The New Sudoku Players' Forum

by **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!

by **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.

by **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.

by **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:

by **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 :?:

by **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?

by **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.

by **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.

by **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.

The New Sudoku Players' Forum

Possible replacement of strong links?

Possible replacement of strong links?