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Nov 9 VH

 
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sdq_pete



Joined: 30 Apr 2007
Posts: 119
Location: Rotterdam, NL

PostPosted: Fri Nov 09, 2007 12:20 pm    Post subject: Nov 9 VH Reply with quote

Well, I shall triumphantly announce the X-moves that solved it for me. I leave it to others to point out the ER's and possible short cuts. They were:
Code:
XY 149 R8C5
X  1   R27
XY 678 R4C6


Peter
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cgordon



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

PostPosted: Fri Nov 09, 2007 12:39 pm    Post subject: Reply with quote

Thank you Pete for letting me show the ER.
There are only two 6's in C4. The bottom 6 lines up with a T shaped hinge in Box 7 (bits of the T are missing). Doesn't matter which is the 6 in C4 - there cannot be a 6 in R6C3.
After that it's a breeze.

Code:
            
+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . . | . . . | . . . |   
| . . . | . . . | . . . |   
+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . . | . . . | . . . |   
| . . 6 | 6 . . | . . . |   
+-------+-------+-------+   
| . . . | . . . | . . . |   
| 6 . 6 | 6 . . | . . . |   
| . . 6 | . . . | . . . |
+-------+-------+-------+
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Fri Nov 09, 2007 3:38 pm    Post subject: Reply with quote

After singles, locked candidates and one naked pair:
Code:
.---------------------.---------------------.---------------------.
| 8      5      46    | 3      9      1     | 246    7      246   |
| 146    146    3     | 8      7      2     | 469    5      469   |
| 7      2      9     | 4      6      5     | 8      3      1     |
:---------------------+---------------------+---------------------:
| 9      1467   1467  | 2      158    68    | 456    48     3     |
| 5      46     8     | 7      3      9     | 1      24     246   |
| 2      3      16    | 16     58     4     | 59     89     7     |
:---------------------+---------------------+---------------------:
| 14     147    1457  | 19     2      78    | 3      6      4589  |
| 146    8      12456 | 169    14     3     | 7      249    2459  |
| 3      9      2467  | 5      48     678   | 24     1      248   |
'---------------------'---------------------'---------------------'

there is a skyscraper that eliminates 6 from r8c4, leaving singles to the end.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Fri Nov 09, 2007 4:11 pm    Post subject: Reply with quote

cg,


I found the same ER for digit <6> in Box 7, the ERI in R8C3 can see one
of the strong links on <6> in R6, eliminating <6> in R8C4, and the puzzle is solved, so the ER can be used in both ways (a double ER?)
Code:

+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . 6 | 6 . . | . . . |
+-------+-------+-------+
|er er. | . . . | . . . |
| 6 .eri|-6 . . | . . . |
|er er6 |  . .  | . . . |
+-------+-------+-------+
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George Woods



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

PostPosted: Fri Nov 09, 2007 4:43 pm    Post subject: A Rose by any other name Reply with quote

cgordon wrote:
Thank you Pete for letting me show the ER.
There are only two 6's in C4. The bottom 6 lines up with a T shaped hinge in Box 7 (bits of the T are missing). Doesn't matter which is the 6 in C4 - there cannot be a 6 in R6C3.
After that it's a breeze.

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


I did this by looking at the two 16 pairs in boxes 4 and 8 as the arms of an W wing- both operating on box 7 (both 16 cannot be 6 else box 7 would have no 6, so one of them must be 1, hence r6c4 cannot be 1 so must be 6....). Logic is almost identical to your's using the ER! I forget to mention that it is not a pure W Wing - but the logic works in spite of the 16 in r8c4 having a 9 attached! If it is not 6 then the pair of 19s deny a 1 to r6c4
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cgordon



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

PostPosted: Fri Nov 09, 2007 4:59 pm    Post subject: Reply with quote

Johan: I kinda lost you there. For clarity, I only showed the 6's relevant to the ER - but below are all of them. I'm pretty sure for an ER you need a row or column with only 2 candidates - which line up with a L, T or + shaped hinge in a box and another candidate. Don't see any more of those here. Not yet anyway.

Code:
            
+-------+-------+-------+   
| . . 6 | . . . | 6 . 6 |   
| 6 6 . | . . . | 6 . 6 |   
| . . . | . . . | . . . |   
+-------+-------+-------+   
| . 6 6 | . . 6 | 6 . . |   
| . 6 . | . . . | . . 6 |   
| . . 6 | 6 . . | 6 . . |   
+-------+-------+-------+   
| . . . | . . . | . . . |   
| 6 . 6 | 6 . . | . . . |   
| . . 6 | . . 6 | . . . |
+-------+-------+-------+
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Fri Nov 09, 2007 5:59 pm    Post subject: Reply with quote

cgordon wrote:
I'm pretty sure for an ER you need a row or column with only 2 candidates - which line up with a L, T or + shaped hinge in a box and another candidate. Don't see any more of those here. Not yet anyway.

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

Box 5 also has an ER, which would allow you to eliminate 6 from r6c3.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Fri Nov 09, 2007 6:28 pm    Post subject: Reply with quote

Quote:
For clarity, I only showed the 6's relevant to the ER - but below are all of them


cg,

The <6> in R6C7 in your posted grid, was not present in my grid because of the naked [16] pair in R6C34, maybe therefore you missed the strong link on <6> in R6?
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cgordon



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

PostPosted: Fri Nov 09, 2007 6:38 pm    Post subject: Reply with quote

Quote:
Box 5 also has an ER, which would allow you to eliminate 6 from r6c3.


Well spotted Bruce !! (Monty Python). I was going to protest - but there is indeed an L shaped hinge in Box 5 which complements the two 6's in R9.
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cgordon



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

PostPosted: Fri Nov 09, 2007 7:00 pm    Post subject: Reply with quote

Johan: You are also very correct. I didn't see the naked [16] pair in R6. So there are three ERs with bases of [6] pairs in R6, R9 and C4. In retrospect I think Re'borns skyscraper was the simpler way to go.
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Asellus



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

PostPosted: Fri Nov 09, 2007 11:15 pm    Post subject: Reply with quote

I hate to spoil things after all that discussion but... re'born's grid is not fully reduced: there's a {248} Locked Set in R9. Here's the grid after basics:
Code:
+--------------+------------+------------+
| 8   5   46   | 3   9   1  | 246 7  246 |
| 146 146 3    | 8   7   2  | 469 5  469 |
| 7   2   9    | 4   6   5  | 8   3  1   |
+--------------+------------+------------+
| 9   467 1467 | 2   158 68 | 456 48 3   |
| 5   46  8    | 7   3   9  | 1   2  46  |
| 2   3   16   | 16  58  4  | 59  89 7   |
+--------------+------------+------------+
| 14  147 5    | 19  2   78 | 3   6  489 |
| 146 8   2    | 169 14  3  | 7   49 5   |
| 3   9   67   | 5   48  67 | 24  1  248 |
+--------------+------------+------------+


Technically, that Skyscraper in R69 eliminates the <6> at R4C6 as well as that at R8C4. (That doesn't matter, though.)

There is also a Skyscraper in R68 that eliminates the <6> at R9C3 and solves the puzzle.

Peter,

Your X-Wing on <1> isn't required; the two XY Wings alone solve the puzzle.... at least in the grid above.
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Sat Nov 10, 2007 9:43 am    Post subject: Reply with quote

Asellus wrote:
I hate to spoil things after all that discussion but... re'born's grid is not fully reduced: there's a {248} Locked Set in R9.

That was by design. The first time I solved the puzzle, I spotted the naked triple and used it, but in the post mortem realized I could apply the skyscraper much earlier making the naked triple superfluous. That is why I was careful to list exactly what techniques I used before the skyscraper (instead of my usual "after basics"). You'll notice I couldn't apply it before the naked pair.
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