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## Mohamed

*Rubik's Cube Puzzle* 


 * Rubik's Cube Puzzle* 

  A Rubik's Cube is a 3-dimensional mechanical puzzle invented in 1974  by Erno Rubik.  The device is a cube, where each side is subdivided  further into nine more smaller cubes in a 3-by-3 grid.  There are a  total of 26 of these smaller cubes, also affectionately referred to as  cubies.  There are 8 corner cubies which lie on the corners of three  faces.  There are 12 edge cubies which each lie on the edges of 2 faces,  and 6 center faces, which each lie on only one face.   	 	
 Each face of each cubie has one of 6 different colors. 		 	
 	 	 Looking at any one of the 6 faces, face on, you can divide the cube  into 3 planes, where the plane closest to you contains 9 cubies, the  plane farthest away also contains 9 cubies, and the plane in the middle  contains 8 cubies.  You get such a decomposition from any of 6 ways of  orienting the cube, but they come in pairs, which are the same.  Each  plane, from any orientation can be independently rotated any multiple of  ninety degrees, permuting the cubies and the colors on the cubies. 		 		
  The puzzle is considered solved when each face has only one  color on it. 			 		
 			 		  It is possible to solve a Rubik's cube with the center cubies  rotated.  Since a normal Rubik's cube has only a single color to a side,  it is impossible to tell if a center cubie has been rotated in place.   Some Rubik's Cubes have pictures on their faces instead of solid colors,  and with these, one must get the orientations of the central cubies  corrected, as well as everything else.  These puzzles are much harder to  do. 			 			 			 		
* How Solve a Rubik's Cube*

 		 		 There are a multitude of ways to solve a Rubik's Cube.  The way  that we will discuss is called solving by layer, and is conceptually one  of the easiest ways to solve the cube.  However, it is far from the  quickest. 		 		
First we will need a way to talk about places on the cube and  rotation of the cube.   			 			
 We fix an orientation of the cube and hold it constant for  the whole time.  The 6 central cubies (one per side) will not move while  we solve it. 			 	

F - front face or 90 degree clockwise rotation thereofB - back face or 90 degree clockwise rotation thereofL - left face or 90 degree clockwise rotation thereofR - right face or 90 degree clockwise rotation thereofU - top face or 90 degree clockwise rotation thereofD - bottom face or 90 degree clockwise rotation thereof
 		 		We will solve the Rubik's cube layer-by-layer.  We solve the top  layer first, then the middle layer, and then the bottom.  The reason  that this is such a slow way to solve the cube is that once we get the  first layer into place, in order to make any more progress, we must  disrupt what we have already built, shuffle some stuff around, and then  reconstitute what we broke up. 			 			
The essence of this solution is to find combinations of moves  which leave most of the cube invariant. 		 		
* Top Layer*

* Top Edges* 

 		 		  You have to get the top edge pieces into position before the  corner pieces 			 			
  Get the selected edge piece into position, and rotate it to  the top. 		 		
* Top Corners* 

 		 		To get a corner into position, rotate the side face where you want  to corner to go by 90 degrees so that that corner is on the bottom.   Rotate the selected corner cubie into that face.  Rotate that face back  into its original position.  Now the selected corner is in position  without disrupting anything else on the top layer.  Repeat for the other  four corners.  If the corner piece you want is already in the top  layer, repeat the trick to dislodge the selected corner piece without  disrupting anything else. 		 		
*Middle Layer*

 		 		 On the middle layer, we only need to get the edges into position  because we consider the central faces to be stationary. 		 		
*Middle Edges*

 		 		Orient the cube so that the edge you want to place into the middle  layer is on the bottom below and to the right of where it should go.   Also the edge should have the correct color on the front face.  If this  is impossible, then simply do the mirror image of the following  instructions.  		
 Do the following moves: DLDDDLLLDDDFFFDF.  Now that edge is in  the correct position.   			 			
If the edge you want is already in the middle layer, but in  the wrong position or orientation, then use this sequence of moves to  dislodge it into the bottom layer, and then put it back correctly. 				 		 		 		 			 			
*Bottom Layer*

 			 			The bottom layer is the hardest, because we have two full layers  on top that cannot be disturbed. 				 				


*Orient Bottom Edges*

 				 				Look at the bottom face.  Now consider it the top face.  The  object is to get the right color facing up.  If you need to get to  rotate two opposite edge pieces, on on the top and one on the bottom, do  FURUUURRRFFF.  If you need to rotate the cubie on the right and bottom,  use FURUUURRRFFF. 				 				
*Permute the Bottom Corners*

 				 				To swap the two corners in the front right and the back right,  use LUUURRRULLLUUURUU. 			 			
 Any other combination of swaps can be achieved by using this  move repeatedly.	 				 				 				 				 				
*Orient the Bottom Corners*

  Twist three corners on  the last layer by using RRRUUURUUURRRUURUU.  This permutes the  front-right, front-left, and back-right edges.  Using this move  repeatedly will orient the bottom corners correctly 				 				
*Permute the Bottom Edges*

 		 		Permute the front, back, and right edges by using RRUFBBBRRFFFBURR.   Again, use this move until the edges are in the correct positions. 		 		
And now the cube is solved!  	 		
See More: Rubik's Cube Puzzle

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## Mohamed

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