Possible replacement of strong links?

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Possible replacement of strong links?

Postby 999_Springs » Sun Jul 22, 2007 7:57 pm

I seem to have noticed that the pattern of three possibilities for a candidate in each of two rows/columns can replace a row/column strong link in many techniques. (Sometimes they must be in the same 3x9 block, other times not.)
Like this:
Code: Select all
...|...|.X.
.X---X--X|.
.X---X--X|.
---+---+-|-
...|...|.|.
...|...|.|.
...|...|.|.
---+---+-|-
.*.|.*.|.X.
...|...|...
...|...|...
(turbot fish)


...|...|...
.@.|.*.|...
.X---X--X..
---+---+---
...|...|...
.*.|.@.|...
.X---X--X..
---+---+---
...|...|...
...|...|...
...|...|...
(y-wing)


...|...|...
...|...|...
.X---X--X..
---+---+---
...|...|...
...|...|...
.X---X--X..
---+---+---
#.#|...|...
...|.*.|*..
#.#|...|...
(empty rectangle)

# = no candidate
* = elimination

Has this been found before?

75th post!
Last edited by l$ on Mon Jul 30, 2007 3:09 pm, edited 1 time in total.
Once upon a time I was a teenager who was active on here 2007-2011
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Postby re'born » Sun Jul 22, 2007 11:26 pm

999_Springs,

I would guess that they are all (or at least the first and last) covered by the fishy eliminations. For instance, I think the first is a finned mutant swordfish with base sets r2,r3,c8 and covering sets c2,c5,b3 with fin r7c8, but I am hardly an expert on big fish. I haven't thought enough about the third to decide what it is and I don't think I understand the second at all. Would you clarify it for me?

In any case, I think those are very nice patterns and I will stay on the lookout for them. I never look for finned mutant swordfish, in general, but your pattern is pretty easy to spot I think.
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Postby ronk » Mon Jul 23, 2007 12:33 am

re'born wrote:I think the first is a finned mutant swordfish with base sets r2,r3,c8 and covering sets c2,c5,b3 with fin r7c8, but I am hardly an expert on big fish. I haven't thought enough about the third to decide what it is and I don't think I understand the second at all.

I agree on the first. The third is a finned franken swordfish with base sets r3, r6, b7 and covering sets c2, c5,c7 with fin r8c13. I don't understand the second either.
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Postby udosuk » Mon Jul 23, 2007 5:01 pm

ronk wrote:I don't understand the second either.

Here is a practical example:
Code: Select all
  .  .  .  |  .  .  .  |  .  .  .
  .  12 .  |  . -2* .  |  .  .  .
  .  1# .  |  .  1# .  |  1# .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  . -2* .  |  .  12 .  |  .  .  .
  .  1# .  |  .  1# .  |  1# .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  .  .  .  |  .  .  .

The 1s on r36 can only be on c257 (the # cells).
So we can eliminate 2 from r2c5 & r5c2 (the * cells), otherwise we'll be forced to have two 1s on r36c7.

These # cells can act as replacements to say, a strong link of 1s on r8c25.:idea:
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Postby ronk » Mon Jul 23, 2007 5:38 pm

udosuk wrote:Here is a practical example:
Code: Select all
  .  .  .  |  .  .  .  |  .  .  .
  .  12 .  |  . -2* .  |  .  .  .
  .  1# .  |  .  1# .  |  1# .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  . -2* .  |  .  12 .  |  .  .  .
  .  1# .  |  .  1# .  |  1# .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  .  .  .  |  .  .  .

The 1s on r36 can only be on c257 (the # cells).
So we can eliminate 2 from r2c5 & r5c2 (the * cells), otherwise we'll be forced to have two 1s on r36c7.

These # cells can act as replacements to say, a strong link of 1s on r8c25.

Very nice. In nice loop form ...
Code: Select all
 [r5c2,r2c5]-2-r2c2-1-r36c2=1={x-wing:r36c57}-1-r5c5-2-[r5c2,r2c5]

which is equivalent to

 [r5c2,r2c5]-2-r2c2=2=r5c5-2-[r5c2,r2c5]

Note that while the upper nice loop is not symmetrical, the inferences are corrrect even when read right-to-left. Anyone have a real world example:?:
ronk
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Postby re'born » Mon Jul 23, 2007 10:50 pm

ronk wrote:
udosuk wrote:Here is a practical example:
Code: Select all
  .  .  .  |  .  .  .  |  .  .  .
  .  12 .  |  . -2* .  |  .  .  .
  .  1# .  |  .  1# .  |  1# .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  . -2* .  |  .  12 .  |  .  .  .
  .  1# .  |  .  1# .  |  1# .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  .  .  .  |  .  .  .

The 1s on r36 can only be on c257 (the # cells).
So we can eliminate 2 from r2c5 & r5c2 (the * cells), otherwise we'll be forced to have two 1s on r36c7.

These # cells can act as replacements to say, a strong link of 1s on r8c25.

Very nice. In nice loop form ...
Code: Select all
 [r5c2,r2c5]-2-r2c2-1-r36c2=1={x-wing:r36c57}-1-r5c5-2-[r5c2,r2c5]

which is equivalent to

 [r5c2,r2c5]-2-r2c2=2=r5c5-2-[r5c2,r2c5]

Note that while the upper nice loop is not symmetrical, the inferences are corrrect even when read right-to-left. Anyone have a real world example:?:


Well, I'm always on the lookout for semi-remote naked pairs (a.k.a. w-wings, a.k.a. y-wing styles), so hopefully one will pop up soon. Is there some way to view this as a Kraken fish?
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Postby ronk » Tue Jul 24, 2007 2:40 am

a retagged pattern that udosuk wrote:
Code: Select all
  .  .  .  |  .  .  .  |  .  .  .
  .  12 .  |  . -2  .  |  .  .  .
  . #1  .  |  . *1  .  | *1  .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  . -2  .  |  .  12 .  |  .  .  .
  . #1  .  |  . *1  .  | *1  .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  .  .  .  |  .  .  .
ronk wrote:[r5c2,r2c5]-2-r2c2-1-r36c2=1={x-wing:r36c57}-1-r5c5-2-[r5c2,r2c5] implies r2c5<>2, r5c2<>2

re'born wrote:Is there some way to view this as a Kraken fish?

The nice loop above pretty much describes it. Either x-wing r36c57 or fin r36c2 is ultimately true.

Code: Select all
kraken x-wing
x-wing: r36c57-1-r5c5-2-
r36c2-1-r2c2-2---------- => r2c5<>2, r5c2<>2

The same eliminations occur by using x-wing r36c27 with fin r36c5.
ronk
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Postby re'born » Tue Jul 24, 2007 10:01 am

ronk wrote:
a retagged pattern that udosuk wrote:
Code: Select all
  .  .  .  |  .  .  .  |  .  .  .
  .  12 .  |  . -2  .  |  .  .  .
  . #1  .  |  . *1  .  | *1  .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  . -2  .  |  .  12 .  |  .  .  .
  . #1  .  |  . *1  .  | *1  .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  .  .  .  |  .  .  .
ronk wrote:[r5c2,r2c5]-2-r2c2-1-r36c2=1={x-wing:r36c57}-1-r5c5-2-[r5c2,r2c5] implies r2c5<>2, r5c2<>2

re'born wrote:Is there some way to view this as a Kraken fish?

The nice loop above pretty much describes it. Either x-wing r36c57 or fin r36c2 is ultimately true.

Code: Select all
kraken x-wing
x-wing: r36c57-1-r5c5-2-
r36c2-1-r2c2-2---------- => r2c5<>2, r5c2<>2

The same eliminations occur by using x-wing r36c27 with fin r36c5.


Thanks ronk. That actually clears up a stupid misconception I had about kraken fish.
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Posts: 551
Joined: 31 May 2007

Postby 999_Springs » Mon Jul 30, 2007 7:16 pm

I also notice that these 3 possibilities in each of 2 rows/columns can also be replaced by 4 possibilities in each of 3 rows/columns, or 5 in each of 4 rows/columns etc. in the bottom two (as they need not be in the same 3x9 block).
e.g.
Code: Select all
.X---X--X-X
...|...|...
.X---X--X-X
---+---+---
...|...|...
...|...|...
.X---X--X-X
---+---+---
#.#|...|...
...|.*.|*.*
#.#|...|...


This generates many more techniques. But over a week has passed, and no practical example has been found of any of these, so I would be surprised if any of these bigger patterns are found.
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
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Posts: 399
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.


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