IV.   E X A M P L E S   A N D   C O N U N D R U M S

In all the examples below, the tableau will be given here in the text as best
as can be done within the limits of the character set.  For those who want to
see the positions more graphically via the program, each example also starts
with a line of apparent garbage that, if selected, can be read using the
[File: Resume from Selection] command to display the position.  (The line is
quite long and may wrap around onto more than one line when you display it;
you have to select it all to restore the position.)

Some of these examples are extremely complex.  Novice players may wish to
step through just the first example, to get an idea of how to play, and save
the other examples for later.  The final example is a deck that is especially
easy to win with (unless you're trying to win with all eight suits still in
the tableau), so you might try that one to boost your confidence if you're
having a lot of trouble getting anywhere.

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Here, to start you off, is an example of the beginning of a game.  We'll step
through it and look at the rationale behind the recommended moves.  Here's
the initial tableau:

 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	10d	 As	 --	 3h	 9s	 --	 Jh	 Qh	 --
 6d			 4s			 3c			 7c

The two primary rules of thumb to bear in mind throughout the game, and
particularly at the start, are (1) try to get a space, and (2) keep your
options open.  The first rule should be fairly clear; the second leads to a
few common strategic decisions.  First, given the choice, make a "natural"
move instead of an "unnatural" one, where a natural move is one that brings
together two cards of the same suit.  This keeps our options open by allowing
us to move the newly combined cards as a unit should we turn up an
appropriate card.  Second, given the choice, move a card (or pile) that has
more than one place it can go.  This keeps our options open by allowing us to
move it to the other place if for some reason we want to dig into the pile
sitting in the first location.  Third, work from the top down.  Thus we move
a 9 onto a 10 before moving an 8 onto the 9 (unless the latter move is
natural while the former is not), since once we move an unnatural 8 onto the
9 we won't be able to move the 9.  Now, with these ideas in mind, let's look
at the play of the above tableau.

Our highest-ranking move is Jack onto Queen, and it's also our only natural
move, so it wins for sure.  We move the Jh from column 8 to column 9, and in
this particular game we chance to turn up a 6s in column 8.  Now we have no
natural moves.  We could try for the space by moving the 6s to column 10, but
that move isn't going to go away, so instead we go from the top down by
moving the 10d from 2 to 9.  This time we turn up a 4c.  No hesitation about
this one!  We move the 3c from 7 to 2.  (Note that we still have the 4s onto
which we can, eventually, move the 3h, so we're not giving up our option of
digging into pile 5.  But even if we didn't have the other 4, making the
natural move would be the better play.)  In column 7 the card turned up is a
2c, which we promptly move to column 2, turning up a 10h.  The tableau is
now:

 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 4c	 --	 --	 --	 --	10h	 6s	 --	 --
 --	 3c	 As	 --	 3h	 9s			 Qh	 --
 6d	 2c		 4s					 Jh	 7c
								10d

Having once again run out of natural moves, we revert to working from the top
down, and move the 9s from 6 to 9.  This also follows the rule of moving a
pile that has more than one place to go; if we find ourselves interested in
digging through column 9 we can move the 9s to column 7 instead.  But for
now, since column 7 looks like a more likely place to dig, we'll bury column
9 a bit more.  In column 6 we turn up a Kc.  Since we have no place to move
the 10d from column 9, we are unable to get pile 9 moved onto the newly
revealed King.  Them's the breaks.

Continuing from the top down, we decide it's time to move a 6 onto the 7c.
Which 6 should we move?  Neither is natural, but the one in column 8 looks
like a better one to move since we're only 3 cards away from getting a space
in that column.  So we move the 6s from 8 to 10 and turn up a 6c.  We're
getting low on things to do now; we can move the 3h or the As.  Going by the
top-down rule, we move the 3h from 5 to 4, turning up a 2h, which we move
onto the 3h (now in column 4).  This time we turn up a 9d:

 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 --	 --	 --	 9d	 --	 --	 6c	 --	 --
 --	 4c	 --	 --		 Kc	10h		 --	 --
 --	 3c	 As	 --					 Qh	 --
 6d	 2c		 4s					 Jh	 7c
 			 3h					10d	 6s
 			 2h					 9s

We could now move the 9d from 5 to 7, but instead we choose to move the As
from column 3, since there are two places to put it.  Column 4 is already
unnatural, so we'll move it there.  The card turned up is the other As.  We
could move this Ace onto the other deuce, but this would lose us our option
of moving the first Ace there should we want to dig into column 4, so we'll
let the top-down rule take precedence and move the 9d.  But let's not be
hasty!  Instead of moving the 9d from 5 to 7, we'll move the 9s from 9 to 7
and then move the 9d from 5 to 9; this puts the 9d with a 10d, which it can't
hurt to do.  This time we turn up a Qh.  Since we're so close to a space now,
we keep going by moving the Qh from 5 to 6, turning up a 10d:

 --	 --	 --	 --	10d	 --	 --	 --	 --	 --
 --	 --	 --	 --		 --	 --	 --	 --	 --
 --	 --	 --	 --		 --	 --	 6c	 --	 --
 --	 4c	 As	 --		 Kc	10h		 --	 --
 --	 3c		 --		 Qh	 9s		 Qh	 --
 6d	 2c		 4s					 Jh	 7c
			 3h					10d	 6s
			 2h					 9d
			 As

Only one move left to try: we move the As from 3 to 2, turning up a 7h.  Once
again, we shuffle things around a bit so keep as many piles natural as
possible; we move the 6s from 10 to 3 and the 6c from 8 to 10, turning up a
5d.  We move the 5d from 8 to 1 (natural) and turn up a 3s:

 --	 --	 --	 --	10d	 --	 --	 3s	 --	 --
 --	 --	 --	 --		 --	 --		 --	 --
 --	 --	 7h	 --		 --	 --		 --	 --
 --	 4c	 6s	 --		 Kc	10h		 --	 --
 --	 3c		 --		 Qh	 9s		 Qh	 --
 6d	 2c		 4s					 Jh	 7c
 5d	 As		 3h					10d	 6c
			 2h					 9d
			 As

We have no more moves (aside from useless maneuvers such as moving the 9d
from 9 to 5), so it's now time to deal a new round.  We never did get a
space, but we got two piles down to a single card each, so we are quite
likely to get a space soon after the new deal.  This game is going somewhat
better than average and will very likely be won with proper play.  If you
actually do get a space in the first round, you're doing particularly well.

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Now, for your first "Spider problem", here is a relatively simple position.
In the tableau shown below, what should you do?  First off, what are your
options?  On what should you base your choice?  (After the tableau is the
"solution", so don't read further until you're ready!)

10h	(sp)	 --	 Ad	 --	 Qc	 --	 3s	 Qh	 --
		 --	 7d	 --	 Jh	 --	 2s		 --
		 --	 6d	 Kh	10d	 --			 --
		 8s	 5d	 Qc	 6c	 --			 7d
		 7s	 Qs	 Jc	 4c	 Qd			 6d
		 6s	 Js	10c	 3d	 Jd			 5d
			10d	 9c	 2d	10h			 4d
				 8c		 Js			 3d
				 7c		10s			 2c
				 6c		 9s			 As
				 5c		 8h
				 4c		 7h
				 3c		 6h
				 2c		 5h
				 Ac		 4s
				 Qd		 3h
				10c		10s
				 9c		 8c
				 8s		 7h
				 7s		 6h
				 6s		 5h
				 5s		 4h
				 4s		 3h
				 3s		 2h
				 2s		 Ah

Solution:

First, the options.  There's no way to get through column 5 or 7 to turn up a
new card.  (This should be pretty obvious; we'll save detailed analyses of
this sort of thing for cases where it's not as clear.)  Nor does it do us any
good to dig into column 4 or 6.  We don't have any complete suits showing, so
there's no way we can try to put one together.  That leaves three fairly
simple options: (1) we could move the 8-6s from column 3 into the space,
turning up a new card, (2) we could dig through column 10 (moving the Ace
onto a deuce, the 2c into the space, 5-3d onto the 6s in column 3, 2c out of
the space and back onto the 5-3d, and finally the 7-6d into the space) and
turn up a new card there, or (3) we could fill in the space and deal a new
round.

It's usually a good idea to turn up more cards when possible rather than bury
everything under a new deal, so we'll discount the third option.  That leaves
us with the choice of which column to dig through, 3 or 10.  The two are
equally close to becoming new spaces (three face-down cards each), so that's
not a consideration here.  Let's consider what the face-down card might be
that will be revealed.  If it's a Jack, 4, or King, we can get back the space
(which we'll have lost in the process of getting to the new card).  If it's a
9 or 8, we MIGHT get the space back right away; it depends on whether we
moved the 8 (from column 3) or the 7 (from column 10) into the space.
Looking at the tableau, we see there are five 8's visible, but only three
9's.  Thus it's more likely we'll turn up a 9, so we should go for column 3.
(Sorry for all this gory detail, but this is after all intended as an
introductory example.)

So it looks like the best thing to do is move the 8-6s from column 3 into the
space.  But wait!  Suppose the card turned up isn't a Jack, 4, King, or 9,
and furthermore isn't an Ace or 5 (which we would be able to move elsewhere
immediately)?  Is there anything we can do ahead of time to hedge our bets?
Yes!  We can move the spade Ace from column 10 to column 5, then use the
space to swap the deuces in columns 6 and 10 (move one deuce into the space,
move the other deuce to the other column, and move the first deuce out of the
space).  Now column 10 contains just the 7 through deuce of diamonds, and if
we chance to turn up an 8 in column 3 we can move the 7-2d onto it.  Note
that we have to do this BEFORE we move the 8-6s into the space, since we need
the space to swap the deuces.  In fact, in the game where this particular
tableau arose, the card turned up in column 3 was the diamond 8.  The
preparations made in column 10 eventually produced not one but TWO spaces!
(Play it out using the program and see for yourself.)

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Turn up another face-down card WITHOUT dealing more cards or "using up" the
space.  (You may, of course, use the space, so long as you are sure you can
get it back no matter what the card turned up turns out to be.)  Note that
there are enough clubs and hearts showing to form complete sets of those
suits.  Here's the tableau (again, the solution follows the tableau):

 --	 --	(sp)	 --	 Qh	 --	 --	 --	 --	 --
 --	 --		 Ks	 Jh	 --	 Jc	 --	 --	 --
 --	 --		 2s	 7h	 --	 8h	 --	 --	 Kh
 --	 --		 As		 As	 7h	 Kc	 --	 Qc
 Jc	 Kd		 9h		 9h		 Qc	 Kc	 Jh
10h	 9d		 8d		 8s		 Jd	 7s	 Js
 9c	 8d				 7c		 5s	 6s	 3d
 8s	 7d				 6c		 4h	 Qh	 2c
 7d	 3h				 5c		 3c	 Js	 Ad
 6h	 2h				 4h		 2c	 8c	 8h
 5d	 Ah				 3s		 Ac
 3d	 2d				 2s		10s
 2d					 5c		 9s
 Ah					 6d		 8c
 9s					 5h		 7s
10c							 6s
							 5s
							 4c

Solution:

First, we ascertain that we can't get a second space.  The only place where
we might be able to do so is column 5, and to move the Q-Jh we need to find a
King that doesn't already have a Queen on it.  (We'll call this a "free
King", for short.)  There are three free Kings, but the one in column 9 is
useless since we need another free King to get to it, and those in columns 2
and 4 are inaccessible since there are no free 3's.  Hence, whatever we do,
we have to do it using only the one space.

Next, can we remove a complete set of clubs or hearts?  Well, hearts are out,
because the only Kh showing is in column 10, and the only 10h is in column 1,
and getting to each of them requires that we move a 3 onto a free 4.  Since
there's only one free 4 (in column 8), we lose.  How about clubs?  They don't
work out, either, but the proof is trickier.  The only 9c is in column 1 and
getting to it will require our sole free 4.  Thus we can't use the Qc in
column 10, and must instead use the Qc from column 8.  To reach it we need a
free 6; we have exactly one free 6, namely in column 9.  We CAN get to this
6, without losing the space, by a fairly convoluted sequence of moves.  You
may want to figure out how it can be done before reading on. . . .  Ready?
Okay, proceed as follows: 7h from 5 to 10, 10c from 1 to 5, 8c from 9 to 1,
Js from 9 to 3 (into the space), 10c from 5 to 3, Jh from 5 to 9, 10c from 3
to 9, Js from 3 to 5, 10c from 9 to 5, Q-Jh from 9 to 3, 7-6s from 9 to 4,
and finally Q-Jh from 3 to 9, getting the space back.

Having determined that we can, if desired, obtain a free 6, let's get back to
the question of the clubs.  The only 7c is in column 6, and getting to it
requires a free 6.  But we need the free 6 to get to the Qc as well.  So we
again lose.  We are thus reduced to uncovering a card without removing any
suits and without getting any more spaces.  Which column is it to be?  It
obviously can't be a column containing a King, since (given that we can't
remove any completed suits) the only place a King can go is into the space.
And it can't be column 1 or 7, since that would require a free Queen, and
there isn't any.  So it must be column 6.  We can get through that column by
first digging through to the free 6 as described earlier, and then playing:
5h from 6 to 4, 6d from 6 to 10, 5c from 6 to 10, 3-2s from 6 to 3, 4h from 6
to 4, 3-2s from 3 to 4, 7-5c from 6 to 1.  The tableau now looks like this:

 --	 --	(sp)	 --	 Qh	 --	 --	 --	 --	 --
 --	 --		 Ks	 Js	 --	 Jc	 --	 --	 --
 --	 --		 2s	10c	 --	 8h	 --	 --	 Kh
 --	 --		 As		 As	 7h	 Kc	 --	 Qc
 Jc	 Kd		 9h		 9h		 Qc	 Kc	 Jh
10h	 9d		 8d		 8s		 Jd	 Qh	 Js
 9c	 8d		 7s				 5s	 Jh	 3d
 8s	 7d		 6s				 4h		 2c
 7d	 3h		 5h				 3c		 Ad
 6h	 2h		 4h				 2c		 8h
 5d	 Ah		 3s				 Ac		 7h
 3d	 2d		 2s				10s		 6d
 2d							 9s		 5c
 Ah							 8c
 9s							 7s
 8c							 6s
 7c							 5s
 6c							 4c
 5c

Once again, it's time to make contingency plans.  If we just move the 9h-8s
onto the 10c and the As onto the 2s, we could be in trouble if we turn up a
King.  The lone space won't be sufficient for us to be able to move the stuff
out of column 5 onto the King.  So we undo some of what we did in the course
of getting the free 6: Jh from 9 to 3, 10c from 5 to 3, Js from 5 to 9, 10c
from 3 to 9, Jh from 3 to 5.  While we're at it, it can't hurt to move the 4c
from 8 to 1, and in a moment we'll match the 8s with a 9s, too.  We now
proceed: 8s from 6 to 3, 9h from 6 to 9, 8-5c from 1 to 9, 8s from 3 to 1,
and finally As from 6 to 4.  (Once again, preparation pays off; in the game
where this took place, the card turned up was indeed a King.)

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Again, complete sets of clubs and hearts are available.  Without dealing any
more cards or turning up any face-down cards, remove a set of clubs AND a set
of hearts (not necessarily in that order).  Can you remove them in the other
order?

 --	 --	 8c	 Ks	 Kh	 5c	 Kc	 --	(sp)	 --
 --	 --		 Qh	 Qh			 --		 --
 --	 --		 Jc	 Jh			 --		 Kh
 --	 --		10c	10c			 Kc		 Qc
 Jc	 Kd		 9c	 9h			 Qc		 Jh
10h	 9d		 8c	 8d			 Jd		 Js
 9s	 8d		 7c	 7d			10h		 3d
 8s	 7d		 6c	 6d			 9h		 2c
 7s	 3h		 5c	 5d			 8h		 Ad
 6s	 2h		 4c	 4h			 7h		 8h
 5s	 Ah		 3c	 3d			 6h		 7h
 4s	 2d		 2c	 2d			 5h
 3c	 Ah		 Ac				 4h
 2s							 3h
 As

Solution:

The clubs look like the better bet, since the Jack through Ace are already
assembled and there's a King-Queen in column 8.  Let's see what can be done.
Since there are no free 9's or 6's, we have to remove the first completed
suit without the benefit of any additional spaces.  Since we are also short
on free 4's, this means we can't use the Qc in column 10.  That seems okay;
the one in column 8 looks easier to get to anyhow.  All we have to do is move
the Jd somewhere (along with the 10-3h).  There are no free Queens, so the
Jack will have to move into the space (or some other Jack must move into the
space to free up a Queen).  But we can't move the Jd anywhere while the
hearts are there, and the only free Jack is in column 10 where we can't get
at it.  We could move the 10-3h into the space, but then what do we do with
the Jack?  Looks like the clubs aren't going to work after all.

Let's try the hearts.  It looks like we'll have the same problem, since we
have to move the 10c from column 5 somewhere else to clear off the K-Jh.  The
only place we can move the 10c is the space, and to do that we have to do
something about the 9h attached to the 10c.  Since we don't have any free
10's, what can we do?  The idea is to use the space to swap things around
such that the sequences of a single suit are where we need them most.  We do
it as follows:  First we get the 4h out of the way by moving 3-2d from 5 to
9, 4h from 5 to 6, and 3-2d from 9 to 6.  Then we move 8-5d from 5 to 9, 8-3h
from 8 to 5, 8-5d from 9 to 8, 9-3h from 5 to 9, 9-Ac from 4 to 5, 9-3h from
9 to 4, 8-5d from 8 to 9, 8-3h from 4 to 8, 8-5d from 9 to 4 (we certainly
have made a mess of all those nice clubs in column 4, haven't we?), 10-Ac
from 5 to 9, 10-3h from 8 to 5, 10-Ac from 9 to 8.  Now we can move the Ah
from 2 to 6, 2d from 2 to 9, and 2-Ah from 2 to 5 to complete the hearts.
The 2d comes out of the space and back to column 2, and removing the hearts
gives us a second space.  With two spaces we have no trouble straightening
the clubs back out and completing a set.

Note that, rather than removing the completed set of clubs from column 8, we
should pile a Q-Ac into column 7 and remove the suit from there.  We can
always move the Kc from column 8 into the newly created space in column 7 if
we wish, but by getting the space we keep our options open.  Note also that,
had there been a 10d around, we might have been able to pull the same trick
with the Jd in column 8 as we did with the 10c in column 5; since there
wasn't, though, we had to go after the hearts first.

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In the tableau below, there are two deals (20 cards) remaining.  What do you
do?

 Kh	 Ks	 Kh	 Qh	 Jc	 Qd	 Js	 9s	10s	 6d
 Qh	10h	 Qs	 Ac	10c	 Jh	 Kc	 9c	 Kd	 Qs
 Jd	 9d	 8s	 Ac	 9h	10h	 Qc	 Kc	 Qd	 Js
10s	 8d	 7h	 4s	 8h	 6s	 Jc	 9h	 Jd
 9s		 6h	 3h		 5s	10c	 8h	10d
 8s		 5h			 4h	 9c	 7h	 9d
 7s		 4h			 3h	 8c	 6h	 8c
 6c		 8d			 2h	 7c	 5d	 7s
 5c		 7d			 As	 6c	 4s	 6s
 4c		 6d				 5c		 5s
		 5d				 4c
		 4d				 3c
		 3d				 2c
		 2d				 3s
		 Ad
		 7d

Solution:

If you grabbed at the opportunity to remove a set of clubs from column 7,
shame on you!  Once you do that, you're stuck, and except for a little bit of
"naturalising" (swapping cards so as to create longer runs in a single suit)
you can do nothing but deal out another round.  In fact, it is possible to
remove TWO suits, get two spaces, and straighten out almost all the suit
changes before running out of steam.  But let's start by looking at the
various options available to see what our reasoning should be.

Ignoring for the moment whether we can remove any suits, can we get a space?
Obviously, we can't get a space in any column containing a King, which leaves
columns 4, 5, 6, and 10.  Column 5 is hopeless because the only free Queens
(columns 3 and 4) cannot be reached without either two free 9's or two free
deuces.  We have one free deuce (column 7) and both free 9's are trapped
under a King.  Getting through any of the other columns requires a free
King.  The King in column 8 cannot be reached without the temporary use of a
free 6, and the only such 6 is under a Queen and thus requires another free
King to reach.  On the other hand, we CAN reach the King in column 2.  But in
order to do so we need temporary use of a free 10, which means we'll have had
to move the 6s from column 6 onto our only free 7.  Thus, though we might be
able to move the Qs out of column 10, we wouldn't have any place to move the
6d.  And, since we lack a free Queen on which to park the Jh from column 6,
the free King won't be enough to get through that column.  Column 4 we've
already identified as being hopeless.  Thus we conclude that we can't get a
space without removing any suits.

Now what?  If we remove the clubs from column 7, all we get is a free Jack,
which we have no use for, and which we can't move out of the way.  We can't
remove a set of spades since we have no 2s showing, and likewise there's no
Ah visible.  We can't remove diamonds (at least, not first) because we can't
get to the Kd without a free 9 on which to park the 8c, and both free 9's are
trapped under a Kc.  So it looks like the first order of business is to
remove a set of clubs from column 8, if possible.

That's a big "if"; it looks rather hopeless.  Digging through to the Kc
requires temporary use of a free 5 and 6, and permanent use of a free 10.
Well, a moment ago we said we might be able to reach the 6d in column 10.
Can we in fact do so?  Yes, if we're VERY careful!  Once we uncover the Ks in
column 2, we want to be able to move the Q-Js from column 10, so we can't
afford to put the 10h from column 2 on top of them.  That means we have to
find a 10s to move to column 10, thereby freeing up a different Jack.  Such a
10 is in column 1, and we'd better move it BEFORE using up the free 7!
Without further ado, here we go: 6-4c from 1 to 3, 10-7s from 1 to 10, 3s
from 7 to 8, As from 6 to 7, 4-2h from 6 to 9, 6-5s from 6 to 10
(conveniently the correct suit), 9-8d from 2 to 6, 10h from 2 to 1, Q-5s from
10 to 2, 4-3s from 8 to 2, 5d from 8 to 10, 9-6h from 8 to 1, As from 7 to 9,
Q-2c from 7 to 8, 3h from 4 to 3, 4s from 4 to 10, Ac from 4 to 8, and voila!
we remove a set of clubs from column 8.  Here's the new tableau:

 Kh	 Ks	 Kh	 Qh	 Jc	 Qd	 Js	 9s	10s	 6d
 Qh	 Qs	 Qs	 Ac	10c	 Jh	 Kc	 9c	 Kd	 5d
 Jd	 Js	 8s		 9h	10h			 Qd	 4s
10h	10s	 7h		 8h	 9d			 Jd
 9h	 9s	 6h			 8d			10d
 8h	 8s	 5h						 9d
 7h	 7s	 4h						 8c
 6h	 6s	 8d						 7s
	 5s	 7d						 6s
	 4s	 6d						 5s
	 3s	 5d						 4h
		 4d						 3h
		 3d						 2h
		 2d						 As
		 Ad
		 7d
		 6c
		 5c
		 4c
		 3h

Unfortunately, though we've uncovered a free 9, there's no longer anything we
can do with it, because we've added some crud to column 9, not to mention
column 3.  Furthermore, if we're going to form a set of diamonds, we'd best
not lose track of the stuff in column 3.  So let's go back to the very
beginning and try again, this time keeping things a bit more available: 7d
from 3 to 5, 6-4c from 1 to 5, 10-7s from 1 to 10, 3s from 7 to 8, As from 6
to 7, 4-2h from 6 to 9, 6-5s from 6 to 10, 9-8d from 2 to 6, 10h from 2 to 1,
Q-5s from 10 to 2, 4-3s from 8 to 2, 5d from 8 to 10, 9-6h from 8 to 1, 4-2h
from 9 to 10, As from 7 to 10, Q-2c from 7 to 8, 3h from 4 to 5, 4s from 4 to
9, Ac from 4 to 8, and again we are able to remove a set of clubs from column
8.  Now, however, the tableau looks like this:

 Kh	 Ks	 Kh	 Qh	 Jc	 Qd	 Js	 9s	10s	 6d
 Qh	 Qs	 Qs	 Ac	10c	 Jh	 Kc	 9c	 Kd	 5d
 Jd	 Js	 8s		 9h	10h			 Qd	 4h
10h	10s	 7h		 8h	 9d			 Jd	 3h
 9h	 9s	 6h		 7d	 8d			10d	 2h
 8h	 8s	 5h		 6c				 9d	 As
 7h	 7s	 4h		 5c				 8c
 6h	 6s	 8d		 4c				 7s
	 5s	 7d		 3h				 6s
	 4s	 6d						 5s
	 3s	 5d						 4s
		 4d
		 3d
		 2d
		 Ad

Now we can get out a set of diamonds as follows: 7-4s from 9 to 6, 8c from 9
to 8, 8-Ad from 3 to 9, and remove the diamonds:

 Kh	 Ks	 Kh	 Qh	 Jc	 Qd	 Js	 9s	10s	 6d
 Qh	 Qs	 Qs	 Ac	10c	 Jh	 Kc	 9c		 5d
 Jd	 Js	 8s		 9h	10h		 8c		 4h
10h	10s	 7h		 8h	 9d				 3h
 9h	 9s	 6h		 7d	 8d				 2h
 8h	 8s	 5h		 6c	 7s				 As
 7h	 7s	 4h		 5c	 6s
 6h	 6s			 4c	 5s
	 5s			 3h	 4s
	 4s
	 3s

Well, looking better, but it's still not obvious where we can find a space.
Based on the "free" cards, there are only two possibilities: either we use
the 10s in column 9 to uncover the 9s in column 8 and thus the Qs in column 3
and thus get a space in column 5, or we dig through column 6.  Column 5
doesn't work because we need temporary use of a free 7.  It may be that, by
judicious advance planning, we could have arranged to have a clearer path
through this column (e.g., by building column 1's hearts in column 5), but we
needn't go back for a third try because we can get through column 6 anyway.
We'll need temporary use of an 8, 10, and Queen, and getting the Queen will
require permanent use of the 10, so we have to do things in the right order
again.  Moreover, we have to be careful not to build anything new in column 6
that will be hard to move out later.  So we do it this way: 7-4s from 6 to 8,
9-8d from 6 to 9, 7-4s from 8 to 9, 9-6h from 1 to 6, 9-8c from 8 to 1, 7-4h
from 3 to 1, 8s from 3 to 8, J-6h from 6 to 3, Q-3s from 2 to 7 (to prepare
for later), and Qd from 6 to 2.  And here we are:

 Kh	 Ks	 Kh	 Qh	 Jc	(sp)	 Js	 9s	10s	 6d
 Qh	 Qd	 Qs	 Ac	10c		 Kc	 8s	 9d	 5d
 Jd		 Jh		 9h		 Qs		 8d	 4h
10h		10h		 8h		 Js		 7s	 3h
 9c		 9h		 7d		10s		 6s	 2h
 8c		 8h		 6c		 9s		 5s	 As
 7h		 7h		 5c		 8s		 4s
 6h		 6h		 4c		 7s
 5h				 3h		 6s
 4h						 5s
						 4s
						 3s

Without detailing the exact moves from here on, the next steps should
probably be something like this: Jc-3h from column 5 onto Qd in column 2,
getting second space.  Swap 9-8d in column 9 with 9-8s in column 8 to form
10-4s in one chunk.  Move Kc-3s from column 7 into a space and get the space
back by moving 10-4s onto Js.  Move Ac from column 4 into a space and get the
space back by moving J-6h from column 3 onto Qh and J-4s onto Qs.  After a
bit more "naturalising", you should have a tableau something like:

 Kh	 Ks	 Kh	(sp)	 9d	 Kc	 Qs	 Ac	(sp)	 6c
 Qh	 Qs	 Qh		 8d	 Qd	 Js			 5c
 Jc	 Js	 Jh		 7d	 Jd	10s			 4c
10c	10s	10h		 6d	10h	 9s
 9c	 9s	 9h		 5d	 9h	 8s
 8c	 8s	 8h		 4h	 8h	 7s
	 7s	 7h		 3h	 7h	 6s
	 6s	 6h			 6h	 5s
	 5s	 5h				 4s
	 4s	 4h
	 3s	 3h
		 2h
		 As

This is as much straightening out as you can accomplish with the cards
available, so it's finally time to deal another round.  But first, you have
to fill in the spaces (them's the rules!).  So how should you fill them in?
It's largely a matter of personal preference, but one likely possibility is
to move the Q-Jd into one space and the 10-6h into the other.  The reason for
this is that there's already a Queen in a space, so by creating a free King
you have an extra chance at a space early in the next round.  Granted that
you are almost certain to win at this point, but you might as well maximise
your chances anyway!

===========================================================================

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Can a set of spades be removed WITHOUT first getting a space or dealing any
more cards?  If so, how?  If not, prove it!  Would it make any difference if
the Js in column 7 were swapped with the Jd in column 9?  (The second
"garbage" line above is for this modified tableau.)  Finally, given that it
can be done, remove a set of hearts (as usual, without dealing any more
cards).  What is the minimum number of other suits that must be removed in
order to do so?  Does the order of the two face-down cards matter?

 Kd	 Jc	 9h	 9c	 Qh	 9d	 Qc	 Ks	 --	 Qs
 Qd	10c	10s	 8c	 Jc	 Qh	 Kc	 Js	 --	 Kc
 Jd	 9c		 5s	10h	 Jh	 Qs	 2d	 Jd	 3c
10d	 8c		 7d	 9h	 Ad	 Js	 Ac	 7d
 9d	 7c		 Kd	 8h		10d	 7h	 6h
 8d	 6c			 6s		 9s		 5c
 7h	 5c			 5s		 8s		 4h
 6d	 4s			 4s		 7s		 3h
 5d	 3s			 3s		 6s		 2d
 4d	 2s			 2c		 Qd		 Ah
 3d	 As			 6h				 4c
 2h	 As			 5d				 3c
 Ah				 4d				 2c
 8h				 9s				 Ac
								 7c

Solution:

This is a complicated one, so take a deep breath!  (If you didn't find it
complicated, then perhaps you weren't thorough in your analysis.  Unless you
(a) decided the spades could not be removed without getting a space, (b)
realised that swapping the Jacks affects this, and (c) considered the 9d in
column 1 at some point in your proof, your analysis is incomplete.)

First let's consider the problem of putting together a set of spades.  We
begin by finding all the pieces.  The only Ks is in column 8; the only Qs we
can possibly get to without a space is in column 7.  (Actually, we shouldn't
be too hasty; if we could remove a set of clubs without getting a space, we
could reach the Qs in column 10.  But in moving the Qs we'd create a space,
whether we needed it or not; and besides, the only Qc is in column 7 with the
other Kc in the way.)  In digging to the Ks and Qs we'll reach both Jacks, so
they shouldn't be a problem.  The 10s is in column 3, and the remaining
spades are at various depths in columns 2, 5, and 7.  Can we pull all these
cards together?

To get to the Ks we need a free 8, a free 3, and a free Queen (even though we
may end up using the Js from column 8, we need some place to put it in order
to get to the King).  The 8 in column 4 is inaccessible unless we can remove
a set of diamonds, which in turn is impossible without a space since the 7d
in column 4 is inaccessible and likewise for the 7d in column 9 due to the
absence of free 5's.  But we have a free 8 in column 1 and another in column
5 (if we can reach it), so there's no problem with that.  We also have
exactly one free 3, and one free Queen.  So far so good.  Can we reach the Qs
in column 7?  That requires a free King, which is no problem.  It also
requires someplace to move the 9-6s and the 10d.  This should pose no problem
either.  Note that, though we need a free 10 and a free Jack for this, we
don't "use up" those free cards by moving the 9-6s and 10d, since we uncover
another 10 and Jack to become new free cards.  However, notice that we're
eventually going to have to reach the 5s in column 5, and this will use up
the free 10.  So we have to dig through column 7 before that.  In fact, we
have to move the 10d out of column 7 before moving the 9s out of column 5,
because once we move the latter we'll have 9's on all the 10's, and the 10d
won't be movable.  Or will it?  If we could put a 9d onto the 10d (freeing up
a different 10), we could move the 9s onto the newly freed 10 and still be
able to move the 10d.  Let's assume for the moment that this is impossible
(we'll prove it later, but don't want to digress too far here).  To repeat,
then, we need to move the 10d out of column 7 before moving the 9s out of
column 5.  Where does the 10d go?  The free Jack in column 9 is inaccessible
without a free 5, and the other free Jacks (in columns 6 and 8) each require
a free deuce (even though the Jack in column 8 doesn't require us to use up
the deuce permanently).  The only free deuce is in column 5, and we can't get
to it without moving the 9s.  So we're stuck!

Now let's follow out that digression and make sure we can't get a 9d onto the
10d.  We certainly can't use the 9d in column 6, since that would create a
space, which is verboten.  In order to reach the 9d in column 1, we'd have to
move the 8h.  If we put it onto the 9s in column 5, we would then be unable
to move that 9s later on (we have only one free 9 available; as we'll see
later, we can't get to the one in column 3 without moving the 9s from column
5).  If we moved the 8-6s from column 7 onto the 9s in column 5, and then
moved the 8h onto the newly freed 9s, we wouldn't be able to move THAT 9s
later, so we either wouldn't be able to reach the Qs (if we had left the 9s
in column 7 when we put the 8h on it) or else we'd be unable to reach the 10s
(if we had moved the 9s there first).  So, although we might be able to get
the 9d from column 1 onto the 10d in column 7, by the time we did so we'd
have made a hopeless mess out of the spades.  The conclusion from all this is
that it's impossible to remove a set of spades without first getting a
space.

Now, what if the Jacks were swapped as described?  In that case, we wouldn't
need a free Jack on which to park the 10d; we could move the J-10d as a
unit.  So the plan is to move the Qd out of column 7, followed by the 9-6s
and J-10d.  Then we can use up the free 10 by moving the 9s out of column 5
and finish bringing together the spades.  The complete sequence is: Qd from 7
to 4, 9-6s from 7 to 3, J-10d from 7 to 4, 9s from 5 to 4, 5-4d from 5 to 3,
7h from 8 to 1, 6h from 5 to 1, 5-4d from 3 to 1, 2c from 5 to 10, 5-3s from
5 to 3, Ac from 8 to 10, and now we have to be careful not to move the 2d
from column 8 onto the spades in column 3, so instead we move 3s from 3 to 1,
2d from 8 to 1, Js from 8 to 7, Q-Js from 7 to 8, 10-4s from 3 to 8, As from
2 to 1, and 3-As from 2 to 8.  Voila!

That was for warm-up; what about removing the set of hearts?  The first step
is easy: we look around to see where all the hearts are and find that the
King and 5 are missing.  Hence these must be the two face-down cards.  It
remains to be seen whether their order is significant.

In the course of discussing the spades, we observed that we cannot remove a
set of diamonds or clubs without first getting a space, and we also proved
the same thing for the spades.  Since we can't get past the 4c in column 9
without a space, it looks like our first order of business is getting one.
Columns 1, 4, 7, 8, 9, and 10 are out, for obvious reasons.  Column 3 looks
like the best bet, but in order to move the 10s we need a free Jack, and that
in turn requires a free deuce, and THAT requires that we move the 9s from
column 5 onto the 10s.  Thus, by the time we manage to move the 10s, we'll no
longer have a free 10 on which to put the 9h to get the space.  Column 6 is
similarly hopeless; in order to move the Ad we need to use up the free 10.
Column 2 is out of the question since there's no place to put the 4-As.  That
leaves column 5.

To get through column 5 we need to use up a 10, two 7's, and a King, and we
also need temporary use of a 6, 3, Jack, and Queen.  Getting the Jack will be
no trouble once we've gotten to the 2c, and getting the 6 just needs another
free King, which we can get from either column 8 or column 10.  Let's use the
one in column 10; the only thing we have to watch out for is that if we wait
too long to uncover that King (in particular, if we wait until we need it to
put the Qh on to clear the space), we may find the 3c is immovable due to our
having moved stuff onto it in the meanwhile.  So we have to move the 3c onto
the 4d at some early opportunity.  Here we go: 9s from 5 to 3, Qd from 7 to
4, 5-4d from 5 to 7, 6h from 5 to 8, 2c from 5 to 10, 6-3s from 5 to 9, 3-2c
from 10 to 7, Ad from 6 to 7, 10-8h from 5 to 6, Jc from 5 to 4, and finally
Qh from 5 to 10.  The tableau now looks like this:

 Kd	 Jc	 9h	 9c	(sp)	 9d	 Qc	 Ks	 --	 Qs
 Qd	10c	10s	 8c		 Qh	 Kc	 Js	 --	 Kc
 Jd	 9c	 9s	 5s		 Jh	 Qs	 2d	 Jd	 Qh
10d	 8c		 7d		10h	 Js	 Ac	 7d
 9d	 7c		 Kd		 9h	10d	 7h	 6h
 8d	 6c		 Qd		 8h	 9s	 6h	 5c
 7h	 5c		 Jc			 8s		 4h
 6d	 4s					 7s		 3h
 5d	 3s					 6s		 2d
 4d	 2s					 5d		 Ah
 3d	 As					 4d		 4c
 2h	 As					 3c		 3c
 Ah						 2c		 2c
 8h						 Ad		 Ac
								 7c
								 6s
								 5s
								 4s
								 3s

Where do we go from here?  Well, we're trying to minimise the number of suits
(other than hearts) removed, so let's see if we can get the hearts out right
away.  We would need to dig through column 9; to do that we would have to
move the 4-Ac into the space (or onto a free 5; we'll come back to this),
after which we would have no place to move the 4-3h.  If we could get a free
5 without using up the space, we might fare better, but the only free 5 is in
column 4, and to get to it we must put the Kd into the space (remember we're
assuming we're not going to remove any other suits) and we have no free 10
with which to restore the space via column 4.  Nor can we get any more
spaces; all columns contain Kings or 9's or Aces, and there are no free 10's
or deuces, so digging through any pile would cost us the space, and would get
us at most one space in return.  Thus we conclude that we must remove another
suit before the hearts.  Which suit is it to be?

It can't be clubs.  To reach the 10c (in column 2) we must move the first As
into the space, since there are no free deuces anywhere.  Having done so, we
have no place to move the 4-As.  (We have already noted that getting to the
free 5 costs us the space.)  On the other hand, we CAN remove either diamonds
or spades.  (If you thought you HAD to remove the diamonds, you might want to
take a moment to study the above tableau and figure out how to remove the
spades instead.)  Let's look at the diamonds first.  Most of them are already
in column 1; all we need to dredge up are the 7, 2, and Ace.  We'll ignore
the diamonds in column 9 (we know we can't reach the 7d there, and the 2d is
less accessible than that in column 8), and proceed thusly: 7-6h from 8 to 6,
Ac from 8 to 5, Ad from 7 to 8, Ac from 5 to 7, 8h from 1 to 3, 2-Ah from 1
to 9, 2-Ad from 8 to 1, Jc from 4 to 10, K-Qd from 4 to 5, 6-Ad from 1 to 4,
7h from 1 to 3, and 7-Ad from 4 to 1.  Removing the diamonds from column 1
would give us this position:

(sp)	 Jc	 9h	 9c	 Kd	 9d	 Qc	 Ks	 --	 Qs
	10c	10s	 8c	 Qd	 Qh	 Kc	 Js	 --	 Kc
	 9c	 9s	 5s		 Jh	 Qs		 Jd	 Qh
	 8c	 8h			10h	 Js		 7d	 Jc
	 7c	 7h			 9h	10d		 6h
	 6c				 8h	 9s		 5c
	 5c				 7h	 8s		 4h
	 4s				 6h	 7s		 3h
	 3s					 6s		 2d
	 2s					 5d		 Ah
	 As					 4d		 4c
	 As					 3c		 3c
						 2c		 2c
						 Ac		 Ac
								 7c
								 6s
								 5s
								 4s
								 3s
								 2h
								 Ah

Now, before we pursue this any further, let's go back and see how we can
remove the spades instead.  If we try to do so in the straightforward manner,
we run into trouble.  Presumably we would uncover the Ks in column 8 by
moving the 7-6h onto an 8 and the 2d-Ac onto a 3 (probably swapping the Ac/Ad
as we did in the previous paragraph).  We would then move the Js out of
column 8 and bring in a pile of spades from columns 7 (Q-J, 8-6), 3 (10-9),
and 9 (5-3), piling them all onto the King.  But then we'd be unable to get
to the 2s in column 2.  (Once we moved the first As into the space, we'd be
unable to swap the 2-As with the 2-Ad (or whatever) blocking off the 3s in
column 8.) The way out of this bind is to wait until the last minute to move
anything onto the 3s, such that when we do it's the 2-As, and thus we won't
need the space afterward.  Here's how we can do it: 7-6h from 8 to 6, Ac from
8 to 5, Ad from 7 to 8, Ac from 5 to 7, 3-Ac from 7 to 5, 5-4d from 7 to 6,
3-Ac from 5 to 6, 8-6s from 7 to 3, 9s from 7 to 5, 10d from 7 to 4, 9s from
5 to 4, 10-6s from 3 to 7, 5-3s from 9 to 7.  Now we're ready to go: As from
2 to 5, 2-As from 2 to 7, 2-Ad from 8 to 2, Js from 8 to 10, and Q-As from 7
to 8.  Removing the suit gives this tableau:

 Kd	 Jc	 9h	 9c	 As	 9d	 Qc	(sp)	 --	 Qs
 Qd	10c		 8c		 Qh	 Kc		 --	 Kc
 Jd	 9c		 5s		 Jh			 Jd	 Qh
10d	 8c		 7d		10h			 7d	 Js
 9d	 7c		 Kd		 9h			 6h
 8d	 6c		 Qd		 8h			 5c
 7h	 5c		 Jc		 7h			 4h
 6d	 4s		10d		 6h			 3h
 5d	 3s		 9s		 5d			 2d
 4d	 2d				 4d			 Ah
 3d	 Ad				 3c			 4c
 2h					 2c			 3c
 Ah					 Ac			 2c
 8h								 Ac
								 7c
								 6s

Now, which of these two positions (resulting from removing either diamonds or
spades) is better with regard to our ultimate goal -- the hearts?  Well, in
the tableau immediately above (with the spades removed), we still can't get
through column 9 (same reasoning as before), nor can we get any more spaces
(column 2 is the only chance, but we can't get through it).  And since we
can't get through column 2, we can't remove a set of clubs yet, so all we can
do is remove a set of diamonds.  If that's the case, we might as well have
removed the diamonds first and then seen whether we could do without removing
the spades!  So we'll use the earlier tableau and proceed from there.

Now we can dig through column 9 and turn up a new card, but we'll lose the
space in the process, because we've got only one free 8 left.  Furthermore,
to get to that free 8 we must use up our only free 6, so no matter which
heart gets turned up we won't be able to move it, nor can it possibly get us
the space back.  Furthermore, we still can't get any additional spaces (short
of removing more suits) due to the lack of free 10's and deuces.  Thus we
can't get out a set of hearts yet, but we're getting closer!

What next?  We can now remove either spades or clubs.  Either way we end up
getting a new space.  Removing the clubs has the advantage that it digs all
the way to the 4-Ac in column 9, so let's try that approach.  We'll start by
dredging out the Qc: 3-Ac from 7 to 1, 5-4d from 7 to 6, 3-Ac from 1 to 6,
9-6s from 7 to 1, 10d from 7 to 10, 9-6s from 1 to 10, Js from 8 to 5, Q-Js
from 7 to 8, Kc from 7 to 1, Qc from 7 to 1.  Now we finish the job: As from
2 to 7, 4-As from 2 to 4, J-5c from 2 to 1, 2-Ah from 9 to 2, 6-3s from 9 to
3, 2-Ah from 2 to 3, 5-As from 4 to 10, 7c from 9 to 4, 4-Ac from 9 to 1.
Removing the clubs from column 1 yields:

(sp)	(sp)	 9h	 9c	 Kd	 9d	 As	 Ks	 --	 Qs
		10s	 8c	 Qd	 Qh		 Qs	 --	 Kc
		 9s	 7c	 Js	 Jh		 Js	 Jd	 Qh
		 8h			10h			 7d	 Jc
		 7h			 9h			 6h	10d
		 6s			 8h			 5c	 9s
		 5s			 7h			 4h	 8s
		 4s			 6h			 3h	 7s
		 3s			 5d			 2d	 6s
		 2h			 4d			 Ah	 5s
		 Ah			 3c				 4s
					 2c				 3s
					 Ac				 2s
									 As

Surely two spaces will suffice!  Except that now we've used up the last of
the free 8's, so both the 7d and the Jd will cost us spaces (we can move the
Jd onto the Qs in column 10, but that too costs us a space).  If the 5h turns
up, we'll be stuck, but what if we get the Kh?  Then, with a bit of judicious
planning, we can move the Qs out of column 10 onto the Kh.  (The planning
involves putting a Js on the Qs so the Jd can go elsewhere.)  But the lone
space won't be enough to get the Kh off of column 9, once the Q-Js are placed
with it.  So we must plan even further and leave a Q-Jh to be picked up by
the Kh.  This is our only hope of getting the hearts out (without removing
the spades), so let's see how it works out: 9-As from 10 to 1, 10d from 10 to
5, 9-As from 1 to 5, 3-Ac from 6 to 1, 5-4d from 6 to 2, 10-6h from 6 to 8,
3-Ac from 1 to 2, Jc from 10 to 1, Jh from 6 to 10, Jc from 1 to 6.  Now
we've got the Jh with the Qh that we can move.  (We can't move the Qh in
column 6 since that would cost us a space.)  Continuing: 5-As from 5 to 8,
3-Ac from 2 to 1, 5-4d from 2 to 5, 3-Ac from 1 to 5, Ah from 9 to 1, 2d from
9 to 2, 2-Ah from 3 to 9, 2d from 2 to 3, Ah from 1 to 3, 4-Ah from 9 to 1,
5c from 9 to 2, 6h from 9 to 4, 5c from 2 to 4, 4-Ah from 1 to 4, Q-Jh from
10 to 1, Kc from 10 to 2, Qs from 10 to 2, 7d from 9 to 10, Jd from 9 to 2,
and we assume the Kh is turned up.  We move Q-Jh from 1 to 9 and reach the
following position:

(sp)	 Kc	 9h	 9c	 Kd	 9d	 As	 Ks	 --	 7d
	 Qs	10s	 8c	 Qd	 Qh		 Qs	 Kh
	 Jd	 9s	 7c	 Js	 Jc		 Js	 Qh
		 8h	 6h	10d			10h	 Jh
		 7h	 5c	 9s			 9h
		 6s	 4h	 8s			 8h
		 5s	 3h	 7s			 7h
		 4s	 2h	 6s			 6h
		 3s	 Ah	 5d			 5s
		 2d		 4d			 4s
		 Ah		 3c			 3s
				 2c			 2s
				 Ac			 As

Unfortunately, despite our best preparations, we will be unable to combine
the hearts once we move the K-Jh into the space and turn up the 5h.  We could
go back and try removing the spades instead of the clubs earlier, but it
wouldn't help.  We must remove both the spades AND the clubs (and the
diamonds) before removing the hearts.  We can't get the spades together
starting with the above tableau -- we can't get through column 3 with only
one space.  So we'll back up to the previous tableau and proceed thusly: 2-Ah
from 3 to 1, 6-3s from 3 to 4, 8-7h from 3 to 2, 10-9s from 3 to 8, 8-7h from
2 to 3, Ah from 9 to 2, 2d from 9 to 4, Ah from 2 to 4, 2-Ah from 1 to 9,
8-As from 10 to 8, and remove the spades.  We now have this:

(sp)	(sp)	 9h	 9c	 Kd	 9d	 As	(sp)	 --	 Qs
		 8h	 8c	 Qd	 Qh			 --	 Kc
		 7h	 7c	 Js	 Jh			 Jd	 Qh
			 6s		10h			 7d	 Jc
			 5s		 9h			 6h	10d
			 4s		 8h			 5c	 9s
			 3s		 7h			 4h
			 2d		 6h			 3h
			 Ah		 5d			 2h
					 4d			 Ah
					 3c
					 2c
					 Ac

With THREE spaces we should have no trouble!  Then again, considering how
careful we had to be to even come close using two spaces, perhaps we should
be cautious!  If we just start dumping things into spaces we may find we
don't have enough spaces to move things around once we know what we want
moved.  So we'll start by gathering what hearts we have: 3-Ac from 6 to 1,
5-4d from 6 to 2, 6h from 6 to 3, 5-4d from 2 to 3, 3-Ac from 1 to 3, 4-Ah
from 9 to 1, 5c from 9 to 2, 6h from 9 to 6, 5c from 2 to 6, 4-Ah from 1 to
6.  Now, if we stuff the 7d and Jd from column 9 into a pair of spaces, and
the 5h turns up, we can move 4-Ah from 6 to 9, 5c from 6 to 8, 5-Ah from 9 to
6, and Q-Ah from 6 onto the newly revealed Kh.  But if the Kh is the first
card turned up, we'll be in rough shape.  So let's prepare for that
contingency just as we did in our earlier attempt.  We move 9s from 10 to 1,
10d from 10 to 5, 9s from 1 to 5, 4-Ah from 6 to 1, 5c from 6 to 2, J-6h from
6 to 8, Jc from 10 to 6, J-6h from 8 to 10, 10-6h from 10 to 6, 5c from 2 to
6, 4-Ah from 1 to 6, Q-Jh from 10 to 8, Kc from 10 to 1, Qs from 10 to 1, 7d
from 9 to 10, and here we are:

 Kc	(sp)	 9h	 9c	 Kd	 9d	 As	 Qh	 --	 7d
 Qs		 8h	 8c	 Qd	 Qh		 Jh	 --
		 7h	 7c	 Js	 Jc			 Jd
		 6h	 6s	10d	10h
		 5d	 5s	 9s	 9h
		 4d	 4s		 8h
		 3c	 3s		 7h
		 2c	 2d		 6h
		 Ac	 Ah		 5c
					 4h
					 3h
					 2h
					 Ah

No matter which heart is revealed when we move the Jd from 9 to 1, we will be
able to finish combining the hearts.

===========================================================================

Ae[bFBe`0XjJA71dJjS2;b0Q9[YT01:>4HQoE;]7OIIXJIB432/DZcKfD>>CSO_H>Zgi[ed:5NPgamO?=mKT\gBR^c=Gd@O^@TM>]QdcD :gKni/^ f15K/8 LRb;/e 8f=HX/D UPH2/> J?B>/H Pa?n0/o ggKE/R oQfL/j ?`9Al/^.

In case you're wondering what it takes to finish a game with all eight
completed suits still sitting in the tableau, here's a deck (again,
encountered in actual play) that makes it possible.  The "solution" is left
as an exercise.

This deck can also be useful as a confidence boost for novices who are having
trouble winning at all, since it is relatively easy to win from this position
if you are willing to remove suits as you complete them.

 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 --	 --	 --	 --	 --	 --	 --	 --	 --
 --	 9s	 Kd	 --	 4s	 8h	 --	 Qd	 7s	 --
10d			 Jd			 Qh			 9d

===========================================================================
[Copyright (c) 1989, Donald R. Woods and Sun Microsystems, Inc.]