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ZeroAssoluto
Joined: 05 Feb 2017
Posts: 941
Location: Rimini, Italy
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 Posted: Sat Nov 06, 2021 10:01 am Post subject: Nov 06 VH |
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Hi everyone,
| Code: |
+------------+-----------+-----------+
| 4 3 2 | 68 68 1 | 9 5 7 |
| 5 1 8 | 9 7 4 | 3 6 2 |
| 6 9 7 | 2 3 5 | 18 48 14 |
+------------+-----------+-----------+
| 379 47 349 | 35 2 89 | 58 1 6 |
| 1 6 5 | 7 4 89 | 2 89 3 |
| 2 8 39 | 35 1 6 | 57 479 49 |
+------------+-----------+-----------+
| 789 27 1 | 68 689 3 | 4 279 5 |
| 39 24 349 | 1 5 7 | 6 29 8 |
| 789 5 6 | 4 89 2 | 17 3 19 |
+------------+-----------+-----------+
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Play this puzzle online at the Daily Sudoku site
XY-Wing 4,8,9 in r35c8,r6c9 and -4 in r3c9,r6c8
Ciao Gianni |
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TomC
Joined: 30 Oct 2020
Posts: 358
Location: Wales
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| Posted: Sat Nov 06, 2021 10:26 am Post subject: |
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Pincers on 9's mean that either r5c8=9 or r9c9=9
This means you can remove the 9's in r6c9 and r78c8 |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sat Nov 06, 2021 4:13 pm Post subject: |
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<68> UR means r7c5 = 9
{ed - still need a step afterwards}
Last edited by Mogulmeister on Sun Nov 07, 2021 11:43 pm; edited 1 time in total |
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TomC
Joined: 30 Oct 2020
Posts: 358
Location: Wales
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| Posted: Sat Nov 06, 2021 4:46 pm Post subject: |
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There is an XY chain which starts in r4c4 which goes 5-8-1-4-9-3-5
So r4c4 <>5 |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sun Nov 07, 2021 10:21 pm Post subject: |
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| TomC wrote: | | There is an XY chain which starts in r4c4 which goes 5-8-1-4-9-3-5 So r4c4 <>5 |
I think that's the contradiction loop Tom that starts in r4c4 with a 5 then creates a loop which removes that 5* and so r4c4 < > 5
*by sticking another 5 in r6c4
Last edited by Mogulmeister on Sun Nov 07, 2021 10:46 pm; edited 1 time in total |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sun Nov 07, 2021 10:27 pm Post subject: |
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The very closely related XY chain starts at the pincers for 5 at r6c4 and r4c7 would go:
not 5
is 8 ......................................................................not 3 is 5
(5=8)r4c7-(8=1)r3c7-(1=4)r3c9-(4=9)r6c9-(9=3)r6c3-(3=5)r6c4 => r4c4 < > 5 |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sun Nov 07, 2021 11:59 pm Post subject: |
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Here's a nice ALS xz
Set A {5,7,8,9} 4 candidates so n-1 =3 squares
Set B {2,7,9} 3 candidates so n-1 =2 squares
Restricted Common is 9 found in r578c8
Common Candidate is 7 in r9c7 which is seen by both 7's in A and B so gets eliminated.
Last edited by Mogulmeister on Mon Nov 08, 2021 12:30 am; edited 2 times in total |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Mon Nov 08, 2021 12:13 am Post subject: |
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I like the above because they are visual and quite easy to spot (imho).
You could take a chain view of course:
1) (7=5)r6c7-(5=8)r4c7-(8=9)r5c8-(9=27)r78c8 ==> r9c7 < > 7
2) You can also put 7 in r9c7 and go round the loop which would then remove it.
+7r9c7-(7=5)r6c7-(5=8)r4c7-(8=9)r5c8-(9=27)r78c8-(7)r9c7 |
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TomC
Joined: 30 Oct 2020
Posts: 358
Location: Wales
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| Posted: Mon Nov 08, 2021 7:49 am Post subject: |
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| Thanks Mogulmeister for the clarification, I was not sure about my XY chain (5-8-1-4-9-3-5) as I couldn't find the pincers, but you show that - 5 in r4c4 (also -5 in r6c7) |
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TomC
Joined: 30 Oct 2020
Posts: 358
Location: Wales
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| Posted: Mon Nov 08, 2021 7:59 am Post subject: |
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My first solution should be an XY chain then as if not 9 in r9c9 it is 9 in r5c8
| TomC wrote: | Pincers on 9's mean that either r5c8=9 or r9c9=9
This means you can remove the 9's in r6c9 and r78c8 |
I didn't see this this way at first, but (using your grid) reasoned that if Green is 9 then use Orange loop to get Red = 1, but if Green is 9 then r9c9 is also 1 |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Mon Nov 08, 2021 9:26 am Post subject: |
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| TomC wrote: |
I didn't see this this way at first, but (using your grid) reasoned that if Green is 9 then use Orange loop to get Red = 1, but if Green is 9 then r9c9 is also 1 |
Exactly. You have just worked through a proof above of the "restricted common" rule in ALS xy eliminations.
Remember
Finally, on a philosophical point regarding Sudoku solving:
There are some who see strange "yellow" teeth in a black mouth rather than the famous symbol! They are different sides of the same coin. |
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