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ZeroAssoluto
Joined: 05 Feb 2017
Posts: 941
Location: Rimini, Italy
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 Posted: Wed Jul 21, 2021 1:03 pm Post subject: Jul 21 VH |
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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 |
+-----------+------------+-----------+
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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: 358
Location: Wales
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| Posted: Wed Jul 21, 2021 2:04 pm Post subject: |
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| The same 3 cells in Gianni's XY wing will give -3 in r456c5 |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Wed Jul 21, 2021 2:12 pm Post subject: |
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| 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: 1151
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| Posted: Wed Jul 21, 2021 2:39 pm Post subject: |
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| 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: 358
Location: Wales
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| Posted: Thu Jul 22, 2021 5:35 am Post subject: |
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| 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: 1151
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| Posted: Thu Jul 22, 2021 7:15 am Post subject: |
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| 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 can’t cater for r6c3 -3. Only one of the pincers catches it so the chain can’t 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: 1151
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| Posted: Thu Jul 22, 2021 7:42 am Post subject: |
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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 3’s in c6. |
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TomC
Joined: 30 Oct 2020
Posts: 358
Location: Wales
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| Posted: Thu Jul 22, 2021 11:16 am Post subject: |
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| Interesting, although all my eliminations relied on the same XY wing cells |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Jul 22, 2021 12:40 pm Post subject: |
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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: 1151
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| Posted: Thu Jul 22, 2021 12:43 pm Post subject: |
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| 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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