.. -*- coding: utf-8 -*-

================================
 Rubik’s Cube Solution & Extras
================================

:Author: David Goodger
:Contact: goodger@python.org

.. sidebar:: Related Pages
   :class: large

   * `My puzzle pages <../>`_
   * `My home page <../../>`_

.. contents::


-----------------------
 Rubik’s Cube Solution
-----------------------

Summarized from the solution pages mirrored at
<http://jjorg.chem.unc.edu/personal/monroe/cube/Denny3x3/> and
<http://www.helmsoft.org/cube/rubikscube/>, written by Denny Dedmore.
The initial instructions (for completing the first/top layer) and move
icon legend have been omitted for brevity.


Middle Layer Edges
==================

Find a middle-layer edge piece in the bottom row.  Rotate it under the
matching side center color.

To move it up & right:

|bl| |rd| |br| |ru| , |br| |fcw| |bl| |fcc|

To move it up & left:

|br| |ld| |bl| |lu| , |bl| |fcc| |br| |fcw|

If an edge piece is already in place but backwards, simply apply the
above sequences twice.  Put a bogus piece from the bottom row in its
place, moving the problem piece to the bottom.


Bottom Corners
==============

Flip the Rubik’s Cube upside down; the former, unfinished bottom side
becomes the top.  Choose a side color, which becomes the front.

Find the two corners on the top layer with the front side’s color
(regardless of orientation).  They’ll either be adjacent or diagonally
opposite.


Adjacent Corners
----------------

Rotate the top layer so the corners matching the front color are in
front.  If they need to be swapped:

|lu| |tr| |ld| |fcw| , |tl| |fcc| |lu| |tl| , |ld| |tl| |tl|


Diagonally Opposite Corners
---------------------------

Rotate the top until the top left corner is in the correct position
and then perform the following procedure to move the other corner into
the top right position:

|tl| |lu| |tr| |ld| , |fcw| |tl| |fcc| |lu| , |tl| |ld| |tl| 


Swapping The Other Two Corners
------------------------------

If the remaining corners need to be swapped, turn the cube around 180
degrees and perform the following procedure:

|lu| |tr| |ld| |fcw| , |tl| |fcc| |lu| |tl| , |ld| |tl| |tl| 


Finishing The Corners
---------------------

Spin the entire cube (keeping the top up) until the top center colors
match one of the 7 patterns below (ignore other colors).

.. image:: images/corners.png

Orient the cube as shown above and perform this sequence:

|lu| |tr| |ld| |tr| , |lu| |tr| |tr| |ld| , |tr| |tr| 

If the corners are not quite finished, match up the new pattern and
perform the sequence once again.  This process may have to be
performed up to three times.


The Last Four Edges
===================

Usually at least one of the 4 remaining edges will be in place.  Find
that piece and rotate the cube until it is positioned in the front.
If no edge is in place, choose any side to be the front.  Perform the
sequence below once then start over.

Perform the moves below to put all 4 pieces in their correct
locations:

|vu| |tr| |vd| |tr| , |tr| |vu| |tr| |vd|

This step may have to be performed twice to get all edges in place.


Adjacent Flipped Edges
----------------------

Orient the flipped edges so one is in the front and one is to the
right.  Then perform this sequence:

|fcc| |lu| |rd| |hl| , |rd| |rd| |hl| |hl| , |rd| |tr| |tr| |ru| ,
|hr| |hr| |rd| |rd| , |hr| |ru| |tr| |tr| , |ld| |fcw|


Opposite Flipped Edges
----------------------

Orient the flipped edges to the left and right.  Then:

|rd| |hl| |rd| |rd| , |hl| |hl| |rd| |tr| , |tr| |ru| |hr| |hr| ,
|rd| |rd| |hr| |ru| , |tr| |tr|


.. |bl| image:: images/bl.gif
.. |br| image:: images/br.gif
.. |fcc| image:: images/fcc.gif
.. |fcw| image:: images/fcw.gif
.. |hl| image:: images/hl.gif
.. |hr| image:: images/hr.gif
.. |ld| image:: images/ld.gif
.. |lu| image:: images/lu.gif
.. |rd| image:: images/rd.gif
.. |ru| image:: images/ru.gif
.. |tl| image:: images/tl.gif
.. |tr| image:: images/tr.gif
.. |vd| image:: images/vd.gif
.. |vu| image:: images/vu.gif


--------
 Extras
--------

Patterns
========

Source: `Pretty Rubik’s Cube patterns with algorithms`__

__ https://ruwix.com/the-rubiks-cube/rubiks-cube-patterns-algorithms/


Six Spots
---------

Permute the centers of the top, front, & right sides (T → F → R → T),
as well as the down, bottom, & left sides (D → B → L → D).

    U D' R L' F B' U D'

Cross
-----

Rotate each corner in-place, resulting in a cross on each face:

    R2 L' D F2 R' D' R' L U' D R D B2 R' U D2


Cube in a Cube in a Cube
------------------------

Rotate the URF & DLB corners, 2×2 & 1×1.

    U' L' U' F' R2 B' R F U B2 U B' L U' F U R F'