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Ajò Dimonios
Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
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 Posted: Thu May 25, 2017 12:00 pm Post subject: Super hard |
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Hi everyone
| Code: |
+-------+-------+-------+
| . . . | . . 1 | . 2 . |
| . . . | . 5 . | 4 . . |
| . 6 . | 7 . . | . . 3 |
+-------+-------+-------+
| . . . | . 4 . | 1 . . |
| 9 . . | 8 . . | . . 7 |
| . . . | . . 2 | . 5 . |
+-------+-------+-------+
| 1 4 . | . . . | . . . |
| . . 5 | . . . | . . . |
| 3 8 9 | 6 . . | . . . |
+-------+-------+-------+
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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
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| Posted: Sat May 27, 2017 11:15 am Post subject: |
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| 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 |
+----------------+-----------------+-------------------+
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Play this puzzle online at the Daily Sudoku site
Ciao a tutti
Paolo |
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dongrave
Joined: 06 Mar 2014
Posts: 572
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| Posted: Sun May 28, 2017 10:44 pm Post subject: |
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Hard is one thing! But just looking at your solution of this one gave me a headache!   |
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Clement
Joined: 24 Apr 2006
Posts: 1113
Location: Dar es Salaam Tanzania
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| Posted: Mon May 29, 2017 6:57 am Post subject: |
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| dongrave wrote: | | Hard is one thing! But just looking at your solution of this one gave me a headache! |
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
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| Posted: Mon May 29, 2017 8:13 am Post subject: |
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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
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| Posted: Mon May 29, 2017 3:06 pm Post subject: |
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| 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
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| Posted: Mon May 29, 2017 3:43 pm Post subject: |
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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
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| Posted: Mon May 29, 2017 6:37 pm Post subject: |
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| 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
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| Posted: Mon May 29, 2017 9:08 pm Post subject: |
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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
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| Posted: Mon May 29, 2017 9:33 pm Post subject: |
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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
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| Posted: Mon May 29, 2017 11:08 pm Post subject: |
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| 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
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| Posted: Tue May 30, 2017 6:43 am Post subject: |
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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
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| Posted: Tue May 30, 2017 12:14 pm Post subject: |
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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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