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Date: Thu, 30 Jul 98 14:16:38 EDT
From: Nichael Cramer
To: cube-lovers@ai.mit.edu
Cc: nichael@sover.net
Subject: "Hints" for Solving the 5X
Since you 1] posted to this list and 2] have a 5X and have solved it
the past, I'm going to make the assumption that really want is not
necessarily a cook-book for solving the 5X, but enough hints to get
you started in the right direction.
If I'm wrong about this, you can stop here. ;-) If not, below is
high-level description of a scheme for solving the 5X that assumes
1] that you're 3X3X3-literate and 2] leaves unspecified the details of
the three other simple operations that you'll need.
(Now, this is far from elegant; and certainly not anything like a
maximal solution. But at least it will 1] get your cube solved and 2]
at least you thinking about these things again.)
---
Step 1:
First, ignore everything except the corner cubies, the center (face)
cubies and the center-edge cubes.
Now, paying attention to those cubies only, pretend that you're
dealing with a 3X and "solve" it.
---
Step 2: Solve the non-center edge-cubies [NCEC].
First devise an operator that allows you to cyclically-swap three of
the NCECs (i.e. without messing with any of the previously solved
cubies). With a little clever permutation, this single operation will
allow you to complete this step (but see Step 2A below).
(Note that since a NCEC _has_ to be in its correct orientation when it
is in its corrected location --i.e. a correctly placed NCEC can't be
simply flipped as can a center-edge cubie in a 3X-- you can complete
this step using this single operation.)
Step 2A: There is one wrinkle at this point.
It is possible to be in an "orbit" in which you can apparently "solve"
all of the NCECs except for two. If you reach this point, leave the
two unsolved NCEC alone for the moment. They will be easier to solve
after completing the next step.
---
Step 3: Solve the remaining non-center face cubies [NCFC].
Similar to the above, devise two operators: one that allows you to
cyclically-swap three "corner-like" NCFCs and one that allows you to
cyclically-swap three "edge-like" NCFCs (i.e. without in either case
disturbing the previously-solved cubies).
Again with a little clever permutation you should be able to complete
this step with this single operation.
(Note that since, for a given color, all four "center-like" NCFCs are
pretty much interchangable --as are all four "edge-like" NCFCs. This
means that that any "bogus" symetries are invisible. What this means
is that, by saving this step 'til last, you don't risk getting all the
way to the and finding out you're in some non-standard "orbit" that
you have to back out of.)
---
Step 2A Continuted:
Assuming that you've got this far, you should now be in a state where
the entire cube is solved except for --at most-- two NCECs.
In short, this state of affairs means that your cube is a wrong
"orbit"; i.e. there is a "hidden" symmetry among that cubies that
allows your cube to appear to be more nearly solved than it is.
The quickest way to get your cube in the "correct orbit" is as
follows:
Choose one of the "internal" slices that contains one of non-solved
NCECs (by "internal", I mean a slice that is neither a face slice nor
one that contains a center cubie).
Now rotate that internal slice by a quarter turn (i.e. by 90 degrees)
in either direction.
Now what you want to do is solve remaining cubies from its current
situation.
The tricky part here is keeping everything straight. There are a
couple of things that you can do help this.
1] If possible, you can first manipulation the NCECs in such a way
that the two unsolved NCEC share the same slice and are on the same
face. Then it will be possible --when performing the quarter-turn as
described above-- to bring one of the unsolved NCEC into its correct
location.
Once that is done, you will now have exactly three unsolved
NCECs. Since these must necessarily be a cyclic permuation, you
should be able to solve these without further ado.
Now, all that remains is solving the remaining newly scrambled
face-cubies.
2] If you are unable to position the two unsolved NCEC as described
above, proceed as follows:
>From the current state, (i.e. after performing the quarter-turn
on the internal slice) re-solve the newly shuffled face-cubies
*while*being*sure*not*to*disturb*any*other*cubies!
Once you have all the faces solved, you should now have four NCEC in
the wrong locations, along the single internal slice. Using the
operation that you developed in Step 2 above, this should be easy to
solve.
---
Step 4: Place your newly-solved cube in a prominent place on your
desk and assume a smug demeanor when asked about it.
Hope this helps
Nichael
--
Nichael Cramer
work: ncramer@bbn.com
home: nichael@sover.net
http://www.sover.net/~nichael/