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7/16 VH - help!
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Captain Pete



Joined: 09 Jun 2007
Posts: 55
Location: Oley, PA

PostPosted: Mon Jul 16, 2007 3:33 pm    Post subject: 7/16 VH - help! Reply with quote

Stuck on 7/16

17,3,9/ 6,5,2/17,8,4
685/147/29,29,3
4,2,17/3,8,9/16,5,67

279,4,3/5,29,8/67,269,1
29,179,6/479,3,14/8,249,5
5,179,8/479,129,6/249,3,27

19,5,124/49,6,3/24,7,8
8,67,47/2,17,5/3,146,9
3,679,247/8,179,14/5,1246,26
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Mon Jul 16, 2007 4:01 pm    Post subject: Reply with quote

XY chain on 1's is a distinct possibility
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Mon Jul 16, 2007 4:10 pm    Post subject: Reply with quote

...or if you're not happy piecing together an xy chain, there are two xy wings in there...try <47> <17> <14> Smile
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Mon Jul 16, 2007 4:22 pm    Post subject: Reply with quote

I haven't even got as far as Capt. Pete. How do you get rid of the 1's in Row 8, Cols 2 & 3 ??
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Mon Jul 16, 2007 4:48 pm    Post subject: Reply with quote

Simple box/line elimination - look at the pair of 1's in box 7 row 8 - they eliminate all the other 1's in that box.
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Captain Pete



Joined: 09 Jun 2007
Posts: 55
Location: Oley, PA

PostPosted: Mon Jul 16, 2007 5:21 pm    Post subject: 7/17 - VH - XY Wing Reply with quote

Herr Mogulmeister - Thanks for the hint, but I just can't seem to see a productive XY Wing. Your hint of 47-17-14 should have been enough, and it seems intuitive that those numbers should provide the key to this puzzle, but... I have a 47 in C3R8. I have 17's in common with that cell in C3R3 and C5R8. There are two 14's, but neither is in common with the cell containing 47. I do see the 74,17,14 XY Wing with 17 as the "corner" in blocks 7 and 8, but that doesn't produce any results.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Mon Jul 16, 2007 6:13 pm    Post subject: Reply with quote

Quote:
Simple box/line elimination - look at the pair of 1's in box 7 row 8 - they eliminate all the other 1's in that box


Yeah - I missed that obvious pair (though it was row 7). But now I'm at the same stage as the Captain. I see the xy wing but all it seems to do is eliminate a 4 from R8C3.
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Asellus



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

PostPosted: Mon Jul 16, 2007 7:01 pm    Post subject: Reply with quote

I think you will find that the fishing is good today!

Solved it in four steps.
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Captain Pete



Joined: 09 Jun 2007
Posts: 55
Location: Oley, PA

PostPosted: Mon Jul 16, 2007 7:17 pm    Post subject: Reply with quote

CGordon, Now you're ahead of me on this puzzle. I don't see the XY Wing that eliminates the 4 in C3R8.
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Mon Jul 16, 2007 7:30 pm    Post subject: Reply with quote

I did mention XY wings plural and outlined the first one there is another ......the XY chain blows it apart in one - making an elimiantion in Block 1.
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Mon Jul 16, 2007 7:34 pm    Post subject: Reply with quote

cg, don't you mean row 9 col 3 ?
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cgordon



Joined: 04 May 2007
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Location: ontario, canada

PostPosted: Mon Jul 16, 2007 8:16 pm    Post subject: Reply with quote

So far - by my reckoning!

There's an xy wing with pivot 17 on R8C5 that eliminates the 4 in R9C3
(you're right Mr. M)

Then an x wing on 7s in R1 and R4

Then an xy with pivot 49 (R7C4) that eliminates 1 in R9C3

Then an xy pivot 72 in R9C3 that eliminates 6 in R9C2

That's 4 steps and I'm still not there. But then I had problems with the easy bits.
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Captain Pete



Joined: 09 Jun 2007
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Location: Oley, PA

PostPosted: Mon Jul 16, 2007 8:17 pm    Post subject: Reply with quote

AHA! Got it. I don't know how I missed that XY-Wing that eliminartes the 4, but that soleves it for me. Thanks Mogulmeister and CGordon. Just when I think I can't be stumped, I am.

Pete
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Captain Pete



Joined: 09 Jun 2007
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PostPosted: Mon Jul 16, 2007 8:22 pm    Post subject: Reply with quote

Actually, once the 4 is gone in C3R9, it was the XY Wing with the pivot in C9R9 eliminating the 1 in C3R3 that solves it for me.
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Mon Jul 16, 2007 8:37 pm    Post subject: Reply with quote

This was nice - pincers in green steps in pink elimination in orange.

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cgordon



Joined: 04 May 2007
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Location: ontario, canada

PostPosted: Mon Jul 16, 2007 9:01 pm    Post subject: Reply with quote

Now you've lost me Mr M. I don't see the greens matching the nos. or positions of the pinks - and there's only one orange.

Still stuck. CG
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Mon Jul 16, 2007 9:19 pm    Post subject: Reply with quote

cg,

The orange is the eliminated 1. The pincer cells (which also have to contain 1) are in green and you build a chain from one pincer to another.

the XY Chain. Check it out on sudopedia.

http://www.sudopedia.org/wiki/XY-Chain
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George Woods



Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK

PostPosted: Mon Jul 16, 2007 11:09 pm    Post subject: two XY wings or 1 "compound" XY wing Reply with quote

Mogulmeister etc.. use two XY wings
47-71-14 to eliminate the 4
followed by 76-62-27
BUT
76-62-(7) 'cos the 2 gives the pair 47 in col3 that is equivalent to a 7.

So is this a valid extension of the XY wing (I Know it is valid - but has it a name?)
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Asellus



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

PostPosted: Tue Jul 17, 2007 6:22 am    Post subject: Reply with quote

George,

I can't follow your argument. However, in trying to figure it out I've found something that may be closely related. It is an implication chain that includes the second XY Wing cells in its structure, though not the first. It doesn't "combine" the two XY Wings, nor does it immediately determine the <2> in R9C3, as you seem to have done. But, it is interesting nonetheless, I believe.

Here is a simplified diagram of the situation:
Code:
+-------+-----+
| @17r  | 76r |
| #47   |  -  |
|  24r7 | 2r6 |
+-------+-----+

This represents the six cells R389C39 from the puzzle.

If we color <7> in @ red, then the <6> and <2> in the right column are red by XY Chaining. Now notice that the bottom left cell can see both red <7> and red <2>. So, the <4> must be red. But, this can't be since it eliminates all candidates from #.

Thus, all the red values can be eliminated.

Note that if the first XY-Wing had been applied, the bottom left cell would have been the bivalue 27 and the contradiction would have shifted there.

So, maybe there's some connection to your "combined" concept.
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jLo



Joined: 30 Apr 2007
Posts: 55

PostPosted: Tue Jul 17, 2007 3:20 pm    Post subject: Reply with quote

Quote:

If we color <7> in @ red, then the <6> and <2> in the right column are red by XY Chaining. Now notice that the bottom left cell can see both red <7> and red <2>. So, the <4> must be red.


I don't think you can make the argument that the <4> must be colored red based only on
those six cells. It works if red is true, but if it is false there are other <2> and <7>
candidates in column three and row nine that come into play.
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