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Please check my logic
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Author:  enxio27 [ Mon Jun 23, 2008 5:40 pm ]
Post subject:  Please check my logic
This example doesn't include other candidates:

Code:
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
6 6 . | . 6 . | . 6 .
. . . | . . . | . . .
. . . | . . . | . 6 .
------+-------+------
. . . | . 6 . | . . .
. . . | . . . | . . .
. . . | . . . | . . .


It seems to me that there is an "almost" X-wing at r4c5, r4c8, r7c5, r6c8. Would that not eliminate the 6s at r4c1 and r4c2? If so, does this technique have a name?
Author:  Jean-Christophe [ Mon Jun 23, 2008 6:32 pm ]
Post subject:  Re: Please check my logic
I'm afraid we lack some crutial information: where are the strong links / conjugate pairs ?
A real example with a full pencil mark would help.
Author:  Børge [ Mon Jun 23, 2008 6:44 pm ]
Post subject:  Re: Please check my logic
enxio27 wrote:
Would that not eliminate the 6s at r4c1 and r4c2?
Definitely NOT. You have to look at this column-wise. c5 can have a 6 in r7 and c8 can have a 6 in r6. These two 6s do not exclude each other, making one of the 6s in c1 and c2 a legal possibility.

EDIT 1: Even having a candidate 6 in r6c5, producing a single-finned X-Wing in c5-c8 or a two-finned X-Wing in r4-r6 would not help at all.

EDIT 2: But as JC wrote, crucial information is missing. If the 6s in r6 and r7 are the only candidate 6s in their rows, then they are not candidates any more, but solutions.
Author:  enxio27 [ Mon Jun 23, 2008 8:29 pm ]
Post subject:  Re: Please check my logic
Jean-Christophe wrote:
I'm afraid we lack some crutial information: where are the strong links / conjugate pairs ?


I'm sorry, I'm not familiar with those terms. Can you explain?
Author:  enxio27 [ Mon Jun 23, 2008 8:35 pm ]
Post subject:  Re: Please check my logic
Børge wrote:
enxio27 wrote:
Would that not eliminate the 6s at r4c1 and r4c2?
Definitely NOT.


I think I see the fault in my logic now. I was thinking that, similar to an X-wing, 6s had to be either in r4c5 AND r6c8 or in r4c8 AND r7c5. I see now that isn't the case. We could have 6s in r6c8 and r7c5 and not in the other two at all.

Quote:
If the 6s in r6 and r7 are the only candidate 6s in their rows, then they are not candidates any more, but solutions.


Sorry! I tried to simplfy my example much. In actuality, there are other candidate 6s in both rows.
Author:  Jean-Christophe [ Mon Jun 23, 2008 9:43 pm ]
Post subject:  Re: Please check my logic
enxio27 wrote:
Jean-Christophe wrote:
I'm afraid we lack some crutial information: where are the strong links / conjugate pairs ?
I'm sorry, I'm not familiar with those terms. Can you explain?
See Sudopedia

Thinking of it, your pattern could be a skyscraper, a finned X-Wing or a sashimi X-Wing
Author:  enxio27 [ Mon Jun 23, 2008 10:17 pm ]
Post subject:  Re: Please check my logic
Jean-Christophe wrote:
enxio27 wrote:
Jean-Christophe wrote:
I'm afraid we lack some crutial information: where are the strong links / conjugate pairs ?
I'm sorry, I'm not familiar with those terms. Can you explain?
See Sudopedia


Ok, so would the 6s in column 5 and the 6s in column 8 both be conjugate pairs?

Quote:
Thinking of it, your pattern could be a skyscraper, a finned X-Wing or a sashimi X-Wing


OK, I grasp the concepts. In the example I gave, though, there are no candidates to be eliminated by the skyscraper, finned X-wing, or sashimi X-wing, correct?
Author:  Jean-Christophe [ Tue Jun 24, 2008 5:14 am ]
Post subject:  Re: Please check my logic
enxio27 wrote:
Ok, so would the 6s in column 5 and the 6s in column 8 both be conjugate pairs?
I cannot tell for sure, because your example doesn't show where the candidates are locked for which house. This is the crutial information I was reffering.
Apparently, it seems the 6 for C5 is locked in R47C5 and the 6 for C8 is locked in R46C8, correct ? If so, these 2 columns indeed form conjugate pairs for 6.
enxio27 wrote:
OK, I grasp the concepts. In the example I gave, though, there are no candidates to be eliminated by the skyscraper, finned X-wing, or sashimi X-wing, correct?
Yes, assuming the 6 is locked for C5 and C8, this does not allow any elimination since it does not form a skyscraper.
Code:
. . . | . / . | . / .
. . . | . / . | . / .
. . . | . / . | . / .
------+-------+------
6 6 . | . 6 . | . 6 .
. . . | . / . | . / .
. . . | . / . | . 6 .
------+-------+------
. . . | . 6 . | . / .
. . . | . / . | . / .
. . . | . / . | . / .
We can deduce that either R7C5 or R6C8 must hold a 6, possibly both R7C5 and R6C8 hold a 6. But there is no common buddies / peers of both R7C5 and R6C8 outside C58, so we cannot eliminate any candidate.


Now, if 6 for C8 were locked in R49C8, then it would have formed a skyscraper allowing to eliminate 6 from R7C79 and R9C46 (cells with *).
Code:
. . . | . / . | . / .
. . . | . / . | . / .
. . . | . / . | . / .
------+-------+------
6 6 . | . 6 . | . 6 .
. . . | . / . | . / .
. . . | . / . | . / .
------+-------+------
. . . | . 6 . | * / *
. . . | . / . | . / .
. . . | * / * | . 6 .
Author:  leeo [ Wed Jun 17, 2009 12:38 am ]
Post subject:  Re: Please check my logic
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. * . | . 6 . | . 6 .
. . . | . . . | . . .
. . 6 | . . . | . 6 .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .

you are probably after a "fish fin", where a candidate 6 outside a subset of rows(columns) touches enough candidates 6 in the row(column) set to make it have two few column(row) places to be. above, the *'d cell would touch most of the 6's except one, and r4, r6 would only then have 6's in c8, which cannot be.
Author:  udosuk [ Wed Jun 17, 2009 1:22 am ]
Post subject:  Re: Please check my logic
leeo wrote:
Code:
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. * . | . 6 . | . 6 .
. . . | . . . | . . .
. . 6 | . . . | . 6 .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .

you are probably after a "fish fin", where a candidate 6 outside a subset of rows(columns) touches enough candidates 6 in the row(column) set to make it have two few column(row) places to be. above, the *'d cell would touch most of the 6's except one, and r4, r6 would only then have 6's in c8, which cannot be.

This is a WRONG example. In this case r4c2=6 would force r6c8=6, and it is still a VALID pattern, so you CANNOT eliminate 6 from the "*'d" cell. :geek:

The following is a correct example:

Code:
. . / | . / . | . . .
. . / | . / . | . . .
. . / | . / . | . . .
------+-------+------
. * / | . 6 . | . . .
. . / | . / . | . . .
. . 6 | . / . | . . .
------+-------+------
. . / | . / . | . . .
. . 6 | . 6 . | . . .
. . / | . / . | . . .

r4c2=6 would force both r8c3 & r8c5 to be 6, invalid.
Therefore r4c2 must not be 6.
(Same elimination can be done to r4c1, r6c4 & r6c6.) :idea:
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