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No XY/XYZ-Wings: Set A Puzzle 13

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Nov 05, 2008 8:52 am    Post subject: No XY/XYZ-Wings: Set A Puzzle 13 Reply with quote

Same Rules!

Code:
 +-----------------------+
 | . . 4 | 2 . 7 | . 5 . |
 | . 2 . | . . 3 | . . . |
 | 3 . 7 | . 6 8 | . . . |
 |-------+-------+-------|
 | 8 . . | 3 . 1 | . . 6 |
 | . . 2 | . . . | . . . |
 | 1 3 6 | 7 . . | 5 . 8 |
 |-------+-------+-------|
 | . . . | . . 4 | 6 . . |
 | 7 . . | . . . | . . 2 |
 | . . . | 6 . 9 | . 3 5 |
 +-----------------------+
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Nov 05, 2008 11:00 pm    Post subject: Reply with quote

Code:
.---------------------.---------------------.---------------------.
| 6      18     4     | 2      19     7     | 1389   5      139   |
| 9      2      158   | 4      15     3     | 178    6      17    |
| 3      15     7     | 59     6      8     | 1249   1249   149   |
:---------------------+---------------------+---------------------:
| 8      479    59    | 3      459    1     | 2479   2479   6     |
| 45     4579   2     | 59     8      6     | 13479  1479   13479 |
| 1      3      6     | 7      49     2     | 5      49     8     |
:---------------------+---------------------+---------------------:
| 25     159    3     | 18     27     4     | 6      1789   179   |
| 7      6      19    | 18     3      5     | 149    1489   2     |
| 24     148    18    | 6      27     9     | 17     3      5     |
'---------------------'---------------------'---------------------'

the grid above is after the initial x-wing on 5
then this use of a naked pair elimination
if r9c2 is not 4 => leaves naked pair on 18 in r19c2, this eliminates the 1 in r3c2
r3c2=> 5
r7c2 <> 5, r7c1 <> 2, r9c1 = 2
which means r9c1 is not 4

I will need help with this AIC notation

(4)r9c2=np(18)r19c2-(1=5)r3c2-(5)r7c2=(5-2)r7c1=(2)r9c1; r9c1 <> 4
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Thu Nov 06, 2008 6:09 am    Post subject: Reply with quote

Norm,

Your AIC uses a 2-cell ALS along the chain. In a bivalue (the smallest possible ALS), it is obvious that there is a strong link (or weak link, since it is conjugate) between the two digits. In an ALS larger than 2 cells, any two (grouped as necessary) digits within the ALS are strongly linked. Here, you are using the 2-cell 148 ALS in r19c2. So, from that, you could, in principle, use (1)r19c2=(4)r9c2 or (1)r19c2=(8)r19c2 or (8)r19c2=(4)r9c2.

In your AIC, you are using the first choice (which is the only useful one since the grouped <8>s do not weakly link to anything). This is how the complete AIC appears:
(4)r9c1 - ALS[(4)r9c2=(1)r19c2] - (1=5)r3c2 - (5)r7c2=(5-2)r7c1=(2-4)r9c1; r9c1<>4

[Edit to fix typo and clarify.]


Last edited by Asellus on Thu Nov 06, 2008 1:43 pm; edited 1 time in total
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Nov 06, 2008 7:56 am    Post subject: Reply with quote

Hint: Don't leave [stack 1].
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Thu Nov 06, 2008 2:08 pm    Post subject: Reply with quote

Norm,

An alternate view that is equivalent to your AIC is the 2 ALS "xz wing" of {1458} in r139c2 and {245} in r79c1. The shared exclusive <4>s give shared common pincer <5>s in r3c2 and r1c7, eliminating <5> from r7c2. As an AIC, it is:
(5)r7c2 - ALSr139c2[(5)r3c2=(4)r9c2] - ALS[(4)r9c1=(5)r7c1] - (5)r7c2; r7c2<>5

I don't know if that's what Danny is hinting at.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Thu Nov 06, 2008 4:42 pm    Post subject: Reply with quote

Asellus wrote:
I don't know if that's what Danny is hinting at.

I see a (half) M-wing there.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Nov 06, 2008 6:32 pm    Post subject: Reply with quote

ravel wrote:
Asellus wrote:
I don't know if that's what Danny is hinting at.

I see a (half) M-wing there.

Bingo Exclamation
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Thu Nov 06, 2008 7:31 pm    Post subject: Reply with quote

can anyone give me a graphical representation of what a ALS-xy, ALS-xz looks like? the reason I ask is because nothing i have read on the subject has brought me closer to finding them. for my money, these set counting techniques are better left for an algorithm in a basic program. Rolling Eyes what I can guartentee in return is a fat smile and total gratification once this concept is finally integrated in my blind brain. what I don't want to do is read 4 pages of examples. I want candidates circled, I want arrows, I want lines of thought, I want descriptions of why the candidates have a relationship, etc, etc, etc Exclamation Exclamation please???
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keith



Joined: 19 Sep 2005
Posts: 3164
Location: near Detroit, Michigan, USA

PostPosted: Thu Nov 06, 2008 11:11 pm    Post subject: Reply with quote

> can anyone give me a graphical representation
> of what a ALS-xy, ALS-xz looks like?

And, please put your reply in the "Solution Techniques" thread.

Thank you,

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Nov 07, 2008 12:10 am    Post subject: Reply with quote

storm_norm wrote:
can anyone give me a graphical representation of what a ALS-xy, ALS-xz looks like? the reason I ask is because nothing i have read on the subject has brought me closer to finding them. for my money, these set counting techniques are better left for an algorithm in a basic program. Rolling Eyes what I can guartentee in return is a fat smile and total gratification once this concept is finally integrated in my blind brain. what I don't want to do is read 4 pages of examples. I want candidates circled, I want arrows, I want lines of thought, I want descriptions of why the candidates have a relationship, etc, etc, etc Exclamation Exclamation please???

Everything you ever wanted to know (and a whole lot more) about ALS.

http://www.sudoku.org.uk/SudokuThread.asp?fid=4&sid=10326&p1=1&p2=11
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Sun Nov 09, 2008 5:05 am    Post subject: Reply with quote

I just want to say that I think that the ALS tutorial in the link from the previous post is excellent! I agree with the author that terms such as "xz-wing" are less useful than grasping the power of ALS in general. (And, nowhere is subset counting used, which, I agree, is more for computers than for people.)
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