximums are; it looks like the optimal solution usually requires 5-6 moves for the 2x1 puzzle and 8-10 moves for the 2x2 puzzle. This should mean that earning the black belt in 2x1 shouldn't be too difficult, while for 2x2 it will be a lot harder.

Well done to Grifia for implementing such a slick interface and for recognizing the shortcomings of their initial release and quickly addressing them.

Summary

Nontrivialness	★★★★☆
Logical Reasoning	★★★★☆
User Interface	★★★★☆
Presentation	★★★★★
Loading Time	★★★☆☆
Saves Partial Progress	✘
Status Bar	✘

©2013 Nicola Salmoria. Unauthorized use and/or duplication without express and written permission is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Nicola Salmoria and nontrivialgames.blogspot.com with appropriate and specific direction to the original content.

Review: Spinpossible for iPhone and iPad

Eric Kelsic of ALX Games contacted me about the free puzzle game that he and his friends Alex Sutherland and Alex Sheive have developed: Spinpossible.

The basic idea is simple: take a puzzle based on group theory, like Rubik's Cube, but easier; and make the main goal of the game not just to reach the solved position, but to do it in the optimal number of moves.

The playing board of Spinpossible is a 3x3 grid, containing numbers. A move consists in rotating a rectangle of any size (including 1x1) by 180 degrees.
For example here is the starting position of one of the tutorial levels:

the first move we make is to rotate the 1x2 rectangle containing the 2 and the 5, leading to this position:

now we rotate the 3x1 rectangle containing 1, 2, and 3, and we have reached the solved state:

If you can solve Rubik's Cube—and by solving I don't mean using a set of operators learnt from a book, but consciously applying the concept of commutator to reach the solved state—you should have no problem with this new set of rules. If you don't, don't despair: the first few levels of the game do an excellent job of explaining the basic concepts.

Attempting to solve every puzzle in the optimal number of moves, however, changes things dramatically. For example, here is one of the early puzzles:

Reaching the solved state would be pretty simple: just rotate the (1,4) and (6,9) rectangles, which brings the numbers in the correct position but upside down; then rotate each number individually. That works, but it takes a total of 6 moves. The green squares at the bottom of the screen, however, indicate that the optimal solution requires just 5 moves. Can you find them?

The authors have written a paper about the mathematics of Spinpossible, and also verified through exhaustive search that 9 moves are sufficient and sometimes necessary to solve every position. However, you can be sure that finding those 9 moves can be extremely hard for a human. 5 moves, like in the example above, is already pretty difficult.

The game has 4 different playing modes:

• puzzle:  the main mode, which contains a tutorial and about 100 selected levels of increasing difficulty;
• arcade: you need to solve puzzles within a time limit; after each puzzle, you get a time bonus depending on how quick you are and how many moves you use;
• random: solve randomly generated puzzles at your own pace;
• multiplayer: compete online with other players.

To access some of the features you need to register on the Spinpossible web site, which is free.

Spinpossible is a must-have for every logic puzzle enthusiast. It is sure to push your brain to its limits, because, as the FAQ says, "no one has beaten all the levels without computer assistance".

The only criticism I have is for the user interface, which is a bit confused, and sluggish on some devices. This is a byproduct of the game being a port of a Flash game rather than a native iPhone app. Hopefully this will be improved in future updates.

Summary

Nontrivialness	★★★★★
Logical Reasoning	★★★★★
User Interface	★☆☆☆☆
Presentation	★★★☆☆
Loading Time	★★★☆☆
Saves Partial Progress	✘
Status Bar	✘

©2013 Nicola Salmoria. Unauthorized use and/or duplication without express and written permission is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Nicola Salmoria and nontrivialgames.blogspot.com with appropriate and specific direction to the original content.

Review: MatCube for iPhone and iPad

Some incredible things can happen on the App Store.
The other day I downloaded MatCube, a free game for iPhone and iPad by Eizo Ono. Nothing on the iTunes page suggested that it could be a great puzzle: I couldn't even understand the description, because it's only in Japanese, and the screenshots made it look more like a proof of concept than a full featured game.

Still, I'm glad I downloaded it, because I was blown away by how clever it is.

Actually, it's not even one puzzle. It's 4, or 8, or 24, depending on how you want to count them. Let me explain.

This is the initial screen after launching the app:

The grid of 3x3 cubes is the goal position. This is the easiest difficulty setting, where each cube has only 2 colors: 2 opposing faces are red, the others are green.
When you tap the Shuffle button, the cubes are randomly scrambled, and you need to get back to the goal position.

The first thing that I thought when I started interacting, was "this is Lights Out on steroids". Lights Out is played on a 2D grid, and MatCube appears to be the natural extension to 3D: when you tap a cube, the cubes that surround it are rotated.

Lights Out is a relatively simple puzzle, because each cell can only have 2 states: ON and OFF. MatCube is a bit more complicated because, at the easy difficulty, each cube can be in 3 states. Also, the side from which you move a cube changes its state in a different way, because the cube rotates around a different axis.

Solving MatCube at this difficulty (and by "solving" I mean finding an algorithm that consistently allows you to get back to the goal position after shuffling) isn't extremely hard, but it isn't a walk in the park either. It took me several attempts to eventually "get it", though the naive method I used doesn't generalize well to the higher difficulties.

When playing at the normal difficulty setting, each face of the cubes has a different color, so each cube can be in 6*4 = 24 different states. This makes things a lot more... interesting.

When playing in full color mode, it's useful to know that you can rotate the cubes in the opposite direction by tapping while touching the screen with another finger.

The number of cubes can also be increased, with a choice between 3x3, 4x4 and 5x5. At 5x5, it looks quite daunting:

But that's not all: what I described so far is just one of the play modes available. There are a total of four different modes.

The second one is similar to the first, but when you tap a cube you rotate all the cubes in the same row and column, instead of rotating only the surrounding ones.

The third one is a surprise: one cube is removed from the grid, and moves are made by rolling cubes towards the hole. Therefore, this could be described as "15 puzzle on steroids". I have tracked down a mechanical puzzle using the same mechanics: Rolling Cubes by John Harris.

The last mode is another surprise: the cubes are no longer laid out in a square grid, and form a pattern reminiscent of the Q*bert videogame:

Tapping a cube rotates all the surrounding ones, which can be up to 6, each one around a different axis.

So that's why at the beginning of the review I said there are 24 different puzzles in this app:
(2 colourings of the cubes) * (3 sizes of the grid) * (4 play modes) = 24 combinations.

Not bad for a free app!


Here's a video by the app developer, showing the Android version:

The main criticism I have about this wonderful puzzle is that playing on an iPhone or iPod the cubes are a bit too small, and it's difficult to tap the one you are aiming at. While this is pretty much unavoidable when playing the 5x5 version, the 3x3 and 4x4 versions could be easily improved by simply making the cubes larger.

A significant missing feature is that the position is not saved when the app goes to the background, which makes it impractical to attempt solving the larger puzzles unless one has a good amount of time to spare.

I also don't like that the only form of score is the timer shown at the top left of the screen. Personally, I would be more interested in the number of moves.

The final criticism is about the color scheme. Here is a simulation of how a person with protanopia would see the goal position in easy mode:

That could be improved by using different colors, or by adding other visual cues to the cube faces (for example, making them look like dice).

Overall, this is certainly a puzzle that will stay on my iPod for some time. Congratulations to its inventor!

Summary

Nontrivialness	★★★★★
Logical Reasoning	★★★★★
User Interface	★★☆☆☆
Presentation	★★☆☆☆
Loading Time	★★★★★
Saves Partial Progress	✘
Status Bar	✔

©2013 Nicola Salmoria. Unauthorized use and/or duplication without express and written permission is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Nicola Salmoria and nontrivialgames.blogspot.com with appropriate and specific direction to the original content.