Thursday, February 28, 2013

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.

Wednesday, February 27, 2013

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.

Tuesday, February 26, 2013

Review: Monorail for iPhone and iPad

Glenn Iba recently wrote me about his puzzle game Monorail for iPhone and iPad.
There was no need to: that game was already installed on my iPod and it's one of the most interesting puzzles I know.
The goal of the game is deceptively simple. You start with a grid of points, with some pre-drawn lines connecting a few dots:
Starting from there, you have to draw a closed loop that touches all points and doesn't intersect itself, like this:
All the grids provided have a unique solution, which is somewhat surprising initially: the pre-drawn lines are such subtle clues that they almost don't seem to be there.

These puzzles are also known as "Round Trip", and have been published in magazines since the early 1990's. Glenn Iba has collected some of them in a book; an extended introduction is available on his web site. It is an interesting read and shows how to approach the puzzles with logical reasoning without trial and error.

The puzzles are similar to Slitherlink, the differences being that in Slitherlink the path doesn't have to touch every point, and the clues are numbers instead of lines. Due to the lack of numbers, I consider Round Trip a "purer", more elegant puzzle.

In addition to the traditional square grid arrangement, Monorail also contains puzzles laid out on a hexagonal grid, like this:

The game contains 50 free grids. If you want to play more, there are a few packs available through in-app purchases, for a total of over 800 grids.


The user interface is quick and easy to use, and it makes the game enjoyable. The only criticism I have is the same one that I made for CounterBalancE: there is no way to put a cross on the grid, as a reminder that a line cannot be in that position. This is odd since the use of crosses is explained in the book introduction I mentioned above, so the author clearly knows that they are useful. Annoyingly, the feature was actually available in an earlier version of the game, but was removed when the undo/redo functionality was added. It would be great if it could be reintroduced in a future update.

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.

Friday, February 22, 2013

Review: Pudding Monsters for iPhone and iPad

You probably don't need to learn from me about Pudding Monsters, a top quality game from Zeptolab, the makers of the classic Cut the Rope.

The basic idea at the core of this puzzle game has been used before. You make the pudding monsters slide on the floor; once they start moving, they won't stop until they hit something. If they don't hit anything and leave the screen, you lose and have to start again.
Even if the basic idea isn't new, I don't recall it having been used this way. When two monsters touch, they join to form a larger monster. The level is solved when all monsters are merged.
There is a lot of variety in the puzzles, because all kinds of different elements are introduced throughout the game: monsters that leave a sticky trail, sleeping monsters that cannot move until another monster joins with them, ice blocks that break after being hit, cloning machines, arrows, and so on.

Additionally, there's the customary three star rating system; stars are earned by finishing the level with monsters sitting on top of the stars.
The levels don't have a single solution, and after solving all levels for the first time, the game encourages you to play them again and earn 0, 1, 2 and 3 stars; when you do that, you earn a crown.

There are also funny Game Center achievements like "form a monster shaped like a hot dog".


Curiously, I've seen this game criticised both because it's "only" a logic game (by people that expected another action game like Cut the Rope) and because it is too easy as a logic game (by people that expected some hard core logic puzzle).

I don't think those criticisms are fair. Clearly, the first thing that strikes while playing the game is the incredible quality of the presentation: the animations are beautiful and full of humour, and the sound is great too. However the puzzles, while not terribly hard, can be challenging, especially if you want to earn all crowns. I've had many a-ha! moments when an elusive alternative solution finally clicked. Frankly, I don't think we could expect anything more than this from a game that is designed to sell millions of copies.

Every time I play, I'm amazed by the beauty of the level select screen. As you flick through the pages, the image in the background zooms out, sort of like in Powers of Ten™, starting from a cup of tea, through the roof of the house, to show the whole neighborhood (for now; it's easy to guess that we'll keep zooming out with future updates).


An update was released just today, adding 25 more levels, bringing the total to precisely 100. Even that way, and even playing each level multiple times to get the crown, it still feels a bit short, and you're left begging for more. But I think the main reason for this is that the game is so utterly enjoyable that you'd want to keep playing. Hopefully Zeptolab will continue to release updates in the future, like they did with Cut the Rope.

What do you think, is this game worthy of being labelled nontrivial?

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.

Wednesday, February 20, 2013

Review: Khalou for iPhone and iPad

Khalou is a very nice free puzzle game for iPhone and iPad by Aurelien Wenger.

The instructions are only in French, so understanding the rules might be difficult, but don't despair! I'm here to help.
The game is played on a 4x4 board, filled with stones. Stones are white on one side and black on the other, and are randomly placed at the beginning:
The goal is to make all stones white. This is done by making a number of moves, where all the stones in a group are turned upside down.
As you can see in the instructions page, the only allowed moves are:
  • Turn all 4 stones in a row, column, or major diagonal;
  • Turn all 3 stones in a L shape, anywhere on the board.
The instructions continue with an example:
At the top is the start position. Then the first and second columns are toggled, leading to the position in the middle. Then a L-shape in the center of the board is toggled, leading to the bottom left position. Then the final L-shape leads to the solved state in a total of 4 moves.

Now if you think about the rules for a moment, you'll realise that the L-shape moves would be all that's needed to solve the puzzle, because there is a sequence of three L-shape moves that toggles a single stone, and could be applied all over the board (figuring out the sequence is left as an exrcise for the reader).

The interesting thing is that, with the full set of rules, all positions can be solved in a maximum of 5 moves. It took me some time to get the hang of it, but when it finally clicked, attempting to always solve the puzzles in no more than 5 moves is an interesting—and difficult—challenge.

The game also has a scoring mechanism, if you're so inclined. When you start playing, you have a time limit of 5 minutes. During that time you must solve as many puzzles as you can; for each puzzle solved, you score points depending on the number of moves and the time taken. But be careful, because if you take more than 5 moves, your score is always 0. At the end of the 5 minutes, your total score is computed and uploaded to Game Center.

Overall, this is a nicely presented way to flex your brain muscles with come challenging, but not overly difficult, logical reasoning.

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.

Sunday, February 17, 2013

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.

Friday, February 15, 2013

Review: Lazors for iPhone and iPad

It looks like this is a good time to talk about Lazors, a brilliant puzzle game for iPhone and iPad by Pyrosphere. The game was originally released in 2010 as a paid app, but after a major update released last week, has changed its monetization scheme and is now free. There is the possibility of buying hints through in-app purchases, but that's completely optional.
The changes seem to have propelled Lazors to the top spots in the charts all over the world. At the time of writing, it's #2 in the US in the Free Apps chart, which is no small feat.
When these things happen, one thinks that there is still hope for humanity. Or for puzzle game developers, at least.

The goal of the game is to deflect a laser beam so that it passes across one or more specific points.This is an idea that has been used multiple times in the past, but usually in this kind of games one starts with an empty grid and needs to add and rotate mirrors or prisms. In Lazors, instead, the grid is already populated with square blocks, which need to be moved around. Blocks may be moved in any free cell of the grid (i.e. this is not a sliding blocks puzzle).

There are a few different types of blocks:

Normal blocks, which reflect the beam at a 90 degrees angle:
Glass blocks, which split the beam in two: part is reflected and part passes through the block
Dark blocks, which just absorb the beam:
Additionally, some blocks may be nailed in position so they can't be moved:
As far as I know, every puzzle has a single solution.
The great thing about these puzzles is that the play area is often quite small (4x4 is a common size), but the solution isn't necessarily easy to find, and might require many reflections in a small space.

The game contains 120 puzzles, split into packs of 10. All packs are accessible from the start, but the puzzles in a pack must be completed in order. This is where buying hints might be useful; also note that when you complete a pack you get some extra hints for free.

Each pack has a theme, e.g. "Braid" features two intersecting lasers instead of one, "Tiny" has particularly small grids, "Darkroom" uses dark blocks, and so on.

In terms of logical reasoning, I found that using logic helps, but often times I reached the solution just by accident. The limited size of the boards means that there are often not that many possible positions of the blocks, so one can reach the solution even by random tinkering. This should make the game appealing to casual players that are just looking for a quick distraction and are not interested in deep thinking.

Graphics are simple, clear, and very well done. I love the transparency effect on the glass blocks.
There's also some appropriate sound effects which add to the atmosphere.

Overall, this game is a perfect execution. Simple rules, ingeniously used to produce devious puzzles of apparent simplicity, and a no-frills interface that gets the job done flawlessly.

Well done Pyrosphere!

Update 2 March 2013: version 2.1 has been released with new features.

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.

Wednesday, February 13, 2013

Review: CounterBalancE for iPhone and iPad


CounterBalanceE is a logic puzzle for iPhone and iPad by George Menhorn which was originally released back in 2009.
A free version called CounterBalancE Lite is also available.
According to the app description, the game was inspired by a puzzle created by Craig Kasper.
The concept is pretty good and original.
You start with a grid containing some holes and some labelled nodes, like this:
You can tap holes to turn them into extra nodes; this will create links to the closest labelled nodes in the same row or column, if they exist.
The goal is for the total length of the links starting from each labelled node to be equal to the label of the node. So the solution of the above puzzle would be:
Of course this is an easy puzzle; the game contains about 100, of increasing difficulty, with the largest ones using a 9x9 grid.
Note that the solution above is not unique, because you could put an extra node in the bottom left corner. However, that node wouldn't contribute to the solution in any way since it wouldn't develop any new link to a numbered node. This is true for every puzzle included in the game: there is always a single solution except for the occasional possibility of adding additional, isolated, nodes.

Can the puzzles be solved with logic alone, without resorting to trial and error?
I suspect they could, however the game doesn't give the player the means to do so.
As an example, here's one of the puzzles at the highest difficulty level:
At first glance this might seem discouraging, but simply counting the lengths of the possible links, one can exclude a good number of cells:
Then, with a few more logical steps never involving trial and error, the solution is eventually reached:
Unfortunately to do this I had to print the puzzle and solve it with paper and pencil, because the game doesn't allow to put crosses on the board.

That's a shame: simply adding the ability to put down a cross by tapping and holding on a cell would make the game a lot deeper and enjoyable. As it currently is, the more difficult puzzles feel more like randomly moving nodes around attempting to get closer to the solution.

Update 14/02/2013: George Menhorn kindly answered to this review, promising to add this feature in a future update. Thanks George!

Another annoyance is that the current position isn't saved when sending the app to the background, so if you don't solve a puzzle in a single session, you risk having to start from scratch the next time you run the game.

A final nitpick is that the red/green color of the nodes is the only clue (short of counting the length of all the links) of whether a node is correctly connected or not. This might make it difficult for color blind people to play the game. For example here is a simulation of how a person with protanopia would see the puzzle above; it's pretty difficult to see that one of the 4's is of a different color.

This is still a very good logic puzzle and for 99 cents I can wholeheartedly recommend it, but if the user interface were improved, it would become excellent.

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.

Monday, February 11, 2013

Welcome!

There are dozens of logic games released weekly in the "Puzzles" category of Apple's App Store.

Most of them are—by definition—mediocre. Or, as a mathematician could say, "trivial".

Some of them are good, very few are brilliant.

I've been interested in logic puzzles for many years, and by now have grown strong opinions about what I think makes a good puzzle. If you like to play with your brain, this is the place to look for in-depth reviews. Maybe I'll help you find some hidden gem.

Mind you: I will occasionally talk about high profile titles, with high budget productions and terrific presentations. Most of the time, however, I'll be dealing with simple games from a indie developers; the important thing is that they are original, challenging, enjoyable.

In a word, nontrivial.


©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.