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.
===========================================================================
J6m\ZM^3>gU82j]`LGMFl8o0WeDimHa;d^1QcHGKQdQAZ6l;oK/QmbbBhNhiMiWe=FOHD >Kg74/^ YoT[/6 HCcF/P \MNXm/Q EK25/k 9^0M/c KF0@W/N \JHY/: 9GLR/L \W8hH/2.
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.
===========================================================================
1;]mcD96:2o6j1J7Fj>N/\j?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?P O DLV/7V[ N=^cfil 8_/R<3d9NC4I^SDY?F\bfKl16[ k;]>Hhn ak\k/Z\2O[<@FkLPWZ[;>CdINS 9A C L75/1;\aFJo.
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 5card. (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.)
===========================================================================
?jT\Ne61gU/3`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?P LF^Q/lLQ7[]`8Qe^_ B\^CO9M@4I] Q=Lh/C;aS2o D0/b6;[MEXM.
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.)
===========================================================================
?jT\Ne61gU/3`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?P LF^Q/lLR4Y^cDjm3 XCkS/QENCCAV`O 3 ]:na6K<1F[LAV =Dil1W9>CgJN b P 4:[/eQW8\afKl16 @J/8\QA7o279 C.
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.
===========================================================================
C576XV@Ra`MgY>9XFSnF/^j?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?Pe:O`5J_0EZo@Uj?P 3>0f9NC7I^ H=Zn HUUgKl1YC4I^SDYR PFeM2 B1D[ C:^>LPV;] MAK\1F[lAVk\QBCTSZ`23d9N@7I^SGYN 1Ti>Sd9Mc4IZ NM ZnhZM =1f9NFCfhOcV;\] UH8.
3^SD>\QBCTSZ`23d9N@7I^SGYN 1Ti>Sd9Mc4IZ NM ZnhZM =1f9NFCfhOcV;\] UH8.
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.]