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If you want to learn about fishing...

 
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Tue Sep 19, 2006 8:59 pm    Post subject: If you want to learn about fishing... Reply with quote

... this is your puzzle! I have never come accross a puzzle more susceptible to advanced x-wing/fishy thingies and yet so impervious to solution. It is Krazydad's Insane, Book 78, Sudoku #1.

Code:
.6......3
...2...4.
9.2.6....
.4.1..92.
1...7...5
.3...9.8.
....3.8.1
.9...8...
8......5.


I get to here easily:

Code:
457    6    14578  5789  1589 157  2    179 3
357    1578 13578  2     1589 157  756  4   69
9      157  2      3     6    4    75   17  8

756    4    5678   1     58   3    9    2   76
1      28   9      468   7    26   436  36  5
2567   3    756    456   245  9    1    8   467

24567  257  4567   45679 3    2567 8    769 1
234567 9    134567 4567  1245 8    3467 367 426
8      127  13467  4679  1249 1267 3467 5   2469


Now I see an old, familiar, simple fishy thing in the 8s in boxes 1, 2, 4, and 5:

Code:
..8  88.
.88  .8.
...  ...

..8  .8.
.8.  8..
...  ...


I don't know what it is called, but I know I can eliminate the 8 from r1c3 and r2c5. Seeing the pattern in boxes 3 and 4 is always a welcome sight. The eliminations don't help, but we are just getting started. Next up, and one degree more difficult, I see a familiar pattern in the 2s in boxes 3, 4, 6, 7, and 9:

Code:
...  ...
.2.  ..2
2..  .2.

22.  ..2  ...
2..  .2.  ..2
.2.  .22  ..2


That pattern again, with the locked set kicker in box 9. Whatever you want to call it and however you want to notate it, there are only two ways the 2s fit, and neither of them involve cells r9c2, r8c5, or r9c6.

EDIT (9-20-06): The above statement is incorrect; only the 2 in r9c2 is eliminated. Sorry. Embarassed

Still no help (for me) in revealing anything. Next up are the 3s in boxes 1, 7, 9 and 6 (because that is the order of how they are linked):

Code:
...  ...  ...
3.3  ...  ...
...  ...  ...

...  ...  ...
...  ...  33.
...  ...  ...

...  ...  ...
3.3  ...  33.
..3  ...  3..


If r2c3 = 3 ==> r5c8 = 3
and if r5c7 =3 ==> r2c1 = 3
but in any event, neither r8c3 nor r8c7 = 3.

EDIT (9-20-06): The above statement, though persausive when I first wrote it, is incorrect. It is faulty logic as it fails to consider the possibility (r2c1=3 and r5c8=3). Sorry again. Embarassed

Still no help!!?? Sad

So I look at the pattern on the 9s, and it is the twin brother of the pattern on the 8s, but the balanced version that doesn't exclude any candidates. Then I think I see a possible swordfish on 5s in columns 2, 6, and 7, except there is an extra 5 in the cell at r1c6. The pattern looks like this (remember, these are only exclusive placements with respect to the columns):

Code:
...  ..5  ...
.5.  ..5  5..
.5.  ...  5..

...  ...  ...
...  ...  ...
...  ...  ...

.5.  ..5  ...
...  ...  ...
...  ...  ...


So ignoring the 5 in r1c6 for the moment, there is either going to be a 5 in column 7 at row 2, which will dictate a 5 in column 6 at row 7, which will dictate a 5 in column 2 at row 3, or there will be a 5 in column 7 at row 3, which would create an x-wing on 5s in columns 2 and 6.

In either case, we could eliminate the 5s as candidates in any other cells in rows 2, 3, and 7.

But we are stuck with the 5 in r1c6. Except there is one cell where it doesn't matter where the 5 falls in column 6 -- it can't be a 5 under any scenario -- and that is the candidate 5 in row 2 at column 5 because it is in the same box as the "extra" 5 in column 6. (I think this is called a finned swordfish.)

So now, after all that, I am here:

Code:
457    6    1457   5789  1589 157  2    179 3
357    1578 13578  2     19   157  756  4   69
9      157  2      3     6    4    75   17  8

756    4    5678   1     58   3    9    2   76
1      28   9      468   7    26   436  36  5
2567   3    756    456   245  9    1    8   467

24567  257  4567   45679 3    2567 8    769 1
234567 9    14567  4567  145  8    467  367 426
8      17   13467  4679  1249 167  3467 5   2469


And now I am exhausted and Evil or Very Mad . I don't see anything... I see that the {17} in r9c2 and r3c8 either both have to be {1} or {7}, but I didn't get anywhere from there.

Anyway, I need a break. Just thought I'd share...

EDIT (9-19-06): Marty pointed out a typo -- it was {5789} in r1c4. I fixed in both big grids.


Last edited by AZ Matt on Wed Sep 20, 2006 4:08 pm; edited 3 times in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5063
Location: Rochester, NY, USA

PostPosted: Tue Sep 19, 2006 9:26 pm    Post subject: Reply with quote

Matt, your fishy thing on the 8s is a jellyfish (four rows) and the 2s (five rows) is--don't ask me why--a squirmbag.

You'll probably kick yourself, but in the last posted position, column 4 has only one possibility for "8." I don't know how far that can take you. Sorry to have to break the news. :cry:

Code:
457    6    1457  579    1589 157  2    179 3
357    1578 13578  2     19   157  756  4   69
9      157  2      3     6    4    75   17  8

756    4    5678   1     58   3    9    2   76
1      28   9      468   7    26   436  36  5
2567   3    756    456   245  9    1    8   467

24567  257  4567   45679 3    2567 8    769 1
234567 9    14567  4567  145  8    467  367 426
8      17   13467  4679  1249 167  3467 5   2469
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Tue Sep 19, 2006 10:27 pm    Post subject: Oops... Reply with quote

A transcription error. I fixed it. There is an {8} in r1c4. Thanks Marty.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Sep 20, 2006 12:36 pm    Post subject: Reply with quote

Matt,

Code:
 . .#8  -8 8 .
 .+8 8   .#8 .
 . . .   . . .

 . .+8   .-8 .
 .-8 .  +8 . .
 . . .   . . .

The 8's can be eliminated with turbot fish/2 strong links (r2c2-r5c2,r5c4-r1c4), two empty rectangles or multiple coloring.
Code:
 . . .  . . .      
 . 2 .  . . 2      
 2 . .  . 2 .       
         
 2 2 .  . . 2  . . .
 2 . .  . 2 .  . . 2
 . 2 .  . 2 2  . . 2

The 2 in r9c2 with x-cyle (r9c2=2 => r8c9=2 => r7c6=2 => r6c5=2 => r5c2=2).
You cannot eliminate the 2 in r8c5 or r9c6, because these patterns are possible:
Code:
 . . .  . . .               . . .  . . .      
 . . .  . . 2               . 2 .  . . .      
 2 . .  . . .               . . .  . 2 .       
                      
 . 2 .  . . .  . . .        2 . .  . . .  . . .
 . . .  . . .  . . 2        . . .  . . .  . . 2
 . . .  . 2 .  . . .        . . .  . . 2  . . .

You also cant eliminate the 3's in r8c3 and r8c7:
Code:
 . . .  . . .  . . .    . . .  . . .  . . .      . . .  . . .  . . .
 3 . 3  . . .  . . .    3 . .  . . .  . . .     3 . .  . . .  . . .
 . . .  . . .  . . .    . . .  . . .  . . .     . . .  . . .  . . .
                             
 . . .  . . .  . . .    . . .  . . .  . . .     . . .  . . .  . . .
 . . .  . . .  3 3 .    . . .  . . .  . 3 .     . . .  . . .  . 3 .
 . . .  . . .  . . .    . . .  . . .  . . .     . . .  . . .  . . .
                             
 . . .  . . .  . . .    . . .  . . .  . . .     . . .  . . .  . . .
 3 . 3  . . .  3 3 .    . . 3  . . .  . . .     . . .  . . .  3 . .
 . . 3  . . .  3 . .    . . .  . . .  3 . .     . . 3  . . .  . . .

The puzzle is rather hard, you need chains to solve it. This is, how you can eliminate 1 from r8c5 and r9c5:
Code:
457    6    1457   5789  1589 157  2    179 3
357    1578 13578  2     19   157  756  4   69
9      157  2      3     6    4    75   17  8

756    4    5678   1     58   3    9    2   76
1      28   9      468   7    26   436  36  5
2567   3    756    456   245  9    1    8   467

24567  257  4567   45679 3    2567 8    769 1
234567 9    134567 4567  1245 8    3467 367 426
8      17   13467  4679  1249 1267 3467 5   2469
r89c5=1 => r2c5=9 (=> r14c5=58 => r6c5<>5) => r2c9=6 => r4c9=7 => r6c9=4 => r5c4=4 (=> r6c5<>4) => r5c2=8 => r6c1=2 => r6c5<>2 => r6c5 is empty.
=> r9c6=1, r8c3=1

But still at least another forcing chain is needed to solve it finally.
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Wed Sep 20, 2006 4:16 pm    Post subject: Sheesh... Reply with quote

I apologize for the technical error on the 2s (I just made a mistake with my pencil) and for the mental error on the 3s (although exercises in "fallacy" logic, which is what I did, can be instructional).

I have edited the post to point out my errors. I apologize. This is what happens when one tries too hard to solve a puzzle.
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Wed Sep 20, 2006 6:01 pm    Post subject: This is a hard one Reply with quote

Hi, Matt!

I did solve this puzzle by concentrating on two "double-implication chains". The first one started from r4c5, and the second one (later) started from r6c5. I'll have to reconstruct it before I can post my solution, though -- I had to think pretty hard to get through this one! (Oh -- I started from the beginning, so didn't notice any problems with the "3"s.) dcb
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Wed Sep 20, 2006 10:12 pm    Post subject: Using chains to solve this one Reply with quote

Here's how I solved this puzzle. The first time through I concentrated on r4c5; going over it again, I noticed that it's easier to work from r5c2. Basic stuff got me here.
Code:
*-----------------------------------------------------------------------------*
| 457     6       1457    | 5789    1589    157     | 2       179     3       |
| 357     1578    13578   | 2       19      157     | 567     4       69      |
| 9       157     2       | 3       6       4       | 57      17      8       |
|-------------------------+-------------------------+-------------------------|
| 567     4       5678    | 1       58      3       | 9       2       67      |
| 1       28*     9       | 468     7       26      | 346     36      5       |
| 2567    3       567     | 456     2*45    9       | 1       8       467     |
|-------------------------+-------------------------+-------------------------|
| 24567   257     4567    | 45679   3       2*567   | 8       679     1       |
| 2*34567 9       134567  | 4567    1245    8       | 3467    367     246     |
| 8       127     13467   | 4679    1249    1267    | 3467    5       2*469   |
*-----------------------------------------------------------------------------*

I placed all the "2"s assuming r5c2 = 2, as follows.

r5c2 = 2 ==> r6c5 = 2
r5c2 = 2 ==> r5c6 = 6 ==> r5c8 = 3 ==> r5c7 = 4 ==> r5c4 = 8 ==> r4c5 = 5
r5c7 = 4 ==> {6, 7} pair in r46c9 ==> r2c9 = 9 ==> r2c5 = 1 ==> {5, 7} pair in r12c6
({5, 7} pair & r5c6 = 6) ==> r7c6 = 2
(r7c6 = 2 & r5c2 = 2) ==> r8c1 = 2 ==> r9c9 = 2

So now we've placed all the "2"s, assuming that r5c2 = 2. See the asterisks in the grid above. We easily derive a contradiction as follows:

(r2c5 = 1 & r4c5 = 5 & r6c5 = 2) ==> r8c5 = 4
({6, 7} pair in r46c9 & r9c9 = 2) ==> r8c9 = 4

So we can put an "8" in r5c2, and make quite a bit of progress, to here.
Code:
*-----------------------------------------------------------------------------*
| 47      6       147     | 8       159     157     | 2       179     3       |
| 3       157     8       | 2       19      17      | 567     4       69      |
| 9       157     2       | 3       6       4       | 57      17      8       |
|-------------------------+-------------------------+-------------------------|
| 567     4       567     | 1       8       3       | 9       2       67      |
| 1       8       9       | 46      7       2       | 346     36      5       |
| 2       3       67      | 456     45      9       | 1       8       467     |
|-------------------------+-------------------------+-------------------------|
| 4567    2       4567    | 4579    3       56      | 8       679     1       |
| 4567    9       134567  | 457     1245    8       | 3467    367     246     |
| 8       17      13467   | 479     124     16      | 3467    5       2469    |
*-----------------------------------------------------------------------------*

Now we can show that r1c6 = 5, using a double-implication chain.

A. r6c5 = 4 ==> {6, 7} pair in r46c9 ==> r2c9 = 9 ==> r1c5 = 9 ==> r1c6 = 5
B. r6c5 = 5 ==> r1c6 = 5

The rest is easy. dcb
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Wed Sep 20, 2006 11:18 pm    Post subject: Cool... Reply with quote

Thanks David, I'll take a look. There was something not right about the pattern on the 2s, but I couldn't articulate it.

It took me a finned swordfish and a jellyfish to remove the 5 and 8, respectively, as candidates in r2c5 to get to the bivalue {19} cell, which is critical to your solve. You got there on basic moves? I must have missed something.
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Thu Sep 21, 2006 12:01 am    Post subject: Well, maybe it wasn't so basic ... Reply with quote

Hi, Matt!

You're right -- I did have to depend on a "finned swordfish" to eliminate the "5" at r2c5. And having a pair in that cell is essential to the forcing chains I found. I guess the "finned swordfish" is a bit exotic. But I spot them fairly easily now, because Ruud sticks so many of them in his Nightmare puzzles.

Eliminating the "8" at r2c5 depended on a "fork" on the "8"s in column 2 and in box 5. This one was a little harder to spot than some, because the candidates in box 5 go slantwise. Again, I plead too much practice -- I've also come to think of the "fork" as a fairly simple technique. dcb Rolling Eyes
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Thu Sep 21, 2006 3:46 pm    Post subject: Basic Moves Reply with quote

I was pretty proud of spotting the finned swordfish in this puzzle becuse you had to look around so many 5 candidates to see it.

I'd be in favor of ratcheting up the definition of basic moves, too. To my mind, the Brainbasher's super hards entail all basic moves. I don't know that I'd make the leap to finned swordfish, forks, and jellyfish, though I could be persuaded.

Did you note the squirmbag (so called per Marty above -- a five-level x-wing I think) on the 2s removing the 2 from the {127} in r9c2 and leaving a bivalue cell. I am trying like heck to make that critical to a solve for this puzzle because Keith once said that I'd never see a squirmbag.

EDIT (9-21-06): Keith said "need," not "see." Quote below.


Last edited by AZ Matt on Thu Sep 21, 2006 10:44 pm; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5063
Location: Rochester, NY, USA

PostPosted: Thu Sep 21, 2006 4:59 pm    Post subject: Reply with quote

Quote:
I am trying like heck to make that critical to a solve for this puzzle because Keith once said that I'd never see a squirmbag.


I certainly can't speak for Keith. But I've used a squirmbag and a 6-fish, whose name I forgot. However, the theoreticians here (that definitely does not include me) have said, if I recall correctly, that there is never a need to use more than a jellyfish, because there are complementary fish. As in if there's a squirmbag in rows, there's a jellyfish in columns. This was discussed in a recent thread here. At any rate, I'll be interested to see why Keith told you what he did.

He also told me that it's not necessay or productive to take the time to look for swordfish and more, advice which I have been following.
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Thu Sep 21, 2006 5:37 pm    Post subject: Squirmbag Reply with quote

I made the observation that a swordfish is basically two interconect x-wings, and this was Keith's helpful reply:

Quote:
The most basic fish is a naked single.

The next is an X-wing, in which two candidates in each of two rows line up in two columns.

The next is a swordfish, in which three candidates in three rows line up in three columns.

Jellyfish for four, squirmbag for five. You will never need a squirmbag.
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Thu Sep 21, 2006 6:52 pm    Post subject: It's a finned X-Wing Reply with quote

AZ Matt wrote:
Did you note the squirmbag (so called per Marty above -- a five-level x-wing I think) on the 2s removing the 2 from the {127} in r9c2 and leaving a bivalue cell. I am trying like heck to make that critical to a solve for this puzzle because Keith once said that I'd never see a squirmbag.

No, Matt -- I missed it. I get tired of looking for exotic fish, and probably start working with the "DIC" technique before I really have to. Once I've got 15 or 20 bi-valued cells in the puzzle, the "DIC"s usually work for me. In this case I found an "8" at r5c2 (because of a contradiction), and the "2" at r9c2 was eliminated when I followed up on that

Anyway, the formation that allows one to eliminate the "2" directly is a finned X-Wing, as shown below.
Code:
*-----------------------------------------------------------------------------*
| 457     6       14578   | 45789   14589   1457    | 2       179     3       |
| 357     1578    13578   | 2       1589    1357    | 1567    4       6789    |
| 9       1578    2       | 34578   6       13457   | 157     17      78      |
|-------------------------+-------------------------+-------------------------|
| 567     4       5678    | 1       58      356     | 9       2       67      |
| 1       28X     689     | 3468    7       2346X   | 346     36      5       |
| 2567    3       567     | 456     245     9       | 1467    8       467     |
|-------------------------+-------------------------+-------------------------|
| 24567W  257X    4567    | 45679   3       24567X  | 8       679     1       |
| 234567  9       134567  | 4567    1245    8       | 3467    367     2467    |
| 8       127     13467   | 4679    1249    12467   | 3467    5       24679   |
*-----------------------------------------------------------------------------*

This is what the puzzle looks like at the outset, except that I've placed a "2" at r1c7. It was an isolated value -- a "hidden single", I guess.

Anyway, I've marked the X-Wing pattern with X, and the "wing" with W:

A. r7c1 = 2 ==> r9c2 <> 2
B. r7c1 <> 2 ==> X-Wing in r57c26 ==> r9c2 <> 2

So to my (sort of stodgy) way of thinking, these "winged fish" look a lot like double-implication chains, with the fishy pattern falling out as part of one of the chains. Maybe that's why I don't spot all of them -- I'm sort of looking for a "DIC" whenever I do spot a "winged fish", and that may not be the first useful chain I stumble across. dcb
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Thu Sep 21, 2006 8:13 pm    Post subject: Cool... Reply with quote

Wow, that was easy, and I think know now why Keith said I'd never need (not "see") a squirmbag. If you have a five level x-wing, it will contain a simpler x-wing type solve to get to the same place.
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Fri Sep 22, 2006 1:27 am    Post subject: Re: Cool... Reply with quote

AZ Matt wrote:
Wow, that was easy, and I think know now why Keith said I'd never need (not "see") a squirmbag. If you have a five level x-wing, it will contain a simpler x-wing type solve to get to the same place.

Yes, but I've been worrying about this. I still have some thinking to do.

From my reading (not my understanding) you will never need a squirmbag. Because a 5X Wing (in the row / column) must have at least a simpler 4X dual (in the column / row).

Really? What if four values are solved? Can I not then have a 5X Wing with a zero dual?

Keith
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Fri Sep 22, 2006 7:37 am    Post subject: Re: Cool... Reply with quote

keith wrote:

Really? What if four values are solved? Can I not then have a 5X Wing with a zero dual?

Yes, of course there is one, but it does not help, because there are no candidates in the rest of the squirmbag rows or columns to eliminate.
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Myth Jellies



Joined: 27 Jun 2006
Posts: 64

PostPosted: Fri Sep 22, 2006 7:44 am    Post subject: Reply with quote

When you have solved four locations for a particular digit, the remaining unsolved cells for that digit all fall on a squirmbag pattern. You really can't fit another squirmbag into it.

Make it easier on yourself and consider the case where you have solved seven locations for a particular digit. If you can't solve it immediately, you have four cells unsolved for that digit, 2 in one box and 2 in another, forming a rectangle. There is no way you are going to fit another x-wing into those four cells Smile
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