Rubiks Revenge - Revision history

Admin: /* Solution Procedure */

2019-04-21T21:16:15Z

Solution Procedure

← Older revision		Revision as of 21:16, 21 April 2019
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	1. Solve Centers		1. Solve Centers

	2. Align Double-Edges		2. Align Double-Edges

	3. Solve the 3x3		3. Solve the 3x3

	4. Last Layer Double Edges (even vs odd parity case)		4. Last Layer Double Edges (even vs odd parity case)

	5. Last Layer Corners		5. Last Layer Corners

Admin: /* Double Edge Alignment Algorithms */

2019-04-21T21:13:27Z

Double Edge Alignment Algorithms

← Older revision		Revision as of 21:13, 21 April 2019
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	==Algorithms Cheat Sheet==		==Algorithms Cheat Sheet==

	~~===Double Edge Alignment Algorithms===~~

	~~{\| class="wikitable" cellpadding="100" width="66%"~~
	~~!colspan="4"\|'''Double Edge Algorithms'''~~

	\|-
	~~\|Bring Together Two Opposite Double Edge Cubies'''~~
	~~\|This algorithm should be applied once all four top double edges and all four bottom double edges are solved, and there only remain four double edges to orient.~~

	This algorithm should be applied when two double edge pieces are twins, but both are located across from one another on a cube face. Orient the two twin double edges so they mirror one another, then execute the algorithm:

	~~<pre>~~
	~~d R F'~~
	U
	~~R' F d'~~
	~~</pre>~~
	\|}

	~~(Note this algorithm is also applicable to the [[Professors Cube]], which also has a solution step requiring double edges to be correctly oriented.)~~

	===Last Layer Algorithms===		===Last Layer Algorithms===

Admin: /* Algorithms */

2019-04-21T21:13:16Z

Algorithms

← Older revision		Revision as of 21:13, 21 April 2019
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	For details and pictures for these solution steps, see [[Rubiks Revenge/Layer Method]].		For details and pictures for these solution steps, see [[Rubiks Revenge/Layer Method]].

	==Algorithms==		==Algorithms Cheat Sheet==

	===Double Edge Alignment Algorithms===		===Double Edge Alignment Algorithms===

Admin: /* Algorithms */

2019-04-21T21:09:28Z

Algorithms

← Older revision		Revision as of 21:09, 21 April 2019
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	==Algorithms==		==Algorithms==

			===Double Edge Alignment Algorithms===

			{\| class="wikitable" cellpadding="100" width="66%"
			!colspan="4"\|'''Double Edge Algorithms'''

			\|-
			\|Bring Together Two Opposite Double Edge Cubies'''
			\|This algorithm should be applied once all four top double edges and all four bottom double edges are solved, and there only remain four double edges to orient.

			This algorithm should be applied when two double edge pieces are twins, but both are located across from one another on a cube face. Orient the two twin double edges so they mirror one another, then execute the algorithm:

			<pre>
			d R F'
			U
			R' F d'
			</pre>
			\|}

			(Note this algorithm is also applicable to the [[Professors Cube]], which also has a solution step requiring double edges to be correctly oriented.)

	===Last Layer Algorithms===		===Last Layer Algorithms===

Admin: /* Solution Procedure */

2019-04-21T20:57:23Z

Solution Procedure

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Admin: /* Even Parity (No 3x3 Equivalent) Case */

2019-04-21T20:53:56Z

Even Parity (No 3x3 Equivalent) Case

← Older revision		Revision as of 20:53, 21 April 2019
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	The algorithm that cycles through the four last layer configurations on a 3x3 will not solve either of these arrangements, but when applied to one even parity last layer case, it will result in the other even parity last layer case.		The algorithm that cycles through the four last layer configurations on a 3x3 will not solve either of these arrangements, but when applied to one even parity last layer case, it will result in the other even parity last layer case.

	We want to reach the T shape on the top layer before moving on to the next step. This will leave the cube in a state where all four double edges on the last layer are joining the correct two faces, but one double edge is inside-out.

	~~Here is the algorithm to fix a single inside-out double edge.~~

	{\| class="wikitable" cellpadding="100" width="66%"		{\| class="wikitable" cellpadding="100" width="66%"
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	\|}		\|}

			Get to the T shape on the top layer before applying the algorithm to swap a single inside-out double edge to be right-side in. Each double-edge should be located on the correct edge (i.e., the two colors of the double edge cubies should match the two colors of the faces they connect) and all but one double edge on the last layer should be correctly oriented (i.e., the two color of the double edge cubies match the two colors of the faces they connect ''and'' are correctly oriented).

			Once the cube has the T configuration on the top of the cube, orient the cube so the front top double edge is the inside-out double edge. Then apply the following algorithm to flip the double edge pieces.

	{\| class="wikitable" cellpadding="100" width="66%"		{\| class="wikitable" cellpadding="100" width="66%"

Admin: /* Even Parity (No 3x3 Equivalent) Case */

2019-04-21T20:48:31Z

Even Parity (No 3x3 Equivalent) Case

@@ Line 82: / Line 82: @@
 Here is the algorithm to fix a single inside-out double edge.
 {| class="wikitable" cellpadding="100" width="66%"
@@ Line 87: / Line 100: @@
 |-
 |'''Fix Single Inside-Out Dedge:'''
-|Start with the cube oriented with the inside-out dedge at the top of the front face. Then execute the algorithm (broken into pieces to make it easier to remember):
+|NOTE: Only apply this to the T configuration (above left).
 <pre>
@@ Line 98: / Line 113: @@
 U D r
 </pre>
 |}

Admin: /* Even Parity (No 3x3 Equivalent) Case */

2019-04-21T20:47:59Z

Even Parity (No 3x3 Equivalent) Case

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 The algorithm that cycles through the four last layer configurations on a 3x3 will not solve either of these arrangements, but when applied to one even parity last layer case, it will result in the other even parity last layer case.
-We want to reach the T shape on the top layer before moving on to the next step. This will leave the cube in a state where all four double edges on the last layer are joining the correct two faces, but one double edge is inside-out. There is an algorithm to fix a single inside-out double edge.
+We want to reach the T shape on the top layer before moving on to the next step. This will leave the cube in a state where all four double edges on the last layer are joining the correct two faces, but one double edge is inside-out.
 {| class="wikitable" cellpadding="100" width="66%"

Admin: /* Step 4: Last Layer Double-Edges */

2019-04-21T20:46:58Z

Step 4: Last Layer Double-Edges

← Older revision		Revision as of 20:46, 21 April 2019
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	===Step 4: Last Layer Double-Edges===		===Step 4: Last Layer Double-Edges===

	The last layer is where things diverge from the 3x3 cube.		The last layer is where things can diverge from the 3x3 cube.

			====Even vs Odd Parity on the Cube====

			On the 3x3 cube, and on any cube with an even number of cubies per edge, the total number of states that the cube can reach is cut in half because of the way the Rubik's cube is constructed - on an odd cube, the center faces cannot be rotated, so half of the states (those with the center faces rotated) are inaccessible without physically dismantling the cube.

			On the 4x4 cube, and on any cube with an even number of cubies (greater than 2) per edge, there is no fixed center piece, so any face cubie can be swapped with any other face cubie. This means all states are accessible on the 4x4 cube.

			====Even vs Odd Parity on the Last Layer====

			Step 4 of the solution requires us to solve the last layer on the 4x4 cube. This solution procedure splits into two cases: an even parity last layer scenario, and an odd parity last layer scenario.

			====Odd Parity (3x3 Equivalent) Case====

			Let us first consider the odd parity case, which is easier because solving it is equivalent to solving the last layer of the 3x3 [[Rubiks Cube/Layer Method]].

			When solving the cross on the last layer of a 3x3 cube, there are 4 possible configurations. These four configurations can be cycled through by repeatedly applying a single algorithm.

			The four last-layer configurations for the 3x3 cube are:

	When solving the cross on the last layer of a 3x3 cube, there are 4 possible configurations. These four configurations can be cycled through by repeatedly applying a single algorithm. The four configurations are:
	* A single square (four squares) on the top is in-place		* A single square (four squares) on the top is in-place
	* Three squares (eight squares) on the top are in place (forming an L shape)		* Three squares (eight squares) on the top are in place (forming an L shape)
	* Three squares (eight squares) on the top are in place (forming an I shape)		* Three squares (eight squares) on the top are in place (forming an I shape)
	* Five squares (twelve squares) on the top are in place (forming a cross)		* Five squares (twelve squares) on the top are in place (forming a cross)


	This arrangement will occur some of the time on the 4x4 (this is the "easy case" - solving the 4x4 is exactly like solving the 3x3, no new algorithms required).		This arrangement will occur some of the time on the 4x4 (this is the "easy case" - solving the 4x4 is exactly like solving the 3x3, no new algorithms required).
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	\|}		\|}

			====Even Parity (No 3x3 Equivalent) Case====

	~~On the 4x4 cube, there~~ are ~~two sets~~ of ~~configurations. The first set are the four configurations listed above,~~ that occur on the ~~3x3. The same 3x3 algorithms can be applied to the 4x4 as to~~ the 3x3~~. However, the second set of configurations is~~:		There are a second set of outcomes that can occur on the last layer of the solve that have no 3x3 equivalent:
	* Ten squares on the top are in place (forming a T shape)
	* Six squares on the top are in place (forming an incomplete I shape)

	~~The same algorithm that cycles through~~ the four ~~configurations on the 3x3 can be applied to these configurations on the 4x4 to switch between them. Depending on the orientation of the cube~~, ~~the T shape can be permuted into another~~ T shape, ~~the~~ incomplete I shape ~~can be permuted into another incomplete I shape, or the T and incomplete I can be turned into one or the other.~~		* Ten cubies on the top are in place (four center cubies and six double edge cubies), forming a T shape
			* Six cubies on the top are in place (four center cubies and two double edge cubies), forming an incomplete/stumpy I shape

	~~You can always get to the T shape from an incomplete I shape. There is an~~ algorithm that ~~fixes~~ the one ~~side of~~ the ~~T shape that is not oriented correctly. This is the situation where there is a single double-edge that is "inside out~~."		The algorithm that cycles through the four last layer configurations on a 3x3 will not solve either of these arrangements, but when applied to one even parity last layer case, it will result in the other even parity last layer case.

			We want to reach the T shape on the top layer before moving on to the next step. This will leave the cube in a state where all four double edges on the last layer are joining the correct two faces, but one double edge is inside-out. There is an algorithm to fix a single inside-out double edge.

	{\| class="wikitable" cellpadding="100" width="66%"		{\| class="wikitable" cellpadding="100" width="66%"

Admin: /* Flags */

2018-06-24T04:42:15Z

Flags

← Older revision		Revision as of 04:42, 24 June 2018
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	{{RubiksRevengeFlag}}		{{RubiksRevengeFlag}}

			=References=

			See https://charlesreid1.com/wiki/Rubiks_Cube#References

			This is a fantastic definitive list of algorithms for the 4x4 cube: https://www.speedsolving.com/wiki/index.php/4x4x4_Parity_Algorithms