Next step please

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Next step please

Postby dpburton » Fri Apr 28, 2006 4:29 pm

I keep having problems with the LA Times 5 star puzzles. For example today I got this far:
Code: Select all
 
*--------------------------------------------------------------------*
 | 4      6      5      | 2      8      39     | 39     7      1      |
 | 139    389    138    | 7      4      369    | 2      5      369    |
 | 2      379    37     | 69     1      5      | 3469   34     8      |
 |----------------------+----------------------+----------------------|
 | 39     389    38     | 4      6      1      | 7      2      5      |
 | 167    5      16     | 3      2      78     | 68     9      4      |
 | 76     2      4      | 5      9      78     | 368    1      36     |
 |----------------------+----------------------+----------------------|
 | 8      37     367    | 1      5      69     | 349    34     2      |
 | 36     1      2      | 69     7      4      | 5      8      39     |
 | 5      4      9      | 8      3      2      | 1      6      7      |
 *--------------------------------------------------------------------*

I think I have pairs and triples and xwing down, but don't seem to ever be able to apply the more advanced methods.
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Postby Ruud » Fri Apr 28, 2006 4:43 pm

Hi,

welcome to the forum.

You still have an X-Wing in the grid. Look at digit 9.

There is also a coloring opportunity for digit 6. Or, if you like, you can catch a sashimi swordfish instead.

These 2 are required to setup an XYZ-wing, which breaks the puzzle.

Hope this helps.

Ruud.
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Postby Havard » Fri Apr 28, 2006 5:56 pm

Ruud wrote:There is also a coloring opportunity for digit 6. Or, if you like, you can catch a sashimi swordfish instead.


Quite a nice one, allowing a double elimination:
Code: Select all
Swordfish in columns: 3 6 9
4    6    5    | 2    8    39   | 39   7    1
139  389  18   | 7    4    36X  | 2    5    369X
2    39   7    | 69   1    5    | 46   34   8
---------------+----------------+---------------
39   389  38   | 4    6    1    | 7    2    5
167  5    16X  | 3    2    78   | 68-  9    4
67-  2    4    | 5    9    78   | 368  1    36X
---------------+----------------+---------------
8    7    36X  | 1    5    69X  | 49   34   2
36   1    2    | 69   7    4    | 5    8    39
5    4    9    | 8    3    2    | 1    6    7

.  6  .  | .  .  .  | .  .  .
.  .  .  | .  .  6X | .  .  6X
.  .  .  | 6  .  .  | 6  .  .
---------+----------+---------
.  .  .  | .  6  .  | .  .  .
6  .  6X | .  .  .  | 6- .  .
6- .  .  | .  .  .  | 6  .  6X
---------+----------+---------
.  .  6X | .  .  6X | .  .  .
6  .  .  | 6  .  .  | .  .  .
.  .  .  | .  .  .  | .  6  .
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Postby Sped » Fri Apr 28, 2006 6:28 pm

Code: Select all
 *-----------------------------------------------------------*
 | 4     6     5     | 2     8     39    | 39    7     1     |
 | 139   389   138   | 7     4     369   | 2     5     369   |
 | 2     379   37    | 69    1     5     | 3469  34    8     |
 |-------------------+-------------------+-------------------|
 | 39    389   38    | 4     6     1     | 7     2     5     |
 | 167   5     16    | 3     2     78    | 68    9     4     |
 | 67    2     4     | 5     9     78    | 368   1     36    |
 |-------------------+-------------------+-------------------|
 | 8     37    367   | 1     5     69    | 349   34    2     |
 | 36    1     2     | 69    7     4     | 5     8     39    |
 | 5     4     9     | 8     3     2     | 1     6     7     |
 *-----------------------------------------------------------*


The XY chain

9-(r8c9)-3-(r7c8)-4-(r3c8)-3-(r1c7)-9

allows the exclusion of 9s in r2c9 and r7c7, which solves the puzzle.

In nice loop notation:

[r2c9]-9-[r8c9]-3-[r7c8]-4-[r3c8]-3-[r1c7]-9-[r2c9], => r2c9<>9
[r7c7]-9-[r8c9]-3-[r7c8]-4-[r3c8]-3-[r1c7]-9-[r7c7], => r7c7<>9
Last edited by Sped on Fri Apr 28, 2006 2:35 pm, edited 1 time in total.
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Postby re'born » Fri Apr 28, 2006 6:30 pm

Has anyone noticed how many nice UR examples there are in this grid (starting from after Ruud's x-wing)?

For instance,
Code: Select all
 
 *--------------------------------------------------*
 | 4    6    5    | 2    8    39   | 39   7    1    |
 | 139  389  138  | 7    4    36   | 2    5    369  |
 | 2   *379 *37   | 69   1    5    |%346 %34   8    |
 |----------------+----------------+----------------|
 | 39   389  38   | 4    6    1    | 7    2    5    |
 |#167  5    16   | 3    2   #78   |#68   9    4    |
 |#67   2    4    | 5    9   #78   |#368  1    36   |
 |----------------+----------------+----------------|
 | 8   *37  *367  | 1    5    69   |%349 %34   2    |
 | 36   1    2    | 69   7    4    | 5    8    39   |
 | 5    4    9    | 8    3    2    | 1    6    7    |
 *--------------------------------------------------*


the starred cells from a UR + X-wing on <37> and hence we can conclude that r3c3 = 7 and r7c2=7. Also, the sharped cells (along with r6c9 and r5c3) allow one to conclude that r5c1 != 7 and r6c7 != 8 (though this second deduction becomes redundant by the first). From here, an xy-wing with pivot cell r3c4 solves the puzzle.

Incidentally, another nice UR elimination is in the 'percentaged' cells, allowing us to remove a 3 from r37c7, though this doesn't seem to advance things very much.
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Postby ronk » Fri Apr 28, 2006 7:15 pm

Ruud wrote:There is also a coloring opportunity for digit 6. Or, if you like, you can catch a sashimi swordfish instead.

I'm assuming you spotted the same sashimi described in the immediately preceding post.

In Havard's pencilmarks, there is a finned swordfish in rows 3, 5, and 8 with the fin at r5c3 ... at the same time as the sashimi. So it appears your solver gives "priority" to sashimi over finny. Is that correct? If so, I'd appreciate knowing your reason for that.

Havard, do you do the same?

TIA, Ron

P.S. dpburton, If you desire additional clarification of Ruud's helpful hints, feel free to ask.
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Postby re'born » Fri Apr 28, 2006 7:20 pm

Sped wrote:The XY chain

9-(r8c9)-3-(r7c8)-4-(r3c8)-3-(r1c7)-9

allows the exclusion of 9s in r2c9 and r7c7, which solves the puzzle.



Sped,

In your notation for XY-chains, how do you represent closed chains? What I have in mind is the chain

(1,6)9 > (7,6)6 > (8,4)9 > (8,9)3 > (7,8)4 > (3,8)3 > (1,7)9 => (1,6)!9.

(This chain also solves the puzzle.)

Thanks.
Last edited by re'born on Fri Apr 28, 2006 3:49 pm, edited 1 time in total.
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Postby dpburton » Fri Apr 28, 2006 7:33 pm

I think I had seen the x-wing 9's but didn't get them in my notes. I don't understand the sashimi swordfish though. I did some searching and found a lot of talk about sashimi but couldn't find anything that described it. How does sashimi work?
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Postby Havard » Fri Apr 28, 2006 10:02 pm

dpburton wrote:I think I had seen the x-wing 9's but didn't get them in my notes. I don't understand the sashimi swordfish though. I did some searching and found a lot of talk about sashimi but couldn't find anything that described it. How does sashimi work?


Well, I while back I wrote this thingo about strong links that might get you started into this: http://forum.enjoysudoku.com/viewtopic.php?t=3326

Now after having read this, if you look at the figure this way:

Code: Select all
.  6  .  | .  .  .  | .  .  .
.  .  .  | .  .  6c | .  .  6e
.  .  .  | 6  .  .  | 6  .  .
---------+----------+---------
.  .  .  | .  6  .  | .  .  .
6  .  6a | .  .  .  | 6- .  .
6- .  .  | .  .  .  | 6  .  6f
---------+----------+---------
.  .  6b | .  .  6d | .  .  .
6  .  .  | 6  .  .  | .  .  .
.  .  .  | .  .  .  | .  6  .


you will see that a-b, c-d and e-f are all strong links. Now b and d are "buddies" and c and e are buddies. This means that either f or a has to be true. Now you can eliminate any candidate that can "see" both a and f, and those are the ones marked with "-"

Now for this to be a regular swordfish, either the a has to move down from its current position in r5c3 to r6c3, or f has to move up from r6c9 to r5c9. One way of thinking about the "sashimi" could be that one end (here a or f) is displaced a little, but is still allowing eliminations. If you on the other hand had more candidates present, this would be called "fins", and you would have a "finned swordfish". However I think it is more important to understand the underlying principle that allows these eliminations, and you will hopefully find a bit of that in that post. If you already understand and are using X-wing you are well under way!:)

Havard
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Postby re'born » Fri Apr 28, 2006 10:06 pm

Dpburton,

Let me steal Harvard's picture.

Here would be a traditional swordfish allowing the removal of the 6 from r6c1 and r6c7.

Code: Select all
.  6  .  | .  .  .  | .  .  .
.  .  .  | .  .  6X | .  .  6X
.  .  .  | 6  .  .  | 6  .  .
---------+----------+---------
.  .  .  | .  6  .  | .  .  .
6  .  .  | .  .  .  | 6  .  .
6- .  6X | .  .  .  | 6- .  6X
---------+----------+---------
.  .  6X | .  .  6X | .  .  .
6  .  .  | 6  .  .  | .  .  .
.  .  .  | .  .  .  | .  6  .


Now, if we add a potential 6 to r5c3, it looks like we lose our deductions:

Code: Select all
.  6  .  | .  .  .  | .  .  .
.  .  .  | .  .  6X | .  .  6X
.  .  .  | 6  .  .  | 6  .  .
---------+----------+---------
.  .  .  | .  6  .  | .  .  .
6  .  6* | .  .  .  | 6  .  .
6- .  6X | .  .  .  | 6 .  6X
---------+----------+---------
.  .  6X | .  .  6X | .  .  .
6  .  .  | 6  .  .  | .  .  .
.  .  .  | .  .  .  | .  6  .


However, the theory of finned fish tells you that if a set of cells is an obstruction to a swordfish (or x-wing or other fish), then you can still make any eliminations that see the obstructed cells. In this case, the obstruction is r5c3. You can no longer eliminate the 6 from r6c7 since it doesn't see the obstruction, but you can still eliminate r6c1 since it does see the obstruction. The obstruction is usually called the fin (and this pattern would be a finned swordfish).

Next assume that we get rid of the 6 in r6c3.

Code: Select all
.  6  .  | .  .  .  | .  .  .
.  .  .  | .  .  6X | .  .  6X
.  .  .  | 6  .  .  | 6  .  .
---------+----------+---------
.  .  .  | .  6  .  | .  .  .
6  .  6* | .  .  .  | 6  .  .
6- .  .  | .  .  .  | 6  .  6X
---------+----------+---------
.  .  6X | .  .  6X | .  .  .
6  .  .  | 6  .  .  | .  .  .
.  .  .  | .  .  .  | .  6  .


The claim is that we can still eliminate the 6 from r6c1. This is known as a sashimi swordfish. The idea is that we can pretend as if r6c3 could be a 6. In this case we are in the above example and can make the elimination.

One can similarly eliminate the 6 from r5c7.

I see that Harvard has just wrote something which will probably be more useful to you then my explanation, but I submit it for posterity.
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Postby Havard » Fri Apr 28, 2006 10:08 pm

rep'nA wrote:I see that Harvard has just wrote something which will probably be more useful to you then my explanation, but I submit it for posterity.


I liked yours better:)

Havard
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Postby Havard » Fri Apr 28, 2006 10:13 pm

ronk wrote:Havard, do you do the same?


Actually, I am working on an all-purpose-fisherman's-kit, that should pick up on all different types of fish, (and yes, that includes the franken-fish monsters too...):D So far it seems to be working ok, but it needs a bit more testing before I unleash it...:)

Havard
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Postby re'born » Fri Apr 28, 2006 11:24 pm

Havard wrote:I liked yours better:)

Havard


Thank you. However...

rep'nA's wife wrote:Don't encourage him, unless it's to do the dishes.


Harvard wrote:Actually, I am working on an all-purpose-fisherman's-kit, that should pick up on all different types of fish, (and yes, that includes the franken-fish monsters too...) So far it seems to be working ok, but it needs a bit more testing before I unleash it...


I'm sure all of us (with me at the front of the line) who have appreciated and benefited from your clear expositions and your helpful program are looking forward to it. I understand though that you have to tame the beast before you let it out of its cage.
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Postby ronk » Fri Apr 28, 2006 11:45 pm

Havard wrote:Actually, I am working on an all-purpose-fisherman's-kit, that should pick up on all different types of fish, (and yes, that includes the franken-fish monsters too:D .......

Now I know why I have difficulty picking up on those arcane logic techniques. I can't even figure out if there's an answer to my question in there somewhere.:D OTOH maybe there isn't one.
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Postby Sped » Sat Apr 29, 2006 12:35 am

rep'nA wrote:

Sped,

In your notation for XY-chains, how do you represent closed chains?

I don't have a notation for closed chains (loops, rings?). They don't come up very often. Regular open XY chains come up all the time, though, and often lead to useful eliminations.


What I have in mind is the chain

(1,6)9 > (7,6)6 > (8,4)9 > (8,9)3 > (7,8)4 > (3,8)3 > (1,7)9 => (1,6)!9.

(This chain also solves the puzzle.)


I don't see that as a closed chain. I see it as a regular XY chain starting on r7c6 and meandering to r1c7. It has loose 9s on each end so it allows the elimination of 9s in cells that see both r7c6 and r1c7.. in this case r1c6 and r7c7.

I'd write it like this:

9-(r7c6)-6-(r8c4)-9-(r8c9)-3-(r7c8)-4-(r3c8)-3-(r1c7)-9

The nice loop notation would be:

[r1c6]-9-[r7c6]-6-[r8c4]-9-[r8c9]-3-[r7c8]-4-[r3c8]-3-[r1c7]-9-[r1c6], => r1c6<>9
[r7c7]-9-[r7c6]-6-[r8c4]-9-[r8c9]-3-[r7c8]-4-[r3c8]-3-[r1c7]-9-[r7c7], => r7c7<>9

It does solve the puzzle.
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