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Vanhegan Fiendish September 30, 2012

 
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Sun Sep 30, 2012 5:01 am    Post subject: Vanhegan Fiendish September 30, 2012 Reply with quote

Code:

 *-----------*
 |..1|...|9..|
 |...|318|...|
 |3..|9.2|..8|
 |---+---+---|
 |.7.|253|.6.|
 |..3|.7.|4..|
 |.2.|486|.3.|
 |---+---+---|
 |6..|8.4|..7|
 |...|531|...|
 |..8|...|2..|
 *-----------*


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Clement



Joined: 24 Apr 2006
Posts: 639
Location: Dar es Salaam Tanzania

PostPosted: Sun Sep 30, 2012 4:22 pm    Post subject: Vanhagen Fiendish September 30, 2012 Reply with quote

Code after Basics
Code:

+-------------+-------+------------+
| 24   8  1   | 7 6 5 | 9  24  3   |
| 2479 49 267 | 3 1 8 | 5  247 246 |
| 3    5  67  | 9 4 2 | 16 17  8   |
+-------------+-------+------------+
| 189  7  4   | 2 5 3 | C18 6   19  |
| A58   6  3   | 1 7 9 | 4  B258 25  |
| 159  2  59  | 4 8 6 | 7  3   159 |
+-------------+-------+------------+
| 6    1  59  | 8 2 4 | 3  59  7   |
| 27   49 27  | 5 3 1 | D68 489 E46  |
| 4-5   3  8   | 6 9 7 | 2  145 F145 |
+-------------+-------+------------+
Dual Cell Forcing Chain ABCDEF
(5=8)r5c1-(25-8)r5c8-(1=8)r4c7-(8=6)r8c7-(6=4)r8c9=15r9c89; r9c1<>5 solves it.
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Sun Sep 30, 2012 6:11 pm    Post subject: Reply with quote

Same target; different arrow. Very Happy

Code:

 *-----------------------------------------------------------*
 | 24    8     1     | 7     6     5     | 9    b24    3     |
 | 2479  49    267   | 3     1     8     | 5    b247   246   |
 | 3     5     67    | 9     4     2     | 16   b17    8     |
 |-------------------+-------------------+-------------------|
 | 189   7     4     | 2     5     3     | 18    6     19    |
 |a58    6     3     | 1     7     9     | 4    b258   25    |
 | 159   2     9-5   | 4     8     6     | 7     3     159   |
 |-------------------+-------------------+-------------------|
 | 6     1    c59    | 8     2     4     | 3    b59    7     |
 | 27    49    27    | 5     3     1     | 68    489   46    |
 | 4-5   3     8     | 6     9     7     | 2    b145   145   |
 *-----------------------------------------------------------*
pseudo xy-wing
(5=8)r5c1-(8=9)als:r123579c8-(9=5)r7c3 => -5r6c3,r9c1; stte



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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Sun Sep 30, 2012 11:01 pm    Post subject: Reply with quote

arkietech wrote:

pseudo xy-wing
(5=8)r5c1-(8=9)als:r123579c8-(9=5)r7c3 => -5r6c3,r9c1; stte

I just remembered that bennys named this an ALS xy wing way back in 2005. See here. It was presented in "set form" rather than as an AIC, but it's the same structure. Although I suggested the pseudo term a few days ago, in retrospect the ALS xy-wing term now seems more appropriate.
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Marty R.



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

PostPosted: Sun Sep 30, 2012 11:21 pm    Post subject: Reply with quote

Code:

+-------------+-------+------------+
| 24   8  1   | 7 6 5 | 9  24  3   |
| 2479 49 267 | 3 1 8 | 5  247 246 |
| 3    5  67  | 9 4 2 | 16 17  8   |
+-------------+-------+------------+
| 189  7  4   | 2 5 3 | 18 6   19  |
| 58   6  3   | 1 7 9 | 4  258 25  |
| 159  2  59  | 4 8 6 | 7  3   159 |
+-------------+-------+------------+
| 6    1  59  | 8 2 4 | 3  59  7   |
| 27   49 27  | 5 3 1 | 68 489 46  |
| 45   3  8   | 6 9 7 | 2  145 145 |
+-------------+-------+------------+

Play this puzzle online at the Daily Sudoku site

I used the potential DP 19 in boxes 46. Either r4c1=8 or one of r6c19=5. Common outcome; r6c3=9.
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Sun Sep 30, 2012 11:47 pm    Post subject: Reply with quote

Marty R. wrote:
Code:

+-------------+-------+------------+
| 24   8  1   | 7 6 5 | 9  24  3   |
| 2479 49 267 | 3 1 8 | 5  247 246 |
| 3    5  67  | 9 4 2 | 16 17  8   |
+-------------+-------+------------+
| 189  7  4   | 2 5 3 | 18 6   19  |
| 58   6  3   | 1 7 9 | 4  258 25  |
| 159  2  59  | 4 8 6 | 7  3   159 |
+-------------+-------+------------+
| 6    1  59  | 8 2 4 | 3  59  7   |
| 27   49 27  | 5 3 1 | 68 489 46  |
| 45   3  8   | 6 9 7 | 2  145 145 |
+-------------+-------+------------+

Play this puzzle online at the Daily Sudoku site

I used the potential DP 19 in boxes 46. Either r4c1=8 or one of r6c19=5. Common outcome; r6c3=9.


Very Nice! Very Happy
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Mon Oct 01, 2012 12:42 pm    Post subject: Reply with quote

I also spotted the AUR(19). Initially I viewed the external strong inferences as:
AUR(19)r46c19[(9)r6c3=(1)r4c7]-(1=9)r4c9; => -9r4c1,r6c9 which is not very useful.

Then I tried another variation of the external strong inferences:
AUR(19)r46c19[(9)r6c3=(1)r4c7]-r4c1=r6c1; => -9r6c1 which is not useful by itself, but combined with the prior approach gives r6c3=9

Finally I used the internal strong inferences:
AUR(19)r46c19[(5)r6c19=(8)r4c1]-(8=5)r5c1; => -5r6c3 which completes the puzzle.

For me the lesson is to "keep working a pattern" to explore all possibilities.

Ted
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Mon Oct 01, 2012 1:35 pm    Post subject: Reply with quote

tlanglet wrote:
Finally I used the internal strong inferences:
AUR(19)r46c19[(5)r6c19=(8)r4c1]-(8=5)r5c1; => -5r6c3 which completes the puzzle.


I have been playing with some new notation. Is this valid?

(5=8)aur:r46c19-(8=5)r5c1 => -5r6c3

I find it easier to understand.

dan
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Mon Oct 01, 2012 2:55 pm    Post subject: Reply with quote

arkietech wrote:
tlanglet wrote:
Finally I used the internal strong inferences:
AUR(19)r46c19[(5)r6c19=(8)r4c1]-(8=5)r5c1; => -5r6c3 which completes the puzzle.


I have been playing with some new notation. Is this valid?

(5=8)aur:r46c19-(8=5)r5c1 => -5r6c3

I find it easier to understand.

dan


Dan,

I am definitely the wrong person to be commenting on notation but here is my opinion.......

1) I tend to be verbose and show detail so that others can easily flow the logic, especially those individuals trying to learn the technique.

2) Your notation is very curt but is fine when using internal strong inferences.

3) I think it is important/required to specify the location of any external strong inferences. How would you suggest to do that?

Ted
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Mon Oct 01, 2012 3:24 pm    Post subject: Reply with quote

tlanglet wrote:

3) I think it is important/required to specify the location of any external strong inferences. How would you suggest to do that?


I do not understand "external". I assume you mean "Local" (Line,Column or Box) rather than within a cell. Confused

I would show any necessary strong (and weak) inferences in the normal manner. eg. =*rncn or -*rncn. ( *=inference rncn=location)

Do you see any important/necessary inferences not shown in this solution?

(5=8)aur:r46c19-(8=5)r5c1 => -5r6c3

I guess it is a personal thing. To me too many details tend to confuse the issue rather than help.

dan
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Mon Oct 01, 2012 4:48 pm    Post subject: Reply with quote

ronk wrote:
arkietech wrote:

pseudo xy-wing
(5=8)r5c1-(8=9)als:r123579c8-(9=5)r7c3 => -5r6c3,r9c1; stte

I just remembered that bennys named this an ALS xy wing way back in 2005. See here. It was presented in "set form" rather than as an AIC, but it's the same structure. Although I suggested the pseudo term a few days ago, in retrospect the ALS xy-wing term now seems more appropriate.


I got so excited about Marty's aur I almost missed your post!

Sometimes an almost naked pair (anp) or triple (ant) seems to fit better than als. Could there be such a thing as an anp xy-wing?

for example:
Code:
*-----------------------------------------------------------*
 | 1     234   2349  | 6     29    8     | 235   2459  7     |
 | 8     7     29    | 3     4     5     | 6     29    1     |
 | 2346  2346  5     | 1     29    7     | 23    2489  48    |
 |-------------------+-------------------+-------------------|
 |b34    1     6     | 8     5     9     | 7     34    2     |
 | 245   8     24    | 7     3     6     | 9     1     45    |
 | 9    a35    7     | 4     1     2     | 8     35    6     |
 |-------------------+-------------------+-------------------|
 | 56    9     1     | 2     68    3     | 4     7     58    |
 |c245   24-5  8     | 9     7     1     |c25    6     3     |
 | 7     236   23    | 5     68    4     | 1     28    9     |
 *-----------------------------------------------------------*
als? xy-wing

(5=3)r6c2-(3=4)r4c1-(4=5)anp:r8c17 => -5r8c2; stte


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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Mon Oct 01, 2012 10:03 pm    Post subject: Reply with quote

arkietech wrote:
tlanglet wrote:

3) I think it is important/required to specify the location of any external strong inferences. How would you suggest to do that?


I do not understand "external". I assume you mean "Local" (Line,Column or Box) rather than within a cell. Confused

I would show any necessary strong (and weak) inferences in the normal manner. eg. =*rncn or -*rncn. ( *=inference rncn=location)

Do you see any important/necessary inferences not shown in this solution?

(5=8)aur:r46c19-(8=5)r5c1 => -5r6c3

I guess it is a personal thing. To me too many details tend to confuse the issue rather than help.

dan


Dan,

Here is a reference to the term "external inferences".

In an earlier post, I used an external inference:

AUR(19)r46c19[(9)r6c3=(1)r4c7]-(1=9)r4c9; => -9r4c1,r6c9

How would you notate the AUR using those conditions?

Ted[/b]
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Tue Oct 02, 2012 12:10 am    Post subject: Reply with quote

tlanglet wrote:
How would you notate the AUR using those conditions?


I would do it this way.

Code:
 *-----------------------------------------------------------*
 | 24    8     1     | 7     6     5     | 9     24    3     |
 | 2479  49    267   | 3     1     8     | 5     247   246   |
 | 3     5     67    | 9     4     2     | 16    17    8     |
 |-------------------+-------------------+-------------------|
 | 189   7     4     | 2     5     3     |b18    6    c19    |
 | 58    6     3     | 1     7     9     | 4     258   25    |
 | 159   2    a59    | 4     8     6     | 7     3     159   |
 |-------------------+-------------------+-------------------|
 | 6     1     59    | 8     2     4     | 3     59    7     |
 | 27    49    27    | 5     3     1     | 68    489   46    |
 | 45    3     8     | 6     9     7     | 2     145   145   |
 *-----------------------------------------------------------*
(9=5)r6c3-(5=8)aur:r46c19-(8=1)r4c7-(1=9)r4c9 => -9r4c1,r6c9
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aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Tue Oct 02, 2012 10:15 am    Post subject: Reply with quote

On notation in an AUR setting :
tlanglet writes :
AUR(19)r46c19[(5)r6c19=(8)r4c1]-(8=5)r5c1; => -5r6c3

the logic here is :
[UR19r46c19]=[5r6c19=8r4c1-(8=5)r5c1] : <5>r6c3
Since UR19r46c19 cannot exist, the first term plays no part, so square brackets could be dropped from it giving
UR19r46c19=[5r6c19=8r4c1-(8=5)r5c1] : <5>r6c3
or even more daringly
UR19r46c19=5r6c19=8r4c1-(8=5)r5c1 : <5>r6c3

arkietech writes
(9=5)r6c3-(5=8)aur:r46c19-(8=1)r4c7-(1=9)r4c9 => -9r4c1,r6c9
which could be expressed
(9=5)r6c3-5r6c19=(AUR-UR)r46c19=1r4c7-(1=9)r4c9
in which the AUR appears in its own right and not so to speak as an explanatory note
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Tue Oct 02, 2012 7:02 pm    Post subject: Reply with quote

aran wrote:
On notation in an AUR setting :
tlanglet writes :
AUR(19)r46c19[(5)r6c19=(8)r4c1]-(8=5)r5c1; => -5r6c3

the logic here is :
[UR19r46c19]=[5r6c19=8r4c1-(8=5)r5c1] : <5>r6c3
Since UR19r46c19 cannot exist, the first term plays no part, so square brackets could be dropped from it giving
UR19r46c19=[5r6c19=8r4c1-(8=5)r5c1] : <5>r6c3
or even more daringly
UR19r46c19=5r6c19=8r4c1-(8=5)r5c1 : <5>r6c3

arkietech writes
(9=5)r6c3-(5=8)aur:r46c19-(8=1)r4c7-(1=9)r4c9 => -9r4c1,r6c9
which could be expressed
(9=5)r6c3-5r6c19=(AUR-UR)r46c19=1r4c7-(1=9)r4c9
in which the AUR appears in its own right and not so to speak as an explanatory note


Aran,

Thanks for the feedback; it is always appreciated.

About 3-4 years ago some mentor on this website suggested the notation form I have been using for AURs; for me, it provides the details I find useful/important. It explicitly shows the external or internal strong inferences derived from the UR, and appears very similar to your daring form.

I find the alternate form you offered for arkietech's notation to be less intuitive and requires greater effort to understand, especially what SIS was used.

To each his/her own preferences.........

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Oct 02, 2012 8:42 pm    Post subject: Reply with quote

Strong links on <1> & <9>, and bivalue in r4c9, force these two eliminations.

Code:
 after basics
 +--------------------------------------------------------------+
 |  24    8     1     |  7     6     5     |  9     24    3     |
 |  2479  49    267   |  3     1     8     |  5     247   246   |
 |  3     5     67    |  9     4     2     |  16    17    8     |
 |--------------------+--------------------+--------------------|
 |  189   7     4     |  2     5     3     |  18    6     19    |
 |  58    6     3     |  1     7     9     |  4     258   25    |
 |  159   2     59    |  4     8     6     |  7     3     159   |
 |--------------------+--------------------+--------------------|
 |  6     1     59    |  8     2     4     |  3     59    7     |
 |  27    49    27    |  5     3     1     |  68    489   46    |
 |  45    3     8     |  6     9     7     |  2     145   145   |
 +--------------------------------------------------------------+
 # 42 eliminations remain

 r46c19  <19> UR via s-link              <> 9    r4c1
 r46c19  <19> UR via s-link              <> 9    r6c1
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Wed Oct 03, 2012 2:14 pm    Post subject: Reply with quote

arkietech wrote:
Sometimes an almost naked pair (anp) or triple (ant) seems to fit better than als. Could there be such a thing as an anp xy-wing?
...
als? xy-wing

(5=3)r6c2-(3=4)r4c1-(4=5)anp:r8c17 => -5r8c2

As you know, each of anp, ant, and anq is an als, so it would be correct. However, what if the ALS xy-wing were comprised of one anp and one ant? Then your approach in the example above would be a good compromise IMO.
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aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Wed Oct 03, 2012 4:35 pm    Post subject: Reply with quote

tlanglet wrote:
aran wrote:

arkietech writes
(9=5)r6c3-(5=8)aur:r46c19-(8=1)r4c7-(1=9)r4c9 => -9r4c1,r6c9
which could be expressed
(9=5)r6c3-5r6c19=(AUR-UR)r46c19=1r4c7-(1=9)r4c9
in which the AUR appears in its own right and not so to speak as an explanatory note

Aran,
[...]
I find the alternate form you offered for arkietech's notation to be less intuitive and requires greater effort to understand, especially what SIS was used.
To each his/her own preferences.........
Ted

Ted
Just to point out that there is no SIS in that chain above. It is a just a series of alternating links.
The trick, if it is one, being use of AUR-UR.
"-UR" is a truth in a sudoku with a unique solution, and as such isn't a consequence of AUR; but on the other hand, being a truth, can be inserted anywhere, so here just after AUR.
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