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Earl
Joined: 30 May 2007 Posts: 658 Location: Victoria, KS

Posted: Fri May 28, 2021 1:23 pm Post subject: May28 VH 


289xywing @R3C3, 9R2C3
Early Earl
PS I spoke too soon. I agree with Don. I needed 689xywing and 268xyzwing to solve it. Thanks Don.
Last edited by Earl on Fri May 28, 2021 3:18 pm; edited 1 time in total 

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dongrave
Joined: 06 Mar 2014 Posts: 443

Posted: Fri May 28, 2021 3:05 pm Post subject: 


After basics:
Code: 
++++
 3 27 4  67 267 9  5 8 1 
 56 29 259  8 1 3  7 26 4 
 678 1 28  57 257 4  26 9 3 
++++
 78 3 89  567 56789 1  69 4 2 
 178 279 6  4 789 28  3 157 58 
 4 5 1289  3 6789 268  169 167 68 
++++
 9 6 15  2 48 58  14 3 7 
 15 8 3  9 46 7  124 12 56 
 2 4 7  1 3 56  8 56 9 
++++

Then I saw Earl's 289 XY Wing w/ pivot at r3c3 as one of 3 possible VH moves (the other 2 being a 698 XY Wing w/ pivot at r4c7 and a 268 XYZ Wing w/ pivot at r6c6) but none of the 3 look like they solve it.
After applying all 3 of these I still had to use a 278 XY Wing w/ pivot at r5c2 to solve it! 

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TomC
Joined: 30 Oct 2020 Posts: 107 Location: Wales

Posted: Fri May 28, 2021 6:05 pm Post subject: 


Code: 
++++
 3 27 4  67 267 9  5 8 1 
 56 29 259  8 1 3  7 26 4 
 678 1 28  567 2567 4  26 9 3 
++++
 78 3 89  567 56789 1  69 4 2 
 178 279 6  4 789 28  3 157 58 
 4 5 1289  3 6789 268  169 167 68 
++++
 9 6 15  2 48 58  14 3 7 
 15 8 3  9 46 7  124 12 56 
 2 4 7  1 3 56  8 56 9 
++++

Play this puzzle online at the Daily Sudoku site
Not sure what this is called but..
r6c9 <> 6 as by using the 6's in c6 you would get no 6's in box 9 or no 6's in c6 

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dongrave
Joined: 06 Mar 2014 Posts: 443

Posted: Fri May 28, 2021 7:23 pm Post subject: 


Note: I have replaced the less than sign immediately followed by the greater than sign in many places below with the text 'is not' due to an apparent bug that screws up the text when posting.
Nice solution Tom! Of course there are a lot of ways to represent your solution. Your solution can be expressed as a typical 'simple coloring' solution involving 5 cells that all include the candidate 6.
When I read the solution exactly as you've described, I read it as follows:
If r6c9 = 6, then r8c9 is not 6 and r6c6 is not 6 so r9c6 = 6 so r9c8 is not 6 so there's no 6 in box 9; so r6c9 is not 6.
But you could instead assume that r6c9 is 6 and reach a contradiction as follows: If r6c9 = 6, then r6c6 is not 6 so r9c6 = 6 so r9c8 is not 6 so r8c9 = 6 contradiction, so r6c9 is not 6.
(The Eureka notation for this would be: 6r6c9  r6c6 = r9c6  r9c8 = r8c9 contradiction => r6c9 is not 6.)
But even a little nicer than a chain with a contradiction would be a forcing chain with pincers on both ends. I learned this from Marty and Clement a few years ago and the logic goes as follows:
If r6c6 = 6 then r6c9 is certainly not 6 and if r6c6 is not 6 then I can show you that r8c9 = 6 so either way r6c9 is not 6.
(The Eureka notation for this would be: 6r6c6 = r9c6  r9c8 = r8c9 => r6c9 is not 6.) 

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TomC
Joined: 30 Oct 2020 Posts: 107 Location: Wales

Posted: Sat May 29, 2021 7:18 am Post subject: 


Thanks, notation for me has always been difficult, but this helps a lot. 

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ZeroAssoluto
Joined: 05 Feb 2017 Posts: 632 Location: Rimini, Italy

Posted: Sat May 29, 2021 8:47 am Post subject: 


Hi everyone,
WWing 5,6 in r2c1,r9c8 SL with number 5 in r8c19 and 6 in r2c8
or
Skyscraper with number 6 in r69c6,r68c9 and 6 in r8c5,r9c8
or
2 String Kite with number 6 in r9c68,r68c9 and 6 in r6c6
or
2 String Kite with number 6 in r69c6,r8c59 and 6 in r6c9
Ciao Gianni 

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