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Jul 21 VH

 
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ZeroAssoluto



Joined: 05 Feb 2017
Posts: 641
Location: Rimini, Italy

PostPosted: Wed Jul 21, 2021 1:03 pm    Post subject: Jul 21 VH Reply with quote

Hi everyone,

Code:

+-----------+------------+-----------+
| 3  5 6    | 8  9    4  | 7   2  1  |
| 1  9 4    | 27 267  67 | 35  35 8  |
| 2  7 8    | 3  5    1  | 4   9  6  |
+-----------+------------+-----------+
| 4  6 1379 | 27 1237 5  | 29  8  23 |
| 79 2 379  | 4  367  8  | 569 1  35 |
| 5  8 13   | 9  1236 36 | 26  7  4  |
+-----------+------------+-----------+
| 79 3 25   | 6  8    79 | 1   4  25 |
| 8  1 29   | 5  4    39 | 23  6  7  |
| 6  4 57   | 1  37   2  | 8   35 9  |
+-----------+------------+-----------+

Play this puzzle online at the Daily Sudoku site

XY-Wing 2,3,6 in r6c67,r8c7 and -3 in r8c6

Ciao Gianni
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TomC



Joined: 30 Oct 2020
Posts: 144
Location: Wales

PostPosted: Wed Jul 21, 2021 2:04 pm    Post subject: Reply with quote

The same 3 cells in Gianni's XY wing will give -3 in r456c5
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Mogulmeister



Joined: 03 May 2007
Posts: 966

PostPosted: Wed Jul 21, 2021 2:12 pm    Post subject: Reply with quote

You can't have a 7 in r2c6 because this would remove the 3 and the 6 in r6c6. r2c6<>7
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Mogulmeister



Joined: 03 May 2007
Posts: 966

PostPosted: Wed Jul 21, 2021 2:39 pm    Post subject: Reply with quote

TomC wrote:
The same 3 cells in Gianni's XY wing will give -3 in r456c5


Yes indeed. Gianni's elimination of the 3 at r8c6 extends making r9c5 = 3 and eliminating all the other 3's in r456c5.


Welding your two ideas together a bit we extend the XY wing to get an XY chain:

(3=6)r6c6-(6=2)r6c7-(2=3)r8c7-(3=5)r9c8-(5=7)r9c3-(7=3)r9c5

r456c6<>3, r8c6<>3 (yellow)



In effect there are two pincers (in red) for 3 at r6c6 and r9c5. Gianni's pincer is extended from r8c7 to r9c5.

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TomC



Joined: 30 Oct 2020
Posts: 144
Location: Wales

PostPosted: Thu Jul 22, 2021 5:35 am    Post subject: Reply with quote

Not sure if it's the same chain or slightly different but r6c3 can also be -3 (yellow)
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Mogulmeister



Joined: 03 May 2007
Posts: 966

PostPosted: Thu Jul 22, 2021 7:15 am    Post subject: Reply with quote

TomC wrote:
Not sure if it's the same chain or slightly different but r6c3 can also be -3 (yellow)


Good spot. No the above chain canít cater for r6c3 -3. Only one of the pincers catches it so the chain canít be relied on.


Last edited by Mogulmeister on Thu Jul 22, 2021 9:38 am; edited 1 time in total
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Mogulmeister



Joined: 03 May 2007
Posts: 966

PostPosted: Thu Jul 22, 2021 7:42 am    Post subject: Reply with quote

So yes - a different structure is needed to make your extra elimination. A contradiction that proves that r6c6 must be 3. A discontinuous (nice) loop.

If we remove 3 from r6c6 (ie assume 6) the loop via r6c7 r8c7 r8c6 insists that 3 goes back into r6c6. R6c6 must be 3 making ALL the eliminations.

I guess you might say that if r6c6 = 6 Then no 3ís in c6.
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TomC



Joined: 30 Oct 2020
Posts: 144
Location: Wales

PostPosted: Thu Jul 22, 2021 11:16 am    Post subject: Reply with quote

Interesting, although all my eliminations relied on the same XY wing cells
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Mogulmeister



Joined: 03 May 2007
Posts: 966

PostPosted: Thu Jul 22, 2021 12:40 pm    Post subject: Reply with quote

OK

Last edited by Mogulmeister on Thu Jul 22, 2021 12:44 pm; edited 1 time in total
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Mogulmeister



Joined: 03 May 2007
Posts: 966

PostPosted: Thu Jul 22, 2021 12:43 pm    Post subject: Reply with quote

TomC wrote:
Interesting, although all my eliminations relied on the same XY wing cells


As does the chain and the contradiction ?
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