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Heise method

2018-05-07T06:46:38Z

Username:

{{Method Infobox
|name=Heise
|image=Heise_method.gif
|proposers=[[Ryan Heise]]
|year=2003
|anames
|variants
|steps=4
|algs=0
|moves=40-
|purpose=<sup></sup>
* [[Fewest Moves]]
* [[Speedsolving]]
}}
The '''Heise method''', invented by [[Ryan Heise]], is a intuitive [[method]] which requires no [[algorithm]]s. It uses extremely few moves, but it may be difficult to get fast times using this method.

==Steps==

# Create four 1x2x2 blocks (also called [[Heise blocks]]), making sure that one color appears on none of the blocks. This color will be the color of the last layer. Note that these blocks do not necessarily have to be paired together when they are built. One of these blocks should be just two centers and an edge.
# Pair up the 1x2x2 blocks, while simultaneously orienting the last-layer edges. Note that you will now have all of F2L minus a corner/edge pair finished.
# Create two corner-edge pairs, and then solve all of the edges and two corners. This is typically a very difficult step for beginners to solve.
# Solve the final three corners with a commutator.

==Pros==
This method is more efficient than any of the main three speedcubing methods, and therefore it's also very good for fewest moves solving. Because there are no algorithms at all, users of this method generally become very good at intuitive blockbuilding and develop a high-level understanding of the cube.

==Cons==
Every turn has to be planned out because there are no algorithms, so fast turners will be disappointed. Some of the steps, especially the third step, can be very difficult to get used to, and beginning cubers might not understand enough cube theory to be able to use this method at all.

==Strategies==
===Step 1===
The first step is [[blockbuilding]]. Knowledge of [[F2L]] can help here, but it is important not to treat the step as just F2L minus a pair. If possible, you should try to plan the first two blocks during inspection. The second block will normally be the inner square, and it can help if the colours match the first block which will give a maximum range of possibilities for the third block. However, you should always be prepared to do things differently.

===Step 2===
Step 2 seeks to orient edge the upper edges while rotating the blocks into an F2L-1 state. Although not compulsory, orienting the edges now makes step 3 easier.

===Step 3===
The third step is the hardest stage to master, particularly the "two pairs" approach which seeks to simultaneously solve the last 5 edges and 2 corners. Ryan Heise's advice is:
<blockquote>First, master solving the 5 edges on their own (ignoring the corners), which you can do using only R-U moves (assuming the edges are already oriented). The last three moves will always be R-U*-R' with U* being one of U, U2 or U'. ... Then, you can try the same with two corners attached to two of the edges. You just try the same strategy as above, treating the corner/edge pairs as just elongated pieces that need to be kept intact. It is rarely possible to do this just using R-U moves.[http://twistypuzzles.com/~sandy/forum/viewtopic.php?f=1&t=6012]</blockquote>

===Step 4===
Step 4 is the 3-corner solve. Ryan Heise explains the 'intuitive' approach using [[commutators]].[http://www.ryanheise.com/cube/corner_3_cycles.html] Alternatively, there are [[Last Three Corners]] algorithm sets available.

==Variants==
===Old Heise===
[[Ryan Heise]] published an earlier version of his method in 2003/4. This early method used a different sequence of steps and made use of algorithms. The method averaged under 45 moves and was also a viable speedcubing method. The steps were:

# Create the four [[Heise blocks]] and join the blocks together (intuitive).
# Insert the remaining middle edge and simultaneously orient the top edges (Mostly intuitive).
# Insert the last corner on the bottom and simultaneously permute the top edges. 17 cases (or 28? including mirrors).
# Solve the [[Last Four Corners]]. 42 cases (or 84 including mirrors).

A notable proponent of this method was [[Andy Camann]] who adopted this method in 2004. He was able to achieve sub-17-second averages, which was close to his [[CFOP]] average.

Internet Archive links:
*[https://web.archive.org/web/20040803122903/http://www.progsoc.uts.edu.au:80/~rheise/cube/ Ryan Heise's 2004 page] (broken applets)
*[https://web.archive.org/web/20100326084444/http://s92824201.onlinehome.us/RyanMethod.htm Andy Camann's Heise pages] (broken images, but there are algorithms for step 3)

===Speed-Heise===
[[Speed-Heise]] is an algorithm set developed by Matt DiPalma. It seeks to systemize step 3 of the Heise method similar to [[ZZ]]. After step 2 the final F2L pair is created in the upper layer and fed to the Front-Right as in the [[Winter Variation]]. An algorithm from a 72-algorithm set (or a 24-algorithm simplified set) is then selected to solve all 4 LL-edges and 1 LL-corner, leaving just the last three corners unsolved.

===FLFL ===
The [[FLFL Method]] simplifies step 3 of Heise. It provides a few algorithms to separately solve the final bottom corner, leaving the [[Last Four Corners]] to solve.

===Heise as a beginner's method===
Since basically all 4 steps of a standard Heise method might be extremely hard for beginners, they could proceed as follows:

# Solve a layer without a corner.
# Solve two layers without an edge-corner pair by means of the working corner.
# Solve remaining edges by means of the working edge.
# Solve remaining corners.

If needed, see "External links" section bellow for details.

== See also ==
* [[Commutators]]
* [[L3C]]
* [[Snyder Method]]

==External links==

* [http://www.ryanheise.com/cube/heise_method.html Ryan Heise's tutorial]
* [http://hlavolam.maweb.eu/rubiks-cube-3x3x3#intuitive-puzzle-solving-method Simplified Heise-like solving approach] especially suitable for beginners

[[Category:3x3x3 methods]]
[[Category:Fewest Moves Methods]]
[[Category:3x3x3 speedsolving methods]]

Permutation

2018-05-02T08:28:14Z

Username:

'''Permutation''' is a mathematical term that refers broadly to rearranging or the rearrangement of objects. In puzzle theory, the term is applied to puzzle pieces. The permutation of pieces refers to their location on the puzzle or, equivalently, to the relocation required to place them in their correct location. One also speaks of a single piece's permutation to mean its location or where it needs to be moved, which contrasts with its [[orientation]], its state (flip/orientation) in place.

== Relation to orientation ==
Although (changes in) permutation and orientation suffice to characterize any legal move on many puzzles, they are in general not independent. In mathematical terms, the group of the puzzle cannot in general be decomposed as a ''direct'' product of the permutation group and the orientation group. For example, on the [[3x3]], the decomposition is instead a ''semi-direct'' product; a general permutation affects orientation.

Orientation and permutation may be viewed independently by restricting to ''pure orientation'' or ''pure permutation'', affecting one but not the other. For example, in [[3OP]] blindfold solving method, pieces are first oriented in place (trivial permutation), then permuted while preserving the orientation. Here, the precise definition of orientation affects which permutations preserve orientation, hence affect the notion of pure permutation.

== Permutation parity ==
On a puzzle with different types of pieces, the permutation naturally breaks down into permutations of the different piece types. For example, the full permutation of a [[3x3]] can be specified by the permutation of its 12 edges and the permutation of its 8 corners. On many puzzles, however, group theoretic considerations show that there are constraints on the possible permutations of different piece types. For example, every legal move on a 3x3 has an even full permutation; corner and edge permutations must be either even and even or odd and odd. This means in particular that a single pair of edges cannot be switched without also switching a single pair of corners.

A '''permutation parity''' refers to a situation where the full permutation cannot be corrected using only permutations of a single piece type. On a 3x3, this means odd corner permutation and odd even permutation, so that pair of corners and a pair of edges must be switched to ''fix the parity.'' This makes it impossible to treat the corners and edges completely independently, which has unpleasant consequences in 3x3 blindfold cubing. In cubes bigger than 3x3, the center pieces of the same type and of the same color are not distinguishable, which makes it impossible to determine the parity of their permutation from centers alone. In 4x4 (or any even number) [[reduction method]]s, which solve the center first, this can lead a full odd permutation in the 3x3 phase that cannot be resolved without permuting the already "solved" centers, another example of a permutation parity.

== See also ==
* [[Parity]]
* [[Orientation]]
* [[Edge Permutation]]
* [[Corner Permutation]]

[[Category:Puzzle theory]]

Parity

2018-05-02T08:24:52Z

Username:

'''Parity''' in a puzzle describes whether a move or sequence of moves swaps pieces an even or odd amount of times. If a puzzle is described as having '''Even Parity''', only moves with even-parity are possible. If a puzzle is described as having '''Odd Parity''' then it can perform both Odd and Even parity moves. For example, a standard 3-cycle (ABC -> BCA) would have Even parity because it is actually 2 swaps A<->B and A<->C. Orientation of pieces is ignored when considering swapped pieces.

The term Parity is often misused in cubing. It is used colloquially to describe an odd permutation of pieces within a certain defined [[orbital]]. It is most commonly used to refer to certain situations that can arise on the [[4x4x4]] and [[5x5x5]] cubes when solving with the [[reduction method]]. The most commonly known example is referred to as OLL Parity, and comes about on cubes of size 4x4x4 and larger. OLL Parity on a 4x4x4 cube happens when two adjacent wing edges are interchanged with each other. When solving with the reduction method these two interchanged wing edges give the two piece edge group the appearance of being a flipped [[3x3x3]] edge. This leads to a case that is impossible to solve using outer layer turns only, and must be solved by performing an odd number of inner slice quarter turns to return the wing edge orbital back to an even permutation.

== See also ==
* [[Permutation Parity]]
* [[4x4x4 Parity Algorithms]]
* [[5x5x5 Parity Algorithms]]

== External links ==
*Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19800 Understanding Parity]
* [http://hlavolam.maweb.eu/parity-problem Parity problem] - detailed explanation of the term "parity problem" and its application on the 4x4x4 Supercube, even and odd permutation

[[Category:Puzzle theory]]

{{Stub}}

Parity

2018-05-02T08:24:32Z

Username:

'''Parity''' in a puzzle describes whether a move or sequence of moves swaps pieces an even or odd amount of times. If a puzzle is described as having '''Even Parity''', only moves with even-parity are possible. If a puzzle is described as having '''Odd Parity''' then it can perform both Odd and Even parity moves. For example, a standard 3-cycle (ABC -> BCA) would have Even parity because it is actually 2 swaps A<->B and A<->C. Orientation of pieces is ignored when considering swapped pieces.

The term Parity is often misused in cubing. It is used colloquially to describe an odd permutation of pieces within a certain defined [[orbital]]. It is most commonly used to refer to certain situations that can arise on the [[4x4x4]] and [[5x5x5]] cubes when solving with the [[reduction method]]. The most commonly known example is referred to as OLL Parity, and comes about on cubes of size 4x4x4 and larger. OLL Parity on a 4x4x4 cube happens when two adjacent wing edges are interchanged with each other. When solving with the reduction method these two interchanged wing edges give the two piece edge group the appearance of being a flipped [[3x3x3]] edge. This leads to a case that is impossible to solve using outer layer turns only, and must be solved by performing an odd number of inner slice quarter turns to return the wing edge orbital back to an even permutation.

== See also ==
* [[Permutation Parity]]
* [[4x4x4 Parity Algorithms]]
* [[5x5x5 Parity Algorithms]]

== External links ==
*Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19800 Understanding Parity]
* [http://hlavolam.maweb.eu/parity-problem Parity problem] detailed explanation of the term "parity problem" and its application on the 4x4x4 Supercube, even and odd permutation

[[Category:Puzzle theory]]

{{Stub}}

Parity

2018-05-02T08:23:14Z

Username:

'''Parity''' in a puzzle describes whether a move or sequence of moves swaps pieces an even or odd amount of times. If a puzzle is described as having '''Even Parity''', only moves with even-parity are possible. If a puzzle is described as having '''Odd Parity''' then it can perform both Odd and Even parity moves. For example, a standard 3-cycle (ABC -> BCA) would have Even parity because it is actually 2 swaps A<->B and A<->C. Orientation of pieces is ignored when considering swapped pieces.

The term Parity is often misused in cubing. It is used colloquially to describe an odd permutation of pieces within a certain defined [[orbital]]. It is most commonly used to refer to certain situations that can arise on the [[4x4x4]] and [[5x5x5]] cubes when solving with the [[reduction method]]. The most commonly known example is referred to as OLL Parity, and comes about on cubes of size 4x4x4 and larger. OLL Parity on a 4x4x4 cube happens when two adjacent wing edges are interchanged with each other. When solving with the reduction method these two interchanged wing edges give the two piece edge group the appearance of being a flipped [[3x3x3]] edge. This leads to a case that is impossible to solve using outer layer turns only, and must be solved by performing an odd number of inner slice quarter turns to return the wing edge orbital back to an even permutation.

== See also ==
* [[Permutation Parity]]
* [[4x4x4 Parity Algorithms]]
* [[5x5x5 Parity Algorithms]]

== External links ==
*Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19800 Understanding Parity]
* [[http://hlavolam.maweb.eu/parity-problem]] detailed explanation of the term "parity problem" and its application on the 4x4x4 Supercube, even and odd permutation

[[Category:Puzzle theory]]

{{Stub}}

Parity

2018-05-02T08:22:34Z

Username:

'''Parity''' in a puzzle describes whether a move or sequence of moves swaps pieces an even or odd amount of times. If a puzzle is described as having '''Even Parity''', only moves with even-parity are possible. If a puzzle is described as having '''Odd Parity''' then it can perform both Odd and Even parity moves. For example, a standard 3-cycle (ABC -> BCA) would have Even parity because it is actually 2 swaps A<->B and A<->C. Orientation of pieces is ignored when considering swapped pieces.

The term Parity is often misused in cubing. It is used colloquially to describe an odd permutation of pieces within a certain defined [[orbital]]. It is most commonly used to refer to certain situations that can arise on the [[4x4x4]] and [[5x5x5]] cubes when solving with the [[reduction method]]. The most commonly known example is referred to as OLL Parity, and comes about on cubes of size 4x4x4 and larger. OLL Parity on a 4x4x4 cube happens when two adjacent wing edges are interchanged with each other. When solving with the reduction method these two interchanged wing edges give the two piece edge group the appearance of being a flipped [[3x3x3]] edge. This leads to a case that is impossible to solve using outer layer turns only, and must be solved by performing an odd number of inner slice quarter turns to return the wing edge orbital back to an even permutation.

== See also ==
* [[Permutation Parity]]
* [[4x4x4 Parity Algorithms]]
* [[5x5x5 Parity Algorithms]]

== External links ==
*Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19800 Understanding Parity]
* [http://hlavolam.maweb.eu/parity-problem] detailed explanation of the term "parity problem" and its application on the 4x4x4 Supercube, even and odd permutation

[[Category:Puzzle theory]]

{{Stub}}

Parity

2018-05-02T08:22:03Z

Username:

'''Parity''' in a puzzle describes whether a move or sequence of moves swaps pieces an even or odd amount of times. If a puzzle is described as having '''Even Parity''', only moves with even-parity are possible. If a puzzle is described as having '''Odd Parity''' then it can perform both Odd and Even parity moves. For example, a standard 3-cycle (ABC -> BCA) would have Even parity because it is actually 2 swaps A<->B and A<->C. Orientation of pieces is ignored when considering swapped pieces.

The term Parity is often misused in cubing. It is used colloquially to describe an odd permutation of pieces within a certain defined [[orbital]]. It is most commonly used to refer to certain situations that can arise on the [[4x4x4]] and [[5x5x5]] cubes when solving with the [[reduction method]]. The most commonly known example is referred to as OLL Parity, and comes about on cubes of size 4x4x4 and larger. OLL Parity on a 4x4x4 cube happens when two adjacent wing edges are interchanged with each other. When solving with the reduction method these two interchanged wing edges give the two piece edge group the appearance of being a flipped [[3x3x3]] edge. This leads to a case that is impossible to solve using outer layer turns only, and must be solved by performing an odd number of inner slice quarter turns to return the wing edge orbital back to an even permutation.

== See also ==
* [[Permutation Parity]]
* [[4x4x4 Parity Algorithms]]
* [[5x5x5 Parity Algorithms]]

== External links ==
*Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19800 Understanding Parity]
*[http://hlavolam.maweb.eu/parity-problem] detailed explanation of the term "parity problem" and its application on the 4x4x4 Supercube, even and odd permutation

[[Category:Puzzle theory]]

{{Stub}}

Parity

2018-05-02T08:21:22Z

Username: update of external links

'''Parity''' in a puzzle describes whether a move or sequence of moves swaps pieces an even or odd amount of times. If a puzzle is described as having '''Even Parity''', only moves with even-parity are possible. If a puzzle is described as having '''Odd Parity''' then it can perform both Odd and Even parity moves. For example, a standard 3-cycle (ABC -> BCA) would have Even parity because it is actually 2 swaps A<->B and A<->C. Orientation of pieces is ignored when considering swapped pieces.

The term Parity is often misused in cubing. It is used colloquially to describe an odd permutation of pieces within a certain defined [[orbital]]. It is most commonly used to refer to certain situations that can arise on the [[4x4x4]] and [[5x5x5]] cubes when solving with the [[reduction method]]. The most commonly known example is referred to as OLL Parity, and comes about on cubes of size 4x4x4 and larger. OLL Parity on a 4x4x4 cube happens when two adjacent wing edges are interchanged with each other. When solving with the reduction method these two interchanged wing edges give the two piece edge group the appearance of being a flipped [[3x3x3]] edge. This leads to a case that is impossible to solve using outer layer turns only, and must be solved by performing an odd number of inner slice quarter turns to return the wing edge orbital back to an even permutation.

== See also ==
* [[Permutation Parity]]
* [[4x4x4 Parity Algorithms]]
* [[5x5x5 Parity Algorithms]]

== External links ==
Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19800 Understanding Parity]
[http://hlavolam.maweb.eu/parity-problem] detailed explanation of the term "parity problem" and its application on the 4x4x4 Supercube, even and odd permutation

[[Category:Puzzle theory]]

{{Stub}}

Intuitive solving

2018-02-20T14:41:13Z

Username:

Intuitive solving consists in solving the Rubik's cube without using any algorithm that you do not understand. In most methods, for example for the last layer, most algorithm are used in such way that there is an input cube in some state, then you apply the appropriate algorithm that you learnt by heart, and quite magically, the cube is in the desired state.

=== Overview ===

Intutive solving can basically be broken into two parts :
* solving most of the cube with intuitive moves ([[F2L|first two layers]] or more)
* solving the remaining pieces with [[commutators]]

You can use any existing method, remove all algorithm and try to do each step with your intuition only. You should be able to complete at least two layers that way. The [[F2L]] methods ([[CFOP]] (AKA Fridrich method), [[Petrus]]) can be done intuitively. Note that before doing the last pair, you have an opportunity to orient the edges. Finally you will need to do the last layer, essentially with [[commutators]].

The [[Heise Method]] is an intuitive method for solving the whole cube, but is very difficult to understand. Nevertheless you can use part of it to solve the first two layers minus one pair.

=== Intuitive F2L ===

==== Cross ====
Place four edges of one face, at their correct location and orientation. It's ok if they are rotated, but in the correct order, because you will always be able to align them by just rotating the chosen face.

You can notice that if an edge is on the opposite face in the correct orientation, you can move it to the correct face with the correct orientation with a half turn. If an edge is in the slice between those faces, you can always move it to the correct face with the right orientation with one quarter turn. Of course, you may need to rotate the destination face so that the edge arrives at the desired location, relative to other edges you have already placed.

You will obtain a cross. Turn the cube so that it is at the bottom.

==== Slots ====
After aligning the edges with the centers next to them, you will get four slots, one for each corner, that can contains two pieces : an edge piece and a corner piece. Notice that you can move some piece out one slot, for example the front-right-bottom slot (if you started with the bottom face), by doing R U' R or F' U F. This three moves are the following :
# Taking the piece out of the slot to the upper face
# Moving this piece out of the way
# Bring back the bottom edge at it's correct place (inverse of step 1)

Conversely, you can put a pair of pieces into one slot :
# Move the slot out, so that the destination is now on the scrambled face
# Move some piece into the destination
# Bring the destination back (inverse of step 1)

Of course, you will need to build pairs, so that you can insert them into the slots. To do so, notice that :
* You can break a pair when pieces are not well oriented relative to each other by hiding the corner piece from the scramble face by moving the appropriate slot out, moving the edge with the scrambled face, and the bring the slot back
* You can build one pair by hiding a corner by moving a slot out, bring an edge next to it, and then bring the slot back

If an edge or a corner is already in place, you can use the [[Keyhole F2L|keyhole]] method, which can be done intuitively. That's all you need to know. There are shortcuts of course, notably when you can form the pair and put it in the slot in three moves (see [[F2L#F2L 4|F2L 4]]).

=== Orienting edges before last F2L pair ===

To orient remaing edges, notice that if you store an edge in a slot, and take it out using the adjacent face, it will be rotated. For example, if you want to flip the front-top edge using the front-right-bottom slot, you can do the following sequence : R U' R' then F' U F.

By doing so, you will flip other edges too, so you must take into account the orientation of the edge currently in the slot so that you bring it out of the slot to the top face with the right orientation (yellow on top if the last layer is yellow). So if you have in the front-right-bottom an edge the has its yellow color to the right, the you must take it out with the F face. If it's in the other direction, you must take it out with the R face.

When you take the edge out, you must take care that it does not replace the other edge that you will place back in the slot. You may need to rotate the upper face to move it out of the way.

So each orientation will be 3 or 4 moves long :
# move some edge out of the way (optional)
# take the edge out of the slot
# bring another edge instead
# put this edge in the slot (inverse of step 2)

You are done when all edges the belongs to the top layer and are in the top layer are oriented (yellow on top). If one edge of the top face remains the the slot, it's ok. You will only need to take care of using the face the brings it out in the right orientation when doing the last pair.

Finally, do the last pair using only two faces : the upper face and another face the allows to bring out the content of the slot.

=== Last layer intutive solving ===

==== Rotating edges ====
Using the method above, the edges should be already oriented. If not, you will need a [[commutator]]. It can be composed with A = "flip an edge in the top face without changing anything else in the top face" and B = "rotate the top face to place another edge to be flipped at the intersection".

If you do not care about the orientation of corners, you can still rotate three edges without using a commutator. So you can place the edges correctly.

By rotating the last layer, you can obtain one of these situations:
# all edges are already placed correctly
# three edges need to be rotated
# two pair of edges need to be swapped

The third one can be solved by rotating any three edges, and then you are back in situation 2.

To rotate edges, notice that when you take one solved pair out of its slot, you can move it out of the way by rotating the upper face and put the slot back to its position. Then, you can turn the upper face to replace it with the edge currently in the slot. When you move the slot out, you can bring back the pair without breaking it and put it back in it's correct place.

For example, using the front-right-bottom slot, you can rotate the top-right edge, top-left edge and top-back edge like this : R U2 R' then U' then R U' R'.

By doing this, you will rotate corners, so if they are alread correctly oriented, you need to use a [[Commutators and Conjugates|conjugate of commutator]] to flip the edges without disturbing the corners. The [[commutator]] can be composed with A = "exchange an edge on the top face with an edge that is not on the top face, while keeping the rest of the top face unchanged" and B = "rotate the top face to put another edge in the intersection". The conjugation will used to place one of the three top edges at the location of the exchange.

You can also compose the commutator with A = "swap two edges on the top face" and B = "rotate the edges so that one swapped edge will be swapped with a third one". In this case, you need to be able to rotate those edges, so they must be either on the same face, or on the same slice.

==== Solving corners ====
You will need [[commutators]] to solve the corners.

You can orient corners by using a commutator like A = "rotate a corner without changing the rest of the top face" and B = "put another corner at the intersection".

To swap corners, use the same principle used for the commutator of edges : a conjugate to move a corner out of the top face, and a commutator with A = "exchange one corner of the top face with the corner not on the top face" and B = "move another corner in the intersection".

You can also rotate and orient corners at the same time by carefully choosing a conjugate and a commutator.

== See also ==

* [[Commutators and Conjugates]]
* [[Commutator]]
* [[Conjugate]]
* [http://hlavolam.maweb.eu/rubiks-cube-3x3x3#intuitive-puzzle-solving-method Intuitive Rubik's cube solution tutorial] (uses interactive animated Rubik's cube simulators for better clarity)

[[Category:3x3x3 methods]]
[[Category:Experimental methods]]
[[Category:3x3x3 beginner methods]]

Intuitive solving

2018-02-20T09:01:36Z

Username:

Intuitive solving consists in solving the Rubik's cube without using any algorithm that you do not understand. In most methods, for example for the last layer, most algorithm are used in such way that there is an input cube in some state, then you apply the appropriate algorithm that you learnt by heart, and quite magically, the cube is in the desired state.

=== Overview ===

Intutive solving can basically be broken into two parts :
* solving most of the cube with intuitive moves ([[F2L|first two layers]] or more)
* solving the remaining pieces with [[commutators]]

You can use any existing method, remove all algorithm and try to do each step with your intuition only. You should be able to complete at least two layers that way. The [[F2L]] methods ([[CFOP]] (AKA Fridrich method), [[Petrus]]) can be done intuitively. Note that before doing the last pair, you have an opportunity to orient the edges. Finally you will need to do the last layer, essentially with [[commutators]].

The [[Heise Method]] is an intuitive method for solving the whole cube, but is very difficult to understand. Nevertheless you can use part of it to solve the first two layers minus one pair.

=== Intuitive F2L ===

==== Cross ====
Place four edges of one face, at their correct location and orientation. It's ok if they are rotated, but in the correct order, because you will always be able to align them by just rotating the chosen face.

You can notice that if an edge is on the opposite face in the correct orientation, you can move it to the correct face with the correct orientation with a half turn. If an edge is in the slice between those faces, you can always move it to the correct face with the right orientation with one quarter turn. Of course, you may need to rotate the destination face so that the edge arrives at the desired location, relative to other edges you have already placed.

You will obtain a cross. Turn the cube so that it is at the bottom.

==== Slots ====
After aligning the edges with the centers next to them, you will get four slots, one for each corner, that can contains two pieces : an edge piece and a corner piece. Notice that you can move some piece out one slot, for example the front-right-bottom slot (if you started with the bottom face), by doing R U' R or F' U F. This three moves are the following :
# Taking the piece out of the slot to the upper face
# Moving this piece out of the way
# Bring back the bottom edge at it's correct place (inverse of step 1)

Conversely, you can put a pair of pieces into one slot :
# Move the slot out, so that the destination is now on the scrambled face
# Move some piece into the destination
# Bring the destination back (inverse of step 1)

Of course, you will need to build pairs, so that you can insert them into the slots. To do so, notice that :
* You can break a pair when pieces are not well oriented relative to each other by hiding the corner piece from the scramble face by moving the appropriate slot out, moving the edge with the scrambled face, and the bring the slot back
* You can build one pair by hiding a corner by moving a slot out, bring an edge next to it, and then bring the slot back

If an edge or a corner is already in place, you can use the [[Keyhole F2L|keyhole]] method, which can be done intuitively. That's all you need to know. There are shortcuts of course, notably when you can form the pair and put it in the slot in three moves (see [[F2L#F2L 4|F2L 4]]).

=== Orienting edges before last F2L pair ===

To orient remaing edges, notice that if you store an edge in a slot, and take it out using the adjacent face, it will be rotated. For example, if you want to flip the front-top edge using the front-right-bottom slot, you can do the following sequence : R U' R' then F' U F.

By doing so, you will flip other edges too, so you must take into account the orientation of the edge currently in the slot so that you bring it out of the slot to the top face with the right orientation (yellow on top if the last layer is yellow). So if you have in the front-right-bottom an edge the has its yellow color to the right, the you must take it out with the F face. If it's in the other direction, you must take it out with the R face.

When you take the edge out, you must take care that it does not replace the other edge that you will place back in the slot. You may need to rotate the upper face to move it out of the way.

So each orientation will be 3 or 4 moves long :
# move some edge out of the way (optional)
# take the edge out of the slot
# bring another edge instead
# put this edge in the slot (inverse of step 2)

You are done when all edges the belongs to the top layer and are in the top layer are oriented (yellow on top). If one edge of the top face remains the the slot, it's ok. You will only need to take care of using the face the brings it out in the right orientation when doing the last pair.

Finally, do the last pair using only two faces : the upper face and another face the allows to bring out the content of the slot.

=== Last layer intutive solving ===

==== Rotating edges ====
Using the method above, the edges should be already oriented. If not, you will need a [[commutator]]. It can be composed with A = "flip an edge in the top face without changing anything else in the top face" and B = "rotate the top face to place another edge to be flipped at the intersection".

If you do not care about the orientation of corners, you can still rotate three edges without using a commutator. So you can place the edges correctly.

By rotating the last layer, you can obtain one of these situations:
# all edges are already placed correctly
# three edges need to be rotated
# two pair of edges need to be swapped

The third one can be solved by rotating any three edges, and then you are back in situation 2.

To rotate edges, notice that when you take one solved pair out of its slot, you can move it out of the way by rotating the upper face and put the slot back to its position. Then, you can turn the upper face to replace it with the edge currently in the slot. When you move the slot out, you can bring back the pair without breaking it and put it back in it's correct place.

For example, using the front-right-bottom slot, you can rotate the top-right edge, top-left edge and top-back edge like this : R U2 R' then U' then R U' R'.

By doing this, you will rotate corners, so if they are alread correctly oriented, you need to use a [[Commutators and Conjugates|conjugate of commutator]] to flip the edges without disturbing the corners. The [[commutator]] can be composed with A = "exchange an edge on the top face with an edge that is not on the top face, while keeping the rest of the top face unchanged" and B = "rotate the top face to put another edge in the intersection". The conjugation will used to place one of the three top edges at the location of the exchange.

You can also compose the commutator with A = "swap two edges on the top face" and B = "rotate the edges so that one swapped edge will be swapped with a third one". In this case, you need to be able to rotate those edges, so they must be either on the same face, or on the same slice.

==== Solving corners ====
You will need [[commutators]] to solve the corners.

You can orient corners by using a commutator like A = "rotate a corner without changing the rest of the top face" and B = "put another corner at the intersection".

To swap corners, use the same principle used for the commutator of edges : a conjugate to move a corner out of the top face, and a commutator with A = "exchange one corner of the top face with the corner not on the top face" and B = "move another corner in the intersection".

You can also rotate and orient corners at the same time by carefully choosing a conjugate and a commutator.

== See also ==

* [[Commutators and Conjugates]]
* [[Commutator]]
* [[Conjugate]]
* [http://hlavolam.maweb.eu/rubiks-cube-3x3x3#intuitive-puzzle-solving-method Intuitive Rubik's cube solution tutorial] (uses interactive animated Rubiks's cube simulators for better clarity)

[[Category:3x3x3 methods]]
[[Category:Experimental methods]]
[[Category:3x3x3 beginner methods]]

List of cubing websites

2016-08-29T08:31:20Z

Username:

* [http://www.speedcubing.com speedcubing.com] comprehensive cubing site, maintained by well-known cubers inc. Chris Hardwick and Ton Dennenbroek.
* [http://www.speedcubing.com.pl speedcubing.com.pl] speedcubing.com's polish cousin.
* [http://twistypuzzles.com/forum/ twistypuzzles.com] Forum for puzzle collectors and designers.
* [http://www.chalkstreet.com/solving-3-by-3-rubix-cube/?utm_source=dac Chalkstreet] Step by Step Tutorial
* [http://www.jaapsch.net/puzzles/ jaapsch.net] Jaap's Puzzle Page. A huge collection of info on many different puzzles and solving methods.
* [http://rubikscube.info/ rubikscube.info] A great resource for CF methods. Info on Ortega, Waterman and beginner CF. Site by Josef Jelinek.
* [http://www.ws.binghamton.edu/fridrich/ Jessica Fridrich's] cubing site. One of the original homes of the Fridrich/CFOP method.
* [http://lar5.com/cube/ Lars Petrus's] cubing site. Home of the Petrus method.
* [http://grrroux.free.fr/ grrroux.free.fr] Gilles Roux's cubing site. Home of the Roux method.
* [http://www.typhoon.fr/ Typhoon.fr] Pierre Bouvier's Cube zone. Host cubing videos and tutorials in french.
* [http://www.francocube.com/ Francocube] French speaking website including a forum.
* [http://www.stefan-pochmann.info/spocc stefan-pochmann.info] Stefan Pochmann's cubing site. Info on blindsolving methods and other tools.
* [http://www.speedcubes.net/ speedcubes.net] Stefan Pochmann's comprehensive site for cube information
* [http://www.cubezone.be/ cubezone.be] Lars Vandenbergh's CubeZone. Algorithms, videos etc.
* [http://www.cubefreak.net/ cubefreak.net] Site by Shotaro Makisumi. Lots of info on speed and blind solving methods.
* [http://www.badmephisto.com/ badmephsto.dyndns.org] Badmephisto's cubing site. (experiences regular down-time)
* [http://www.mustcube.net mustcube.net] Site by Per Kristen Fredlund (prominent FMC cuber). Mostly incomplete. Holds the weekly online FMC challenge.
* [http://www.cubestation.co.uk/ cubestation.co.uk] Dan Harris's new cubing site.
* [http://strangepuzzle.com/ strangepuzzle.com] Chris Hunt's cubing page. Hosts a cubing video database, timer and other tools.
* [http://www.erikku.110mb.com/ erikku.110mb.com] Erik Akkersdijk's cubing site. Cubing info from a world class cuber.
* [http://www.kungfoomanchu.com/ kungfoomanchu.com] Andy Klise's Printable PDF guides for twisty puzzles
* [http://cube.garron.us/ Lucas Garron]
* [http://jmbaum.110mb.com/ Jason Baum]
* [http://mzrg.com Michael Gottlieb]
* [http://pagesperso-orange.fr/absolutemind/ Sébastien Felix's] site, has some nice OH algorithms
* [http://solvethecube.110mb.com/ Joël van Noort]
* [http://www.zborowski.republika.pl/ Zbigniew Zborowski's] site. Home of the ZB method.
* [http://www.speedcubing101.com/ Anthony Brooks (Anthony Searle)]
* [http://www.cutex.info/ cutex.info] Yu Nakajima's Cubing Site (in Japanese). [http://translate.google.co.uk/translate?hl=en&sl=ja&tl=en&u=http%3A%2F%2Fwww.cutex.info English Translation] (site down)
* [http://thomasje.webs.com/ ThomasJE's Cubing Site] Has [[4LLL]] and [[3x3x5]] tutorials; as well as a World Record's quiz to test your knowledge.
* [http://hlavolam.maweb.eu/#english-version hlavolam má web] Intuitive solutions to combinatorial puzzles as well as puzzle related articles.
* [http://cyotheking.squarespace.com/ Christopher Olson's Website] - includes some of the best advanced 2x2 and 3x3 algorithms
* [http://cube.crider.co.uk/ Conrad Rider's Website] - Original cubing software and tutorials, including [http://cube.crider.co.uk/miris.html MirIS], [http://cube.crider.co.uk/zz.php ZZ Method] and [http://cube.crider.co.uk/visualcube.php VisualCube].

== See also ==
* [[List of YouTube cubers]]

[[Category:Resources]]
[[Category:Community]]
[[Category:Lists|cubing websites]]

List of cubing websites

2016-08-29T08:30:31Z

Username:

* [http://www.speedcubing.com speedcubing.com] comprehensive cubing site, maintained by well-known cubers inc. Chris Hardwick and Ton Dennenbroek.
* [http://www.speedcubing.com.pl speedcubing.com.pl] speedcubing.com's polish cousin.
* [http://twistypuzzles.com/forum/ twistypuzzles.com] Forum for puzzle collectors and designers.
* [http://www.chalkstreet.com/solving-3-by-3-rubix-cube/?utm_source=dac Chalkstreet] Step by Step Tutorial
* [http://www.jaapsch.net/puzzles/ jaapsch.net] Jaap's Puzzle Page. A huge collection of info on many different puzzles and solving methods.
* [http://rubikscube.info/ rubikscube.info] A great resource for CF methods. Info on Ortega, Waterman and beginner CF. Site by Josef Jelinek.
* [http://www.ws.binghamton.edu/fridrich/ Jessica Fridrich's] cubing site. One of the original homes of the Fridrich/CFOP method.
* [http://lar5.com/cube/ Lars Petrus's] cubing site. Home of the Petrus method.
* [http://grrroux.free.fr/ grrroux.free.fr] Gilles Roux's cubing site. Home of the Roux method.
* [http://www.typhoon.fr/ Typhoon.fr] Pierre Bouvier's Cube zone. Host cubing videos and tutorials in french.
* [http://www.francocube.com/ Francocube] French speaking website including a forum.
* [http://www.stefan-pochmann.info/spocc stefan-pochmann.info] Stefan Pochmann's cubing site. Info on blindsolving methods and other tools.
* [http://www.speedcubes.net/ speedcubes.net] Stefan Pochmann's comprehensive site for cube information
* [http://www.cubezone.be/ cubezone.be] Lars Vandenbergh's CubeZone. Algorithms, videos etc.
* [http://www.cubefreak.net/ cubefreak.net] Site by Shotaro Makisumi. Lots of info on speed and blind solving methods.
* [http://www.badmephisto.com/ badmephsto.dyndns.org] Badmephisto's cubing site. (experiences regular down-time)
* [http://www.mustcube.net mustcube.net] Site by Per Kristen Fredlund (prominent FMC cuber). Mostly incomplete. Holds the weekly online FMC challenge.
* [http://www.cubestation.co.uk/ cubestation.co.uk] Dan Harris's new cubing site.
* [http://strangepuzzle.com/ strangepuzzle.com] Chris Hunt's cubing page. Hosts a cubing video database, timer and other tools.
* [http://www.erikku.110mb.com/ erikku.110mb.com] Erik Akkersdijk's cubing site. Cubing info from a world class cuber.
* [http://www.kungfoomanchu.com/ kungfoomanchu.com] Andy Klise's Printable PDF guides for twisty puzzles
* [http://cube.garron.us/ Lucas Garron]
* [http://jmbaum.110mb.com/ Jason Baum]
* [http://mzrg.com Michael Gottlieb]
* [http://pagesperso-orange.fr/absolutemind/ Sébastien Felix's] site, has some nice OH algorithms
* [http://solvethecube.110mb.com/ Joël van Noort]
* [http://www.zborowski.republika.pl/ Zbigniew Zborowski's] site. Home of the ZB method.
* [http://www.speedcubing101.com/ Anthony Brooks (Anthony Searle)]
* [http://www.cutex.info/ cutex.info] Yu Nakajima's Cubing Site (in Japanese). [http://translate.google.co.uk/translate?hl=en&sl=ja&tl=en&u=http%3A%2F%2Fwww.cutex.info English Translation] (site down)
* [http://thomasje.webs.com/ ThomasJE's Cubing Site] Has [[4LLL]] and [[3x3x5]] tutorials; as well as a World Record's quiz to test your knowledge.
* [http://www.hlavolam.maweb.eu/#english-version hlavolam má web] Intuitive solutions to combinatorial puzzles as well as puzzle related articles.
* [http://cyotheking.squarespace.com/ Christopher Olson's Website] - includes some of the best advanced 2x2 and 3x3 algorithms
* [http://cube.crider.co.uk/ Conrad Rider's Website] - Original cubing software and tutorials, including [http://cube.crider.co.uk/miris.html MirIS], [http://cube.crider.co.uk/zz.php ZZ Method] and [http://cube.crider.co.uk/visualcube.php VisualCube].

== See also ==
* [[List of YouTube cubers]]

[[Category:Resources]]
[[Category:Community]]
[[Category:Lists|cubing websites]]

List of cubing websites

2016-08-29T08:29:42Z

Username:

* [http://www.speedcubing.com speedcubing.com] comprehensive cubing site, maintained by well-known cubers inc. Chris Hardwick and Ton Dennenbroek.
* [http://www.speedcubing.com.pl speedcubing.com.pl] speedcubing.com's polish cousin.
* [http://twistypuzzles.com/forum/ twistypuzzles.com] Forum for puzzle collectors and designers.
* [http://www.chalkstreet.com/solving-3-by-3-rubix-cube/?utm_source=dac Chalkstreet] Step by Step Tutorial
* [http://www.jaapsch.net/puzzles/ jaapsch.net] Jaap's Puzzle Page. A huge collection of info on many different puzzles and solving methods.
* [http://rubikscube.info/ rubikscube.info] A great resource for CF methods. Info on Ortega, Waterman and beginner CF. Site by Josef Jelinek.
* [http://www.ws.binghamton.edu/fridrich/ Jessica Fridrich's] cubing site. One of the original homes of the Fridrich/CFOP method.
* [http://lar5.com/cube/ Lars Petrus's] cubing site. Home of the Petrus method.
* [http://grrroux.free.fr/ grrroux.free.fr] Gilles Roux's cubing site. Home of the Roux method.
* [http://www.typhoon.fr/ Typhoon.fr] Pierre Bouvier's Cube zone. Host cubing videos and tutorials in french.
* [http://www.francocube.com/ Francocube] French speaking website including a forum.
* [http://www.stefan-pochmann.info/spocc stefan-pochmann.info] Stefan Pochmann's cubing site. Info on blindsolving methods and other tools.
* [http://www.speedcubes.net/ speedcubes.net] Stefan Pochmann's comprehensive site for cube information
* [http://www.cubezone.be/ cubezone.be] Lars Vandenbergh's CubeZone. Algorithms, videos etc.
* [http://www.cubefreak.net/ cubefreak.net] Site by Shotaro Makisumi. Lots of info on speed and blind solving methods.
* [http://www.badmephisto.com/ badmephsto.dyndns.org] Badmephisto's cubing site. (experiences regular down-time)
* [http://www.mustcube.net mustcube.net] Site by Per Kristen Fredlund (prominent FMC cuber). Mostly incomplete. Holds the weekly online FMC challenge.
* [http://www.cubestation.co.uk/ cubestation.co.uk] Dan Harris's new cubing site.
* [http://strangepuzzle.com/ strangepuzzle.com] Chris Hunt's cubing page. Hosts a cubing video database, timer and other tools.
* [http://www.erikku.110mb.com/ erikku.110mb.com] Erik Akkersdijk's cubing site. Cubing info from a world class cuber.
* [http://www.kungfoomanchu.com/ kungfoomanchu.com] Andy Klise's Printable PDF guides for twisty puzzles
* [http://cube.garron.us/ Lucas Garron]
* [http://jmbaum.110mb.com/ Jason Baum]
* [http://mzrg.com Michael Gottlieb]
* [http://pagesperso-orange.fr/absolutemind/ Sébastien Felix's] site, has some nice OH algorithms
* [http://solvethecube.110mb.com/ Joël van Noort]
* [http://www.zborowski.republika.pl/ Zbigniew Zborowski's] site. Home of the ZB method.
* [http://www.speedcubing101.com/ Anthony Brooks (Anthony Searle)]
* [http://www.cutex.info/ cutex.info] Yu Nakajima's Cubing Site (in Japanese). [http://translate.google.co.uk/translate?hl=en&sl=ja&tl=en&u=http%3A%2F%2Fwww.cutex.info English Translation] (site down)
* [http://thomasje.webs.com/ ThomasJE's Cubing Site] Has [[4LLL]] and [[3x3x5]] tutorials; as well as a World Record's quiz to test your knowledge.
* [http://www.hlavolam.maweb.eu/#english-version/ hlavolam má web] Intuitive solutions to combinatorial puzzles as well as puzzle related articles.
* [http://cyotheking.squarespace.com/ Christopher Olson's Website] - includes some of the best advanced 2x2 and 3x3 algorithms
* [http://cube.crider.co.uk/ Conrad Rider's Website] - Original cubing software and tutorials, including [http://cube.crider.co.uk/miris.html MirIS], [http://cube.crider.co.uk/zz.php ZZ Method] and [http://cube.crider.co.uk/visualcube.php VisualCube].

== See also ==
* [[List of YouTube cubers]]

[[Category:Resources]]
[[Category:Community]]
[[Category:Lists|cubing websites]]