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To: "cube-lovers@ai.mit.edu"
Subject: Square One Solution
Date: Thu, 19 Jun 97 21:53:07 -0500
From: Mike Masonjones
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Cube Lovers,
This is long, but complete solutions are long. I even left quite a bit of
the boring and obvious stuff out, and it still took me 3 hours to write it.
Any errors, let me know. I hope this satisfies.
Apparently I have the least extracurricular life of all of you, since I know
how to solve Square One much quicker than any reports I've seen here. Quite
a dubious honor, I suspect. Anyway, here goes my solution, which with a
little practice, guarantees a solution within 75-100 seconds for someone who
can do The Cube in about 55-60 seconds (assuming there's a correlation in
hand speed from puzzle to puzzle).
The solution is completely my own, as is the notation. Sorry if it offends
anyone.
1. Start by getting to the cube state for the top and bottom faces. Ignore
the middle slice til the very end. This can be most efficiently done by
memorizing a table. A pretty good (but not error-free) one is on the only
square-one web site in existence that I know of. Sorry, you'll have to find
the site yourself with a browser, since I can't look it up right now. I
have a scheme written down somewhere that is quite a bit easier to memorize,
but why should I take the fun away from any of you looking for the solution
yourselves. If there is a big response to this letter, then I will dig out
my easy table.
Tables are difficult to memorize, so I usually just try to get to a six
pointed star on one side and all the little wedges plus the remaining 2 big
wedges on the other. It is easy to get to one of the five possible states
that result, thus requiring memorization of only 5 solutions to get back to
a cube. This method takes about 5-10 seconds longer, an average, than the
table technique.
Using a notation where L represents a large wedgie, and S a small wedgie,
the five possible states can be written as:
1) bottom = LLLLLL, top = LLSSSSSSSS
2) bottom = LLLLLL, top = LSLSSSSSSS
3) bottom = LLLLLL, top = LSSLSSSSSS
4) bottom = LLLLLL, top = LSSSLSSSSS
5) bottom = LLLLLL, top = LSSSSLSSSS
For cases 1),3),5), rotate the top face so that it will be sliced
symmetrically between the two L pieces when the center is flipped. The next
move in each of these cases involves moving the top face one way and the
bottom face the other, when looking from the front. (Front will be the term
used from now on to denote the end nearest you of the central cut through
which flipping occurs (a 180 turn of one half of the cube)). After a flip,
cases 1) and 5) should give two barrel shapes (LLSSLLSS), top and bottom.
You should aim in case 3) for two tomahawk (LLSSLSLS) shapes. Any self-
respecting cubist should be able to get home from here.
Cases 2 and 4 are a little more complicated. For both cases align the top
so that the left half of the top face reads, going clockwise, SLSSS. Flip
right side. Now rotate the bottom so that when you flip with the right hand
, the top will read SlSSSSSLL starting from the front and going clockwise.
Now rotate the top 1/12 turn counterclockwise and the bottom so it reads
LLLLSSL going clockwise from the front and flip again. Now you're in an
easy state to get home from (LLLLSSSS on top and LLSLSSLS on bottom).
2. Now that you're in a cube state top and bottom, get all the wedgies on
their correct side (top and bottom face all the same color, respectively).
This is very straightforward and intuitive. I usually start with one large
wedgie, and sequentially put in one at a time next to it going around a face
until you get down to one S wedgie stuck on the wrong side. Sometimes it is
easier to do LSL on one half of the top, and then do LSL on the other, and
then putting in the second to last S between the groups.
Now position the top face so that the Odd S wedgie (O) is positioned as
LSLOLSLS going clockwise from the front. Put the bottom odd wedgie in front
with the bottom square skewed from the top (bottom should read LSLSLSLO
going clockwise from the front). Now do FT4B1FT-4B-1FT4B1FT-3F, where F =
flip with right hand, Bx = turn bottom face clockwise x/12 of a turn, B-x =
same thing counterclockwise, Tx, T-x mean similar things.
3. Now get L's positioned.
Case 1. No L's are correctly adjacent to each other. Position top and
bottom (top = LSLSLSLS, bottom = SLSLSLSL, each going clockwise from front).
Now go
FB3FT-3B-3FT3F, turn the whole puzzle 180 degrees so that the back of the
central cut is now the front, and repeat the move.
Case 2. Two sets of adjacent pairs are out of whack, one on top, and one on
bottom.
Do the move for case 1 once, with the components of the pairs in question
all nearest the front.
Case 3. Only one adjacent pair correct. Position the top so that the
correctly adjacent pair (denoted as A) is positioned as ASASLSLS, and the
bottom reads LSLSLSLS (same conventions as before). Now do FB-3FB3FB-3FB3F.
Case 4. Only one pair incorrect. Position the top (with the incorrect pair)
so that the correctly adjacent pair is positioned as LSASASLS, and the
bottom reads LSLSLSLS. Do the move in Case 3 twice with a T3 between
instances.
Case 5. One side is OK, the other has no correct adjacent pairs. Bad side =
top. top = LSLSLSLS, bottom = LSLSLSLS. Do the move in Case 3 twice with
T6 between instances.
4. Now check for parity.
With the L's in place it is easy to identify whether you need to change the
parity of the system. It should take an even number of switches to right
the S's at this stage. A cycle of three is even, since it would take two
switches to fix it. A cycle of two or four is odd. If the overall parity
is odd, do the following:
starting with top = LSLSLSLS, bottom = LSLSLSLS, go FT3B3FT1B2FT2B2FT-
2FT2B2FT3B2FT-3B-3T-3B-1FT-2B-2F
This may not be the optimum way, but it preserves the corners, and it's easy
to remember the path. (Try it)
5. Place the S's (they should already be on their correct face). The most
useful moves are the below: All permutations of S's can be solved with
application of a maximum of three of these short moves in sequence, combined
with the appropriate turns in between to set things up.
Move 1. Start with top = LOLSLSLO, bottom = LOLSLSLO, where O = pairs that
will be switched on a given side. Do FT-3FT1B1FT2B-1F. Repeated twice with
a T3 between makes a three-cycle on the top side.
Move 2. top = LSLOLSLO, bottom = LSLOLSLO, O definition same as Move 1. Do
FT1B1FT6FT-1B-1F.
There may be quicker solutions than applying these moves for a 4-cycle/2-
cycle combination or a 4-cycle/4-cycle combination, where you have to apply
3 moves in succession. I'd like to hear about suggestions. I haven't
investigated it too much since these modes come up so rarely.
6. Fix middle slice. If square shaped but wrong, do FT6B6F. Otherwise,
position the bad half on the right, and do FB6FB6F.
Congratulations, you have a solved Square One.
Happy cubing.
Mike Masonjones