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Mogulmeister



Joined: 03 May 2007
Posts: 1151
PostPosted: Tue Jul 13, 2021 2:17 pm    Post subject: More Danny Reply with quote
More daj

Code:

 +-----------------------+
 | . . 2 | 9 5 1 | 4 . 8 |
 | . . . | . . 8 | 1 2 . |
 | 4 . 8 | 2 . . | 7 5 9 |
 |-------+-------+-------|
 | 1 . 7 | 5 . . | . . . |
 | 9 . . | . 4 2 | . . . |
 | 2 6 . | . 1 . | . . . |
 |-------+-------+-------|
 | 3 7 9 | . . . | . . . |
 | . 4 6 | . . . | . 9 . |
 | 5 . 1 | . . . | . . 4 |
 +-----------------------+
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immpy



Joined: 06 May 2017
Posts: 574
PostPosted: Wed Jul 14, 2021 6:00 pm    Post subject: Reply with quote
After basics grid:

Code:

+-------+---------------+---------------+
| 7 3 2 | 9   5    1    | 4    6   8    |
| 6 9 5 | 4   7    8    | 1    2   3    |
| 4 1 8 | 2   36   36   | 7    5   9    |
+-------+---------------+---------------+
| 1 8 7 | 5   369  369  | 2369 4   26   |
| 9 5 3 | 678 4    2    | 68   178 167  |
| 2 6 4 | 378 1    379  | 3589 378 57   |
+-------+---------------+---------------+
| 3 7 9 | 16  268  4    | 2568 18  1256 |
| 8 4 6 | 17  23   5    | 23   9   17   |
| 5 2 1 | 367 3689 3679 | 368  378 4    |
+-------+---------------+---------------+

Play this puzzle online at the Daily Sudoku site

cheers...immp
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immpy



Joined: 06 May 2017
Posts: 574
PostPosted: Wed Jul 14, 2021 6:12 pm    Post subject: Reply with quote
Lots of neat ways to go about this one. I started with the UR Type 2 on 36 in r34c56. r4c7 and r6c6<>9. Just what my eyes spotted quickly. As stated, many opportunities here; but it can be solved with only the VH techniques. Several Naked Pairs and Naked Triples as well. Nice multi-step VH puzzle! Thanks to Danny and Mogulmeister.

cheers...immp
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Clement



Joined: 24 Apr 2006
Posts: 1113
Location: Dar es Salaam Tanzania
PostPosted: Wed Jul 14, 2021 7:10 pm    Post subject: More Danny Reply with quote
Three Steps
Code:

+---------------+-----------------------+-----------------------+
| 7     3     2 | 9       5        1    | 4        6       8    |
| 6     9     5 | 4       7        8    | 1        2       3    |
| 4     1     8 | 2       36       36   | 7        5       9    |
+---------------+-----------------------+-----------------------+
| 1     8     7 | 5       369      369  | 2369     4       26   |
| 9     5     3 | 678     4        2    | 68       178     167  |
| 2     6     4 | *378    1       d79-3 | 589-3   *378     5-7  |
+---------------+-----------------------+-----------------------+
| 3     7     9 | 16      268      4    | 2568     18      1256 |
| 8     4     6 | 17      23       5    | 23       9      a17   |
| 5     2     1 | *367    689-3   c679-3| 68-3   b*378     4    |
+---------------+-----------------------+-----------------------+

Step 1: X-Wing (3)r69c48 => - 3r6c67,r9c567
Step 2: Singles Chain: (7)r8c9 = r9c8 – r9c6 = (7)r6c6 => - 7r6c9 Leads to
Code:

+---------------+--------------------+-------------------+
| 7     3     2 | 9      5       1   | 4      6      8   |
| 6     9     5 | 4      7       8   | 1      2      3   |
| 4     1     8 | 2      36      36  | 7      5      9   |
+---------------+--------------------+-------------------+
| 1     8     7 | 5      369     369 | 23     4      26  |
| 9     5     3 | b68    4       2   |c68     17     17  |
| 2     6     4 | 38     1       7   | 9      38     5   |

+---------------+--------------------+--------------------+
| 3     7     9 |a16     268     4   | 5      18     12-6 |
| 8     4     6 | 17     23      5   | 23     9       17  |
| 5     2     1 | 37     89-6   9-6  |d68    37       4   |
+---------------+--------------------+--------------------+

Step 3: Sky Scraper (6)r7c4 = r5c4 – r5c7 = (6)r9c7 => - 6r9c56,r7c9; stte
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dongrave



Joined: 06 Mar 2014
Posts: 572
PostPosted: Wed Jul 14, 2021 8:36 pm    Post subject: Reply with quote
After basics:
Code:
+-------------+---------------+---------------+
| 7   3   2   | 9   5    1    | 4    6   8    |
| 6   9   5   | 4   7    8    | 1    2   3    |
| 4   1   8   | 2   36   36   | 7    5   9    |
+-------------+---------------+---------------+
| 1   8   7   | 5   369  369  | 2369 4   26   |
| 9   5   3   | 678 4    2    | 68   178 167  |
| 2   6   4   | 378 1    379  | 3589 378 57   |
+-------------+---------------+---------------+
| 3   7   9   | 16  268  4    | 2568 18  1256 |
| 8   4   6   | 17  23   5    | 23   9   17   |
| 5   2   1   | 367 3689 3679 | 368  378 4    |
+-------------+---------------+---------------+

Then I used the following chain: 1*r7c8-[(1=6*)r7c4 -(1=7)r8c9]-(7=5)r6c9-(1*56*=2)r7c9-(2=6)r4c9-(6=8)r5c7-(6*8=7)r5c4-(78=1)r5c8 contradiction => r7c8 <> 1; stte.
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Mogulmeister



Joined: 03 May 2007
Posts: 1151
PostPosted: Wed Jul 14, 2021 9:49 pm    Post subject: Reply with quote
That’s great - three different ways that work with different ideas. All good!! Thanks folks!

As we proceed in Sudoku and develop our abilities to see patterns and links we go through stages. For me, I looked at the puzzle and noticed an “almost pattern”. After a while wings present themselves ahead of other possibilities.

For me this focusses on the 68 in r5c7 shown by # (below). You don't have to know what value this cell will be to solve the puzzle. The logic is fun because this is pattern plus!

Code:
+----------------+----------------+----------------+
| 7    3    2    | 9    5    1    | 4    6    8    |
| 6    9    5    | 4    7    8    | 1    2    3    |
| 4    1    8    | 2    36   36   | 7    5    9    |
+----------------+----------------+----------------+
| 1    8    7    | 5    369  369  | 2369 4    26   |
| 9    5    3    | *67-8 4    2   | 68# *17-8 167  |
| 2    6    4    | 378  1    379  | 3589 378  57   |
+----------------+----------------+----------------+
| 3    7    9    | *16  268  4    | 2568 8-1  1256 |
| 8    4    6    | 17   23   5    | 23   9    17   |
| 5    2    1    | 367  3689 3679 | 368  378  4    |
+----------------+----------------+----------------+



If r5c7 is 8 then r5c48<>8 and a <167> XY Wing emerges (shown by *) with vertex at r5c4 and so r7c8<>1 and puzzle solved.

🔥otherwise 🔥

If r5c7 not 8 (ie 6) then (8=6)r5c7-r45c9=r7c9-(6=1)r7c4; once again r7c8<>1 solves
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