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Super hard

 
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy

PostPosted: Thu May 25, 2017 12:00 pm    Post subject: Super hard Reply with quote

Hi everyone
Code:

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

Play this puzzle online at the Daily Sudoku site

Ciao a tutti
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy

PostPosted: Sat May 27, 2017 11:15 am    Post subject: Reply with quote

Code:

+--------------------+--------------------+------------------------+
| 4578  3579  3478   | 349   3689   1     | 56789   2       5689   |
| 278   12379 12378  | 239   5      3689  | 4       16789   1689   |
| 2458  6     1248   | 7     289    489   | 589     189     3      |
+--------------------+--------------------+------------------------+
| 25678 2357  23678  | 359   4      35679 | 1       3689    2689   |
| 9     1235  12346  | 8     136    356   | 236     346     7      |
| 4678  137   134678 | 139   13679  2     | 3689    5       4689   |
+--------------------+--------------------+------------------------+
| 1     4     267    | 2359  23789  35789 | 2356789 36789   25689  |
| 267   27    5      | 12349 123789 34789 | 236789  1346789 124689 |
| 3     8     9      | 6     127    457   | 257     147     1245   |
+--------------------+--------------------+------------------------+

Play this puzzle online at the Daily Sudoku site
if 2 is true in R8C7 --> contradiction, R7C6 is empty then 2 is false and can be eliminated.
If 9 is true in R1C4--> contradiction, R4C3 is empty then 9 is false and can be eliminated.
When each of the 1s in pair r3c38 are made true in turn together the 2 at r2c3, there is a contradiction, so 2 can be removed.
When each of the 1s in pair r3c38 are made true in turn together the 2 at r7c9, there is a contradiction, so 2 can be removed.
When each of the 1s in pair r3c38 are made true in turn together the 2 at r8c9, there is a contradiction, so 2 can be removed.
If 4 is true in R8C8 --> contradiction, R2C4 is empty then 4 is false and can be eliminated
When each of the 1s in pair r68c4 are made true in turn together the 4 false at r5c8, there is a contradiction, so r5c8 can be made equal to 4.
If 2 is false in R4C9 --> contradiction, 4 is absent in line 6, then 2 is true and R4C9 can be made equal to 2.
If 4 is false in R1C4 --> contradiction R7C5 is empty, then 4 is true and R1C4 can be made equal to 4.
If 2 is false in R3C5 --> contradiction, 1 is absent in line 5, then 2 is true and R3C5 can be made equal to 2.
Naked pairs of 17 at r9c58 => -1 r9c9, -7 r9c6
If 1 is false in R2C9 => contradiction, 1 is absent in line 5, then 1 is true and R2C9 can be made equal to 1.
If 1 is false in R5C5 => contradiction, 2 is absent in line 7, then 1 is true and R5C5 can be made equal to 1.
Solution =>stte.
Code:

+----------------+-----------------+-------------------+
| 578  3579 378  | 4    3689 1     | 6789  2      689  |
| 278  2379 378  | 39   5    3689  | 4     6789   1    |
| 4    6    1    | 7    2    89    | 5     89     3    |
+----------------+-----------------+-------------------+
| 5678 357  3678 | 359  4    35679 | 1     3689   2    |
| 9    235  236  | 8    1    356   | 36    4      7    |
| 678  137  4    | 39   3679 2     | 3689  5      689  |
+----------------+-----------------+-------------------+
| 1    4    267  | 2359 3789 35789 | 36789 36789  5689 |
| 267  27   5    | 1239 3789 34789 | 36789 136789 4689 |
| 3    8    9    | 6    7    45    | 2     17     45   |
+----------------+-----------------+-------------------+

Play this puzzle online at the Daily Sudoku site
Ciao a tutti
Paolo
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dongrave



Joined: 06 Mar 2014
Posts: 568

PostPosted: Sun May 28, 2017 10:44 pm    Post subject: Reply with quote

Hard is one thing! But just looking at your solution of this one gave me a headache! Smile Shocked
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Clement



Joined: 24 Apr 2006
Posts: 1111
Location: Dar es Salaam Tanzania

PostPosted: Mon May 29, 2017 6:57 am    Post subject: Reply with quote

dongrave wrote:
Hard is one thing! But just looking at your solution of this one gave me a headache! Smile Shocked
It is a Trial and Error "Technique". Place a digit in a cell that's a possible candidate and look, whether you get a solution, a contradiction or not. If that is enabled, every Sudoku can be solved.
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy

PostPosted: Mon May 29, 2017 8:13 am    Post subject: Reply with quote

Hi everyone

I used the nishio technique .


Ciao a tutti. Paolo
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Mon May 29, 2017 3:06 pm    Post subject: Reply with quote

Quote:
if 2 is true in R8C7 --> contradiction, R7C6 is empty then 2 is false and can be eliminated.
If 9 is true in R1C4--> contradiction, R4C3 is empty then 9 is false and can be eliminated.
When each of the 1s in pair r3c38 are made true in turn together the 2 at r2c3, there is a contradiction, so 2 can be removed.
When each of the 1s in pair r3c38 are made true in turn together the 2 at r7c9, there is a contradiction, so 2 can be removed.
When each of the 1s in pair r3c38 are made true in turn together the 2 at r8c9, there is a contradiction, so 2 can be removed.
If 4 is true in R8C8 --> contradiction, R2C4 is empty then 4 is false and can be eliminated
When each of the 1s in pair r68c4 are made true in turn together the 4 false at r5c8, there is a contradiction, so r5c8 can be made equal to 4.
If 2 is false in R4C9 --> contradiction, 4 is absent in line 6, then 2 is true and R4C9 can be made equal to 2.
If 4 is false in R1C4 --> contradiction R7C5 is empty, then 4 is true and R1C4 can be made equal to 4.
If 2 is false in R3C5 --> contradiction, 1 is absent in line 5, then 2 is true and R3C5 can be made equal to 2.
Naked pairs of 17 at r9c58 => -1 r9c9, -7 r9c6
If 1 is false in R2C9 => contradiction, 1 is absent in line 5, then 1 is true and R2C9 can be made equal to 1.
If 1 is false in R5C5 => contradiction, 2 is absent in line 7, then 1 is true and R5C5 can be made equal to 1.
Solution =>stte.


I agree with Don, this could be headache-inducing.

Is it necessary to execute every one of the eliminations and solved cells in order to solve the puzzle?
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy

PostPosted: Mon May 29, 2017 3:43 pm    Post subject: Reply with quote

Hi everyone,


I would not know. There are probably so many ways to reach the solution. This is one of the many. I believe that all the methods, even the simplest, are always contradictions.

Ciao a tutti
Paolo
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Mon May 29, 2017 6:37 pm    Post subject: Reply with quote

Quote:
I believe that all the methods, even the simplest, are always contradictions.


Paolo,

Don't get me wrong, I'm fine with any solution that solves a puzzle. I've solved plenty of puzzles using contradictions.

For your information. In the Sudoku community that I'm part of, contradictions are much less preferred and respected than positive solutions.
The better players in that group (I am not one of those players) rarely, if ever, post contradiction solutions. In that group, the majority of solutions are AIC's.
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy

PostPosted: Mon May 29, 2017 9:08 pm    Post subject: Reply with quote

Dear Marty, I'm sorry I do not agree with you. Any alternating inference chain is certainly a method that seeks contradiction. It starts with a strong inference by alternating weak inferences, seeking at the end of the chain a contradiction that leads to the elimination of one or more candidates. In fact the eliminations carried out with AIC can be performed using the trial and errors method. Probably seems to be much less elegant but uses the same logic.
Ciao a tutti
Paolo
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy

PostPosted: Mon May 29, 2017 9:33 pm    Post subject: Reply with quote

Dear Marty, probably most people, when using a trial and errors method, do not realize the number of logic chains that are triggered simultaneously. The method does not try to guess a candidate but rather to prove it false.
Ciao a tutti
Paolo
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Mon May 29, 2017 11:08 pm    Post subject: Reply with quote

Ajò Dimonios wrote:
Dear Marty, probably most people, when using a trial and errors method, do not realize the number of logic chains that are triggered simultaneously. The method does not try to guess a candidate but rather to prove it false.
Ciao a tutti
Paolo


Paolo,

I'm like most people, I did not realize that. The only thing I knew about Nishio was the existence of the word.

Ciao a tutti to you too.
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy

PostPosted: Tue May 30, 2017 6:43 am    Post subject: Reply with quote

Hi everyone

I think the word "Nishio" comes from the name of the Japanese sudoku champion Tetsuya Nishio.

Saluti a tutti
Paolo
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

PostPosted: Tue May 30, 2017 12:14 pm    Post subject: Reply with quote

1r3c3 + 4r3c6 -> 0 solution
1r3c3 + 4r3c1 + 1r5c2 -> 0 solution
1r3c3 + 4r3c1 + 1r5c5 -> 1 solution

1r3c8 + 4r5c3 + 1r5c2 -> 0 solution via NP(47)r9c68
1r3c8 + 4r5c3 + 1r5c5 -> 0 solution
1r3c8 + 4r5c8 + 1r9c5 -> 0 solution
1r3c8 + 4r5c8 + 1r9c9 -> 0 solution
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