The graphics of Kublitz Cube are intended to represent a large cube made up of 27 smaller cubes, or cubelets - hence the name Kublitz, a word that sounds the same. Three key features of the Kublitz Cube cubelets are:
The large cube (often referred to as just 'the cube') can also be considered as comprising 9 layers of 9 cubelets: a front layer and a back layer; a top layer and a bottom layer; a right layer and a left layer; and the middle layers lying between each of these pairs.
The large cube is designed so that it has a goal, or reset, state, in which the 9 cubelet faces of each layer of 9 cubelets are the same colour. This is equivalent to the state in which the colours displayed on the outside of every one of the 6 faces of the large cube are all the same colour (a different colour for each of the 6 faces), as shown below. This is effectively the same goal state as a traditional physical cube.
To demonstrate that the opposite faces of a cubelet are the same colour, if we rotate the cube 180 degrees around the top-bottom axis, it now appears as follows:
Note how the cubelets at the front, which were displaying red on their forward-looking faces, are now at the back, displaying red on their forward-facing faces - the faces that had been backward-facing when the cubelets were at the front of the large cube. Likewise, you can see that the cubelets on the right that were displaying blue on their right-facing sides are now on the left, but still displaying blue on their right-facing sides.
This design, and the view you get as shown above, means that you are able to know what colour is on every face of the large cube, since the opposite side of every hidden face, which has the same colour, is visible. This is a major difference, and improvement, on traditional physical puzzle cubes and their visual representations.
You are able to rotate, in increments of 90 degrees, the 9 layers of 9 cubelets on the outside of the large cube in either a clockwise or anticlockwise (counterclockwise) direction. This, of course, disturbs the colours displayed on the 6 faces of the large cube, so that they are no longer all displaying a single colour. A clockwise turn of the right side by 90 degrees, for example, leads to the following state of the cube.
The cube may also be rotated about any of the three axes in increments of 90 degrees, as demonstrated by the first two images above.
By carrying out many layer rotations, the colours on the external large cube faces can become jumbled up. The objective of the puzzle is to carry out your own rotations so that the large cube is restored to its goal state, with the colours displayed on the outside of every one of the 6 faces of the large cube being the same colour.
Cube manipulations and notation
To rotate a layer in a certain direction, first ensure that the button with the word 'Layer' in it has a green background, or, if not, tap on the button to make it green.
There are 12 arrows at the corners of the cube concerned with rotating the 6 outer layers.
Near each pair of arrows you will see a single letter, which refers to the layer to be rotated when the arrows near it are tapped:
Note: to be clear about which layer is which, in the reset (goal) state the Front displays red, the Top white, and the Right blue.
Above the cube, you will see a table, whose six middle columns display one of these 6 letters in the first row. Below each of these headings you will see three cells containing a letter denoting a type of rotation. These are buttons, which you may also tap to rotate the layers. Their meanings are:
We refer to these buttons by the column heading followed by the letter of the cell, e.g. FO, BA or RI. So, pressing the FO button causes a clockwise rotation of the Front layer by 90 degrees, while pressing the BA button causes an anticlockwise rotation of the Back layer by 90 degrees.
Important: Please note that the terms clockwise and anticlockwise are always used to indicate the direction of rotation when facing that particular side or layer from the outside of the large cube. This means that an anticlockwise rotation of the Back layer looks like a clockwise rotation when viewed from the front.
In addition, if you have a touchscreen, you can rotate each of the layers of 9 cubelets by 90 degrees clockwise or anticlockwise by a slide action on any of the outward looking faces on the Top or Front only (N.B. those on the Right are not touch-sensitive). To rotate a layer, select a face on the perimeter of the layer (90 degrees to the main surface) and slide it in the desired direction. This is also the face you would hold with a physical cube to rotate that layer. So, to rotate the Top layer in a clockwise direction, make a leftwards sliding motion on any of the three cubelet faces at the Front along the Top edge.
Rotating the complete cube
To the left of the rotation buttons at the top, you will see two buttons: one with the word Layer and one with the word Cube. Initially, the Layer button has a green background, signifying that any rotations are to be carried out on the relevant layer. If you tap on the 'Cube' button, this then takes the green background to signify that any rotations are to be applied to the entire cube.
So, to rotate the entire cube, first make sure that the 'Cube' button has a green background, or, if not, tap on the button to make it green. Then simply use the same arrows or 'O', 'A' or 'I' buttons as for rotating layers, but now the entire cube will rotate rather than just the particular layer.
Please note that a clockwise rotation of the cube when viewed from the Front side is the same as an anticlockwise rotation when viewed from the Back side.
Below the Cube button is one called Temp, with a gold background. Pressing this when the Layer button has the green background has the effect of switching the Cube button on - but only temporarily. As soon as the cube needs to be redisplayed, e.g. after a cube rotation, the Layer button is reselected. This is very useful, as you will normally be using Layer rotations, but may occasionally need to carry out one cube rotation, before continuing with layer rotations. Just tap Temp before you do the single cube rotation.
To the right of the Cube is a table entitled Top Tools. This includes 8 icons, each of which, when tapped, carries out a sequence of rotations intended to make a particular change on the Top layer, while leaving the two lower levels unchanged. These make it easier for you and make solving the Cube less error-prone.
These tools are described fully later, under Solving the Cube. Try them out on the cube when it is in its goal state (after tapping the Reset button), as this makes their effects easier to see.
Starting the puzzle
To begin the puzzle, press the New button. This carries out many random rotations of the layers, and many random cube rotations. Then, use the various arrows or rotation buttons, and also the tool buttons, to restore the cube to its goal state with each side of the large cube showing only one colour.
To the right of the rotation buttons at the top is a pair of buttons, labelled Front and Top. By default, the Front button has a green background, while Top has a white background. This signifies that the current view of the cube shows the Front face with its cubelet faces looking square. If the Top button is tapped, its background becomes green, and the view of cube changes so that the Top cubelet faces look square. This view is particularly useful when using the Top Tools to solve the last layer of the cube (see below).
The layer letters in the table at the top, above the rotation buttons, are also buttons, concerned with which layers you view. The All button to the right of these is also such a button. Each one has either a green or a white background. Their use is described next.
If you press the All button when it is white, it changes to a green background, and all the layer letters also change to a green background. In this state, all layers are shown (the default). If you then press any of the layer buttons, its colour changes to white and this layer is no longer shown.
If you press the All button when it is green, it changes to a white background, and all the layer letters also change to a white background. In this state, no layers are shown - the cube disappears. If you then press any of the layer buttons, its colour changes to green and this layer is then displayed.
Below the cube, between the Undo and Reset buttons, are buttons labelled 1 to 5. These control the gap between the cubelets. 1 means there is a gap of one quarter the size of the cube, while 5 means the gap is 5 times this. The selected gap setting is shown in white, while the others are shown in silver.
The Expand button, with a gold background, in the table at the top, lets you see a brief display of the cube with all 5 gaps, from 1 to 5, before the view changes back to its original gap. This can be useful if you're viewing the cube with a small gap, and wish to briefly see all colours. This is also activated whenever the New button is tapped.
These view buttons give you great control over how the cube is displayed. For example, when starting off a new puzzle, you would probably want to view the cube with a large gap, so that you can see all the cubelet colours. Towards the end, when some layers are complete and you want to use the Top Tools, you might want to employ a small gap and view only the Top or the top two layers.
The Undo button simply restores the cube to its previous position. You can keep pressing the Undo button to undo previous rotations; to undo the effect of pressing a Top Tool button, a single Undo press is adequate. There is no theoretical limit to the number of rotations you can undo - it should continue to undo moves until you end up where you started (after opening up Kublitz Cube, or after pressing the New or Reset buttons).
Please note that if you have made a 180-degree rotation by pressing one of the 'I' buttons, then only one press of the Undo button is required to undo it; however, if you have carried out a 180-degree rotation using two separate presss of arrows or the 'O' or 'A' buttons, then two presses of the Undo button are required to undo it.
The Reset button takes the cube to its unjumbled state, i.e. to the goal state, with all sides displaying only one colour. This is useful for trying out the Top Tools or your own sequences.
Tap the device back twice to exit the application. The current state is remembered so that you continue when you open it up again.
Solving the Cube
If you are new to the Cube, you will soon learn that solving it is far from easy. This is hardly surprising since there are billions of permutations, and some people have taken decades to solve the traditional physical Cube (and most people who have started it have never completed it). Below, however, we show you an approach to going about this; not only that, but we hope that you will be able to remember how to solve it.
The approach to solving the cube is suitable for beginners, and uses the Top Tools (or rotation sequences) that, we understand, were first developed by David Singmaster. David Singmaster also developed a widely-used notation for describing moves and solutions; however, here we use a notation devised by David Wolstenholme, as it results in word-like strings of letters that are easier to remember.
The basic notation is as described above for the buttons, where we use the letters F, R, T, B, L and D for the layers, and specify rotations of these layers by adding on either an O (clockwise 90-degree rotation), an A (anticlockise 90-degree rotation) or an I (180-degree rotation). So, LA means turns the Left layer 90 degrees anticlockwise.
We use a three-letter specification for cube rotations, in which we add the letter C to the end to signify that the entire cube is to be rotated. So, FOC means that the entire cube is to be rotated around the Front-Back axis in a clockwise direction when viewed from the Front. Note that the cube rotation FOC is the same as the cube rotation BAC.
In the tool sequences below, we generally join two specifications of layer rotations together to form a 4-letter 'word'. So, ROTA specifies a clockwise rotation of the Right layer followed by an anticlockwise rotation of the Top layer.
As will be seen, these 4-letter 'words' and the 3-letter cube specifications often form recognizable words or names, or maybe sequences of letters that sound like words. Examples include: FOTO, ROC, BAC, ROTA, RITA, ROTI, or RIFA. This is the primary reason for choosing the notation above, since we humans are good at remembering words and can build stories around them to help us remember them.
Apart from the cubelet at the middle of the large cube, which is grey on all sides, all other cubelets display either one, two or three of the 6 other colours.
Remember that while the individual layers on a cube can rotate, the relative positions of the centre cubelets on each face will remain unchanged. In Kublitz Cube,
Also, if you have the white centre cubelet at the top and look down, you will find that the centre cubelets of the sides are always ordered red, green, pink and blue as you move clockwise. Please note that if you have a physical cube, the colours and their relative positions may be different.
When trying to solve the cube, it is not enough just to get the pieces into the correct position; the pieces also have to have the correct orientation (that is, the colours have to be facing the correct way). Next we introduce two concepts concerned with orientation of the pieces.
You will often find that you would like to 'flip' an edge cubelet. By this, we mean that we would like to take an edge cubelet that has a certain colour on one side of the large cube and do something so that it ends up with the other colour on this side.
You will often find that you would like to 'twist' a corner cubelet. By this, we mean that we would like to take a corner cubelet that has a certain colour on one side of the large cube and do something to it so that a different colour ends up on this side. Because it shows three colours, the effect of doing this is that the colours on the outward-facing sides of the cubelet appear to have twisted round, either clockwise or anticlockwise.
The diagram below shows an anticlockwise twist for the Front-Right-Top corner cubelet. See how the blue colour has moved anticlockwise from the Right side to the Top side.
Corner twists are probably less easy to think about and understand with Kublitz Cube - and easier to get wrong - than with a physical Cube. This is because you can see colours not only on the outside of the Cube, but also on other faces. This means that when you look at the three visible colours, these are not necessarily the outward-facing colours. For example, the same cubelet, if moved around to the Front-Left-Top position, looks as though it needs a clockwise twist to move the blue to the Top. This is because the red side you are seeing is not outward-looking.
To help your thinking about this, look at the visible colours and determine whether a clockwise or anticlockwise twist is required. Then count up the number of visible colours that aren't outward-facing; if the number is even (0 or 2), then the actual twist required is this; if the number is odd (1 or 3), then the actual twist required is the opposite of this. So, for this Front-Left-Top cubelet, the visible colours suggest a clockwise twist. However, as 1 colour (red) is not outward-looking, the actual twist required is the opposite: anticlockwise - as we saw before.
How to flip and twist
As an example, look at the Front edge of the Top layer in the reset state. All the cubelets are white on the Top and Red at the Front. To flip or twist them all, simply do FO to bring these cubelets to the Right edge, then RO to move them back up to the Top, then TO to bring them back to the Front edge. Now, they all have red on the Top and white on the Front - all flipped or twisted.
This has had the desired effect of flipping or twisting these three cubelets. However, every one of the 9 layers has been affected by these moves. Next, we look at Top Tools - some sequences of rotations that have no impact on the bottom two layers.
A Top Tool is a sequence of rotations that is designed to achieve a certain result on cubelets in the Top layer. There are four basic tools described here.
These four tools are not only useful but also easy to describe, since, when considering the Top layer and the two layers beneath it, they have an impact on the Top layer only. The bottom two layers end up unchanged by the application of these tools, so you can make use of them safe in the knowledge that only the Top layer of these three is affected. Each tool is focused on either edge or corner cubelets, and is designed to change either the position or the orientation of some of these cubelets.
Many tools can, of course, be used in more than one way: a screwdriver, for example, can be used not only to tighten a screw, but also to untighten it, i.e. to reverse or undo the impact. These tools can also be used in reverse.
The Top Tools are laid out with the names of the four tools and, underneath each of these, two icons, which act as buttons. The one on the right (beneath the >> symbol near the top, carries out the sequence of rotations specified; the one on the left, beneath the << button near the top, runs the sequence of rotations that undoes or reverses these.
So, if the main sequence of rotations is FOTO ROTA RAFA, as for Flipper, then the first rotation for the reverse will be on the same layer as the last rotation of the basic sequence, i.e. on the F layer, but in the O direction instead of A, i.e. FO. The next rotation will be on the R layer, but this time in the O direction. The complete sequence for the reverse of Flipper is: FORO TORA TAFA. Note that the I direction remains unchanged when reversed, since a 180-degree rotation requires another 180-degree rotation to reverse it.
To distinguish the uses of the tool, we add the word Reverse in front of the name when it is used in reverse, e.g. Reverse Flipper.
These tools can also be used when solving a physical Cube. The notation has been designed to be fairly easy to remember. You only have to remember the main set of sequences, since you can always work out the reverse sequence from that, as above.
These tools will be used at most stages of solving the cube, so we will describe them all now. You will see associated with each tool, and its reverse, an icon that describes the impact. This summarizes the impact by pointing out which corners have been twisted, and in which direction, which edges have been flipped, and which pieces are moved to another location.
The intensity of colours is also important: the intense colours and black signify the primary, intended impact we are looking for, while the less intense colours mean that these changes take place but they are not of primary importance - they are just side-effects.
|FOTO ROTA RAFA|
Flip the edge pieces on the Right and Front sides.
|FORO TORA TAFA|
Flip the edge pieces on the Back and Front sides.
|LOTA RATO LATA ROTI|
Swap the positions of the two Right corner pieces.
|TIRA TOLO TARO TOLA|
Swap the positions of the two Right corner pieces.
|RATA ROTA RATI ROTI|
Twist three corner pieces (all except the Back-Left corner) anticlockwise.
|TIRA TIRO TORA TORO|
Twist three corner pieces (all except the Back-Left corner) clockwise.
|RITA FOBA RIFA BOTA RI|
Move the three rightmost edge pieces around one position anticlockwise, as if looped together.
|RITO BAFO RIBO FATO RI|
Move the three rightmost edge pieces around one position clockwise, as if looped together.
The overall cube-solving strategy employed here is: Fix the four corners of the first layer; then fix the edge pieces in the first two layers of each of the sides; and, finally, solve the last layer.
Fix the four corners of the first layer
We will use white as the first layer. Our objective is to correctly position and orientate all the corner cubelets that have a white side - with the white side displayed on the side with the white centre cubelet.
This is the easiest part of solving the cube, since you do not need to worry about how you disturb the other layers. You can try positioning and orientating the corner cubelets with a white side using your own set of rotations, such as those described next, where the white centre cubelet is positioned on the Top.
First, bring up one of the corners with a white side so that it has its white side on Top. Then rotate the Top so that colours of the sides of the corner cubelet match the colours of the centre cubelet on the sides. In the image below, the white/red/blue corner has its sides correctly matching up with the white, red and blue centre cubelets.
If you're having problems, our recommended approach is to bring the corner piece you wish to position into the Top layer to the Front-Right-Down corner, directly beneath the corner in the Top layer into which it should move. The images below show the way to achieve this in the situation where three of the white cubelets are fully in place and aligned, and the last one is in the Front-Right-Down corner and correctly aligned for moving to the top. Carry out the sequence BO RO BA to bring it to the top: BO moves the back two corners out of the way, RO brings the last corner up to the top, then BA brings the back two corners back into place.
In the situation that the cubelet you wish to move up isn't correctly aligned, you need to twist it first. The images below show the result of turning the cube over, using rotation RIC, so that the misaligned cubelet is now at the Back-Right-Top, then using Reverse Twister to re-align the corner cubelet, and finally using RIC again to bring the cubelet back to the Front-Right-Down corner.
Fix the edge cubelets in the first two layers
Once the corners of the first, white layer have been fixed, we can see that to complete the top two layers (the white layer and the one between white and yellow) we just need to put the eight edge cubelets in these layers into their correct positions with correct orientation.
To do this, we will use the Looper and Reverse Looper tools as our main tools, supported by the Flipper and Reverse Flipper tools and some easy rotations to get the cubelets into the correct starting positions for using these tools. We operate on one of the side colours (all but white and yellow) at a time. To begin doing this, we always start off by putting the first, white layer at the Back if it's not already there (ROC).
Our basic approach is that we work on the Top layer and use the Looper to push the edge cubelet we want to have at the Back edge from the Front to the Right edge, then use the Looper again to push the cubelet we want to have at the Right side from the Front to the Right, which also moves the cubelet that was there to the Back edge where we want it.
To demonstrate this, the image below shows our starting position for doing this on the blue side, where we have the blue/white edge cubelet at the Front (blue on Top). Running the Looper tool pushes this cubelet to the Right edge.
We then move the blue/pink edge cubelet into position and use the Looper tool again to push it to the right, its final position, and also the blue/white cubelet to the Back - again, its final position.
This is a neat use of the tool, since we move the two edge cubelets into position with two uses of Looper. However, we had the ideal starting position in this example, where both edge cubelets were already at the Front and correctly orientated. Often we find that the required edge pieces are not at the Front, and, once moved there, they are not both correctly orientated. So, we need to move edge cubelets forward to the Front layer, and to flip incorrectly orientated pieces.
Bringing edge cubelets to the Front layer
If the edge piece you are interested in is in the Back layer or the layer between the Back and the Front, and needs to be brought to the Front layer ready for use of the Looper as just described, keep the white side to the Back and then turn the Cube so that the cubelet to be brought to the Back is on the Top and simply use the Looper or Reverse Looper to bring it to the Front.
Flip incorrectly orientated cubelets
In this example, where we have already used these techniques on the blue, red and green sides and are trying to complete the pink side, we can see that the pink/white edge cubelet is incorrectly orientated if we were to use Looper to move it to the Back, as white would be on the Top not on the Back side. It therefore needs to be flipped. The pink/green cubelet is also mis-orientated, so also need to be flipped. To flip one or two cubelets, first rotate the Cube so that the white side is on the Down side. Then rotate the Top layer so that the piece you want to flip is in the correct position for flipping by the Flipper or Reverse Flipper (and make sure that any pieces you don't want flipped aren't in a position to be flipped as well).
We can now move the white side to the Back, then use Looper and some simple rotations to push these two edge cubelets into place, leaving us with two layers complete.
Once the first two layers are complete, only one layer needs to be solved: the layer that should display yellow on its main side. To solve this we first bring the yellow side to the top.
Now, as we are going to make changes only to the top of the three layers, principally by using the Top Tools, it is appropriate to change the view of the Cube so that the Top of the cubelets appears square - better matching the layout of the Top Tools icons. We only need to see the Top layer and the centre cubelets of the sides, so we can also reduce the gaps between the cubelets to 2, as shown in the image below.
Each stage makes use of only one of our four tools. You may have noticed that the four tools vary significantly in their side effects, from Flipper which has many, to Looper, which has none. As we move through the stages we use a more refined tool.
The order in which the tools are used and their names have the same initial letter, which helps you to remember them:
To begin the last layer, now on the Top, we first form a yellow cross by ensuring that the four edge cubelets have yellow showing on the Top. It is important to note that we don't, at this stage, care whether or not they're in the correct positions (i.e. whether their side colours match up with the centre cubelet of the sides).
Clearly, if some of them are not displaying yellow on the top, we need to flip them using Flipper or Reverse Flipper. Now, you will find that you begin with one of the following scenarios:
If none of the edge cubelets were showing yellow, you would first run Flipper, which results in two yellow edges opposite each other, then rotate the Top 90 degrees (TO or TA) and run Reverse Flipper.
We now have the yellow cross (edge cubelets correctly orientated but not necessarily correctly positioned), so we can move to the next stage.
Now we rotate the Top to see whether we can get all the corners in their correct positions, regardless of the fact that they may not have yellow showing on the Top. So, we're looking to position the red/blue/yellow corner in the corner where the red, blue and yellow sides meet, for example. If you find that you can rotate the Top so that all four are correctly positioned, then this stage is complete.
If the four corners aren't all correctly positioned, then we need to look to find two that can be correctly positioned, leaving the other two incorrectly positioned. This often seems difficult to do, due to the fact that corners may be twisted, but do persevere and you will find two that can be correctly positioned.
Once you have found the two corners that are correctly positioned, you need to swap the positions of the two that aren't. If the two that need swapping are on one side, we just rotate the cube to bring them to the Right side and use the Swapper.
If the two that need swapping are diagonally opposite each other, just use Swapper to swap over any two corners. After doing that, you will find that you then have two corners that need swapping on one side, so you can just rotate the cube to get these on the Right side and use Swapper again.
We now have the edge cubelets correctly orientated and the corner cubelets in their correct positions, but not necessarily correctly orientated.
3. Orientate corner cubelets
Now that the corners are in their correct positions, you will probably find that some of them are not correctly orientated and need twisting. If you're lucky enough to find that they're all correctly orientated, just move on to the last stage.
Check each corner in turn to see what sort of twisting is required to orientate it, if any, and count up the numbers needing clockwise and anticlockwise twists. Clearly you're going to use the Twister or Reverse Twister tool, but it is not always easy to work out how to use them. If you think about what they do you should be able to work out how to use them, but the following guide gives details.
Don't forget the issue about corner twists - the twists required are not necessarily those that seem to be required by looking at the visible colours. The image below, of a Top layer, shows in parentheses, for every corner, the twist that appears to be required if we look at the visible colours and wish to end up with the yellow colour on Top. After that is the actual twist required. In this, O means clockwise, A means anticlockwise. We can see that we require two clockwise and two anticlockwise twists. From this point, we would do TO then use Twister, then TO and Twister again, to end up with all cubelets displaying yellow on top.
You may find that all the edge cubelets are correctly positioned. If not, you may find that 3 or 4 edges are in the wrong position.
If there are four incorrectly positioned edges, run Looper, which results in three incorrectly positioned edges. Then bring the correctly positioned side to the Left and run either Looper or Reverse Looper, as appropriate, to position the three remaining edge cubelets correctly and complete the puzzle.
In the image above, there are only three incorrectly positioned, so we can just use Reverse Looper to complete the last layer, and the puzzle.
Our four top-layer tools can, of course, be used with a physical cube - and can you really say you've solved the cube until you've solved a physical cube? If you want to solve the cube without having instructions around, you'll need to remember the tool sequences. To help you remember these, here are some mnemonics. You'll have to get used to thinking of eating rat, and know that a roti is a flat bread, often eaten as a wrap.
FOTO ROTA RAFA (photo rota rougher)
Flipper and his dolphin friends are forming a photo rota to have their pictures taken in turn, but the rougher sea may prevent this.
LOTA RATO LATA ROTI (lotta rat-oh latter roti)
Lunch arrives: Cheese and a lotta rat! Oh, I'd rather swap the latter for a roti.
RATA ROTA RATI ROTI (ratter rota ratty roti)
The Ratter Rota shows the rat-catchers' work plans for the week, but with a twist, as it says who has to make the ratty roti for lunch.
RITA FOBA RIFA BOTA RI (Rita Fo B.A. reefer boater rye)
Loopy Rita Fo B.A. is celebrating her graduation smoking a reefer, wearing a boater and drinking rye whiskey.
Also, don't forget that the initial letters of the names of the tools are the same as the initial letters of First, Second, Third and Last - the stages at which they are used when solving the final layer.
Finally, remember that you can work out the sequences of the Reverse tools by carrying out each of the rotations in the main sequence in reverse order and in the opposite direction. It's also worth knowing that for the Reverse versions of Flipper, Twister and Looper, running the main tool twice in succession yields the same intended impact as the Reverse tool (but double Flipper has different side-effects compared to Reverse Flipper).
About Kublitz Cube
This Kublitz Cube application has been designed by Dr David Wolstenholme, who also developed the idea of separated cubelets to enable the colours on all sides to be known without turning the cube.
This software may be used for personal purposes only. It may not be used for commercial purposes.
The software, code and script of this application may not be copied or be distributed to others.
The software, code and script may not be altered in any way.
Copyright of the software, code and script, and its help documentation, is owned by TopAccolades Limited. No part of the software, code, script or documentation may be copied or used in another application or document.
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TopAccolades Limited shall not be liable for any damages whatsoever arising out of the use of or inability to use this application or the provision of or failure to provide support.
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