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May28 VH

 
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Earl



Joined: 30 May 2007
Posts: 660
Location: Victoria, KS

PostPosted: Fri May 28, 2021 1:23 pm    Post subject: May28 VH Reply with quote

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: 450

PostPosted: Fri May 28, 2021 3:05 pm    Post subject: Reply with quote

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 28-9 XY Wing w/ pivot at r3c3 as one of 3 possible VH moves (the other 2 being a 69-8 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 27-8 XY Wing w/ pivot at r5c2 to solve it!
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TomC



Joined: 30 Oct 2020
Posts: 144
Location: Wales

PostPosted: Fri May 28, 2021 6:05 pm    Post subject: Reply with quote

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: 450

PostPosted: Fri May 28, 2021 7:23 pm    Post subject: Reply with quote

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: 144
Location: Wales

PostPosted: Sat May 29, 2021 7:18 am    Post subject: Reply with quote

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



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

PostPosted: Sat May 29, 2021 8:47 am    Post subject: Reply with quote

Hi everyone,

W-Wing 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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