## (UVW)XYZ-Wing Present ?

Post the puzzle or solving technique that's causing you trouble and someone will help

### (UVW)XYZ-Wing Present ?

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` +-----------------------+ | . . . | . 2 9 | . . . | | . 6 . | . . 7 | . 1 . | | . . . | 5 . . | . 7 . | |-------+-------+-------| | . . 9 | . 6 . | . 2 . | | 1 . . | 9 . 8 | . 3 . | | 6 3 . | . 5 . | . 8 1 | |-------+-------+-------| | . . . | . . . | . 6 . | | . 1 3 | 2 7 6 | 5 9 . | | . . . | . . 1 | . . 7 | +-----------------------+   # Set NNP 72`

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` Singles gets us to this point. +-----------------------------------------------------+ |  7    4    1    |  6    2    9    |  8    5    3    | |  259  6    25   |  3    8    7    |  24   1    49   | |  3    289  28   |  5    1    4    |  26   7    69   | |-----------------+-----------------+-----------------| |  58   578  9    |  1    6    3    |  47   2    45   | |  1    257  257  |  9    4    8    |  67   3    56   | |  6    3    4    |  7    5    2    |  9    8    1    | |-----------------+-----------------+-----------------| |  89   789  78   |  4    3    5    |  1    6    2    | |  4    1    3    |  2    7    6    |  5    9    8    | |  25   25   6    |  8    9    1    |  3    4    7    | +-----------------------------------------------------+ # 27 eliminations remain`

I know that a 4-cell XY-Chain cracks it. I know there isn't an XY/XYZ-Wing present. What I don't know is if a higher (UVW)XYZ-Wing is present. Help please!
daj95376
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### Re: (UVW)XYZ-Wing Present ?

daj95376 wrote:I know that a 4-cell XY-Chain cracks it. I know there isn't an XY/XYZ-Wing present. What I don't know is if a higher (UVW)XYZ-Wing is present. Help please!

For me, all the (uvw)xyz-wings have been subsumed by the ALS xz-rule. In your pencilmarks there is a 4-cell ALS xz that cracks it, but it's not simpler than your xy-chain.
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` +-----------------------------------------------------+ |  7    4    1    |  6    2    9    |  8    5    3    | | A259  6    25   |  3    8    7    |  24   1   B49   | |  3    289  28   |  5    1    4    |  26   7    69   | |-----------------+-----------------+-----------------| |  8-5  578  9    |  1    6    3    |  47   2   B45   | |  1    257  257  |  9    4    8    |  67   3    56   | |  6    3    4    |  7    5    2    |  9    8    1    | |-----------------+-----------------+-----------------| |  89   789  78   |  4    3    5    |  1    6    2    | |  4    1    3    |  2    7    6    |  5    9    8    | | A25   25   6    |  8    9    1    |  3    4    7    | +-----------------------------------------------------+Sets: A = {r29c1} = {259}; B = {r24c9} = {459}    x,z = 9,5   r4c1 <> 5`
ronk
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Thanks ronk for checking and the extra info!
daj95376
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Joined: 15 May 2006

### Re: (UVW)XYZ-Wing Present ?

ronk wrote:For me, all the (uvw)xyz-wings have been subsumed by the ALS xz-rule.

And all ALS xz is equivalent to the hidden pair/triple/quad chain z*=x-x=#z, where * and # are the candidates other than the restricted common in the respective ALSs.

The advantage of the latter in practice is that it is more intuitive, less manufactured than the former :
in the present example the hidden pair 25r29c1 suggests itself rather immediately as a potential eliminator of 5r4c1. One then quickly checks that out without needing ever to have heard of ALS xz :
25r29c1=9r2c1-(9=4)r2c9-(4=5)r4c9 : =><5>r4c1.
Last edited by aran on Thu Jan 29, 2009 10:18 pm, edited 1 time in total.
aran

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### Re: (UVW)XYZ-Wing Present ?

ronk
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Don't you think you looked a bit juvenile in the exchange you sigh over ?
I guess not, otherwise I suppose you wouldn't be quoting it.
aran

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Joined: 02 March 2007

If both ALS xz and chains with hidden set logic allow one to arrive at the same objective, the question for me as average Joe solver is which will I be better able to utilize.

I'm always delighted to find an ALS xz. It's such a rare occasion! I'm lousy at it. My problem is that I can't "target" them as easily as I can using certain chains. By the word "target" I simply mean finding something that points one toward a potential victim. Dan's PM is a good example of that, and here's another from my old "stuck file":
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`Ruud's Sunday Nightmare, 1/6/08.27....3.94...35..1...2........9...3..93.46..3...6........1...4..28...75.5....98. *--------------------------------------------------------------------* | 58     2      7      | 49     58     16     | 14     3      169    | | 9      4      68     | 167    78     3      | 5      126    12678  | | 1      368    3568   | 49     2      5678   | 478    469    6789   | |----------------------+----------------------+----------------------| | 2458  *1678   14568  | 1257   9      12578  | 12478  1245   3      | | 258   *178    9      | 3      578    4      | 6      125    1278   | | 3     *178    1458   | 1257   6      12578  | 12478  12459  12789  | |----------------------+----------------------+----------------------| | 78     9      38     | 2567   1      2567   | 23     26     4      | | 6     *13     2      | 8      4      9      | 13     7      5      | | 47     5      14     | 267    3      267    | 9      8      126    | *--------------------------------------------------------------------*`

The hidden set of (1678) seems promising because it "targets" all the extra 8's in box 4 or column 2. One doesn't have to do many pushups to find:
(1678)r4568c2=(3)r8c2-(3=8)r7c3 => r46c3 <> 8. If a short chain is more "elegant" then that's gotta be pretty slick .

Now I have two eliminations without ever finding x or z, or even the other set, and I had a good reason to look for the chain in the first place. Now that I look at the PM after the elims, there's another one waiting to be scooped up. This seems to work pretty well for me as compared to ALS xz.

Luke
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Luke451 wrote:Now I have two eliminations without ever finding x or z, or even the other set, and I had a good reason to look for the chain in the first place. Now that I look at the PM after the elims, there's another one waiting to be scooped up. This seems to work pretty well for me as compared to ALS xz.

Whether or not one looks at a deduction in terms of sets or chains is a Point Of Personal Preference (POPP). I try to follow Mike Barker's stated policy of not debating POPPs.
ronk
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Ronk, the concept of POPP makes perfect sense to me, even though this is my first encounter with it. I'm obviously not fully aware of which topics fall into the taboo categories.

Some of these more advanced techniques are very new to me and I'm excited about the things I'm learning. I've learned much from you, and for that I'm grateful. What I wrote is my own honest and humble opinion based on what I've studied and picked up from others much smarter than I.

I personally have no history debating the relative merits of things I've only just learned about in the last six weeks. I apologize for being late to a match that has already been played . I'm sure I'm not the only one playing catch-up.

Luke
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It's all very well to evoke point of personal preference.
But I can't imagine that Mike Barker proclaimed an end to discussion.
What for example of the person who is undecided about whether to adopt a sets or chains approach and wishes for some guidance ?
One solid argument is this : ALS xz are subsumed into hidden sets, which therefore have more scope.
aran

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Joined: 02 March 2007

Luke451 wrote:Ronk, the concept of POPP makes perfect sense to me, even though this is my first encounter with it. I'm obviously not fully aware of which topics fall into the taboo categories.

Sorry, my post was not in any way intended to criticize your commentary, but rather to express my intent to not defend an earlier ALS-xz presentation.
ronk
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Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Luke451 wrote:
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`Ruud's Sunday Nightmare, 1/6/08.27....3.94...35..1...2........9...3..93.46..3...6........1...4..28...75.5....98. *--------------------------------------------------------------------* | 58     2      7      | 49     58     16     | 14     3      169    | | 9      4      68     | 167    78     3      | 5      126    12678  | | 1      368    3568   | 49     2      5678   | 478    469    6789   | |----------------------+----------------------+----------------------| | 2458  *1678   14568  | 1257   9      12578  | 12478  1245   3      | | 258   *178    9      | 3      578    4      | 6      125    1278   | | 3     *178    1458   | 1257   6      12578  | 12478  12459  12789  | |----------------------+----------------------+----------------------| | 78     9      38     | 2567   1      2567   | 23     26     4      | | 6     *13     2      | 8      4      9      | 13     7      5      | | 47     5      14     | 267    3      267    | 9      8      126    | *--------------------------------------------------------------------*`

The hidden set of (1678) seems promising because it "targets" all the extra 8's in box 4 or column 2. One doesn't have to do many pushups to find:
(1678)r4568c2=(3)r8c2-(3=8)r7c3 => r46c3 <> 8. If a short chain is more "elegant" then that's gotta be pretty slick .

Just for the heckuvit, as another Joe solver , this would be my first move targeting another hidden set:
ht(145)r469c3=(5)r3c3-r3c6=r1c5-(5=8)r1c1-(8=6)r2c3 => r4c3<>6 -> r4c2=6

(BTW, to no one in particular: We can never be sure that one man's Point Of Personal Preference is the Point Of Optimal Preference. )
DonM
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My POPP can only handle simple things. Yes, you can snicker now!

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`(8=3)r7c3 - (3=1)r8c2 - (1=78)r56c2  =>  [r46c3]<>8`

BTW: If we interpret the above chain as part of a forcing network, then we can add cells [r2c3],[r4c2]=6 to get [r4c3]<>6 as well. This leaves a <145> Naked Triple in [c3] that results in [r3c3]<>5 and a lot of subsequent action. (sorry, Im rambling again.)
daj95376
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Joined: 15 May 2006

DonM wrote:
Code: Select all
`Ruud's Sunday Nightmare, 1/6/08.27....3.94...35..1...2........9...3..93.46..3...6........1...4..28...75.5....98. *--------------------------------------------------------------------* | 58     2      7      | 49     58     16     | 14     3      169    | | 9      4      68     | 167    78     3      | 5      126    12678  | | 1      368    3568   | 49     2      5678   | 478    469    6789   | |----------------------+----------------------+----------------------| | 2458  *1678   14568  | 1257   9      12578  | 12478  1245   3      | | 258   *178    9      | 3      578    4      | 6      125    1278   | | 3     *178    1458   | 1257   6      12578  | 12478  12459  12789  | |----------------------+----------------------+----------------------| | 78     9      38     | 2567   1      2567   | 23     26     4      | | 6     *13     2      | 8      4      9      | 13     7      5      | | 47     5      14     | 267    3      267    | 9      8      126    | *--------------------------------------------------------------------*`

Just for the heckuvit, as another Joe solver , this would be my first move targeting another hidden set:
ht(145)r469c3=(5)r3c3-r3c6=r1c5-(5=8)r1c1-(8=6)r2c3 => r4c3<>6 -> r4c2=6

Don, with this : ht(145)r469c3=(5)r3c3, I see that you took the express route
aran

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aran wrote:Don, with this : ht(145)r469c3=(5)r3c3, I see that you took the express route

Yes
DonM
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