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User:Arjun sunel/Solvability of a 3x3x3 Rubik's Cube State?: Difference between revisions
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==Solvability Understanding Using A Solved Cube==
===Case 1: Twist a corner===
Suppose, you are holding a solved Cube. Now, pick a corner and twist it clockwise
(or anticlockwise) by 120 degree (by removing it out and rotate by 120 degree and put it again in the same place)
The cube state so obtained is unsolvable because it is not possible to solve the twisted corner without disturbing the positions of already solved cubies using any legal moves.
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File:flip_edge.png|Flip an edge.
File:Swap_edges.png|Swap just two edges.
File:Swap_corners.png|Swap just two
</gallery>
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===Edge Parity Test===
Correctly-oriented edge:
If after applying such rotations, we get the edge flipped, then the edge is not correctly-oriented.
It should be noted that rotation of the above four faces
But, we have two more faces. They are FRONT and BACK.
Rotation of these two faces by 90 degrees, flips all the four edges on that face.
Let,
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Since, LEFT, RIGHT, TOP and BOTTOM flips zero edges while rotation of FRONT and BACK by 90 degrees flips 4 edges. So, any legal move will change the edge-orientation value only by an even number which is divisible by 2.
Hence,
====How to compute edge-orientation?====
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a) Pick an edge and initialize n=0.
b) Try to bring the edge in the position where it
c) When the edge is in the correct position, check whether the edge is correctly-oriented or
d)
e) Check whether n=total number of flips is divisible by 2 or not. If yes, then the Cube state passes the Edge-
==Rubik's Cube Solvability:==
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