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Nov 06 VH

 
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ZeroAssoluto



Joined: 05 Feb 2017
Posts: 868
Location: Rimini, Italy

PostPosted: Sat Nov 06, 2021 10:01 am    Post subject: Nov 06 VH Reply with quote

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 |
+------------+-----------+-----------+

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: 349
Location: Wales

PostPosted: Sat Nov 06, 2021 10:26 am    Post subject: Reply with quote

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

PostPosted: Sat Nov 06, 2021 4:13 pm    Post subject: Reply with quote

<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: 349
Location: Wales

PostPosted: Sat Nov 06, 2021 4:46 pm    Post subject: Reply with quote

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

PostPosted: Sun Nov 07, 2021 10:21 pm    Post subject: Reply with quote

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

PostPosted: Sun Nov 07, 2021 10:27 pm    Post subject: Reply with quote

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

PostPosted: Sun Nov 07, 2021 11:59 pm    Post subject: Reply with quote

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

PostPosted: Mon Nov 08, 2021 12:13 am    Post subject: Reply with quote

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: 349
Location: Wales

PostPosted: Mon Nov 08, 2021 7:49 am    Post subject: Reply with quote

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: 349
Location: Wales

PostPosted: Mon Nov 08, 2021 7:59 am    Post subject: Reply with quote

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

PostPosted: Mon Nov 08, 2021 9:26 am    Post subject: Reply with quote

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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