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Too Hard 022418

 
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immpy



Joined: 06 May 2017
Posts: 199

PostPosted: Sat Feb 24, 2018 4:24 pm    Post subject: Too Hard 022418 Reply with quote

I found this one to be a pretty cool puzzle.
Hope others will, as well. Enjoy...

Code:

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

Play this puzzle online at the Daily Sudoku site

cheers...immp
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Ajň Dimonios



Joined: 01 May 2017
Posts: 325
Location: Sassari Italy

PostPosted: Sat Feb 24, 2018 10:25 pm    Post subject: Reply with quote

Hi everyone

Code:

+------------+--------------+---------------+
| 2  8  67   | 5    37   1  | 367  9    4   |
| 1  67 9    | 237  8    4  | 3567 3567 257 |
| 5  3  4    | 279  279  6  | 8    1    27  |
+------------+--------------+---------------+
| 4  57 57   | 1    36   9  | 36   2    8   |
| 68 9  1    | 3678 3567 2  | 4    3567 57  |
| 68 2  3    | 678  4    57 | 9    567  1   |
+------------+--------------+---------------+
| 9  4  258  | 27   1    3  | 257  578  6   |
| 3  1  2568 | 4    2567 57 | 257  578  9   |
| 7  56 256  | 269  2569 8  | 1    4    3   |
+------------+--------------+---------------+

Play this puzzle online at the Daily Sudoku site
This sudoku has 12 “back-door”( R2C7=5,R2C9=2,R2C4=7.R3C5=2,R5C5=7,R5C9=5,R6C6=5,R6C8=7,R7C4=2,R7C7=7,R7C8=5 and R9C5=5).
The uniqueness of the solution can be demonstrated with a single move showing no validity of 2 in R3C9 or 7 in R5C9 or 7 in R7C4. All these values if supposed true lead to a contradiction, consequently if eliminated individually they make the "back-doors" valid and solve the puzzle. A more classical solution can be obtained by using deletions with the basics fishes and finned fishes techniques.

Ciao a Tutti
Paolo
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immpy



Joined: 06 May 2017
Posts: 199

PostPosted: Sat Feb 24, 2018 11:23 pm    Post subject: Reply with quote

That is an excellent analysis Paolo. In depth as well. Beautiful!
I did not, nor do I usually, bother to check for any back doors, but I see some were found.
I began with a XYZ-Wing 23-7 b2 c4. Thus, r3c4<>7.
Next was an X-Wing on 3 r14c57. Thus, r2c7<>3 and r5c5<>3.

Puzzle is then at this stage:

Code:

+------------+--------------+--------------+
| 2  8  67   | 5    37   1  | 367 9    4   |
| 1  67 9    | 237  8    4  | 567 3567 257 |
| 5  3  4    | 29   279  6  | 8   1    27  |
+------------+--------------+--------------+
| 4  57 57   | 1    36   9  | 36  2    8   |
| 68 9  1    | 3678 567  2  | 4   3567 57  |
| 68 2  3    | 678  4    57 | 9   567  1   |
+------------+--------------+--------------+
| 9  4  258  | 27   1    3  | 257 578  6   |
| 3  1  2568 | 4    2567 57 | 257 578  9   |
| 7  56 256  | 269  2569 8  | 1   4    3   |
+------------+--------------+--------------+

Play this puzzle online at the Daily Sudoku site

...at this point it becomes time to deal with the Strong Links on 6 (pairs), believing there is a fish of some sort with the sixes...Swordfish?
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immpy



Joined: 06 May 2017
Posts: 199

PostPosted: Sat Feb 24, 2018 11:34 pm    Post subject: Reply with quote

^^

Last edited by immpy on Sat Feb 24, 2018 11:38 pm; edited 2 times in total
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ZeroAssoluto



Joined: 05 Feb 2017
Posts: 296
Location: Rimini, Italy

PostPosted: Sat Feb 24, 2018 11:35 pm    Post subject: Reply with quote

Hi everyone,

Code:

+------------+--------------+---------------+
| 2  8  67   | 5    37   1  | 367  9    4   |
| 1  67 9    | 237  8    4  | 3567 3567 257 |
| 5  3  4    | 279  279  6  | 8    1    27  |
+------------+--------------+---------------+
| 4  57 57   | 1    36   9  | 36   2    8   |
| 68 9  1    | 3678 3567 2  | 4    3567 57  |
| 68 2  3    | 678  4    57 | 9    567  1   |
+------------+--------------+---------------+
| 9  4  258  | 27   1    3  | 257  578  6   |
| 3  1  2568 | 4    2567 57 | 257  578  9   |
| 7  56 256  | 269  2569 8  | 1    4    3   |
+------------+--------------+---------------+

Play this puzzle online at the Daily Sudoku site

UR 6,8 in r56c14 and r9c4=6

after basic

Code:

+-------+-----------+------------+
| 2 8 7 | 5  3   1  | 6   9  4   |
| 1 6 9 | 27 8   4  | 57  3  257 |
| 5 3 4 | 9  27  6  | 8   1  27  |
+-------+-----------+------------+
| 4 7 5 | 1  6   9  | 3   2  8   |
| 8 9 1 | 3  57  2  | 4   6  57  |
| 6 2 3 | 8  4   57 | 9   57 1   |
+-------+-----------+------------+
| 9 4 8 | 27 1   3  | 257 57 6   |
| 3 1 6 | 4  257 57 | 27  8  9   |
| 7 5 2 | 6  9   8  | 1   4  3   |
+-------+-----------+------------+

Play this puzzle online at the Daily Sudoku site

Remote Pair 5,7 in r8c6,r6c6,r6c8,r7c8 and -7 in r7c4,r8c7

Ciao Gianni
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immpy



Joined: 06 May 2017
Posts: 199

PostPosted: Sat Feb 24, 2018 11:47 pm    Post subject: Reply with quote

Totally beautiful, Gianni....beautiful!
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Marty R.



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

PostPosted: Sun Feb 25, 2018 4:14 pm    Post subject: Reply with quote

I'm so oriented toward one-steppers that I gave up when I couldn't find one after spending considerable time on it.
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mtharp



Joined: 19 Jun 2006
Posts: 30

PostPosted: Mon Feb 26, 2018 3:42 am    Post subject: Reply with quote

Gianni, what logic did you use to come to the conclusion that:

r9c4=6 to resolve the UR 6,8 in r56c14

I understand that it does. I do not know that I would have found it. Your method would be instructive.

Mike
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ZeroAssoluto



Joined: 05 Feb 2017
Posts: 296
Location: Rimini, Italy

PostPosted: Mon Feb 26, 2018 8:53 am    Post subject: Reply with quote

Hi Mike,

the logic behind the UR is that you can not have 6 and 8 at the same time in cells r5c4, r6c4.
So the possible solutions are r6c4 = 7, r5c4 = 7, r5c4 = 3.
Each of these solutions, combined with the r237c4 cells, shows that r9c4 = 6.
If r6c4 = 7 - r7c4 = 2 - r3c4 = 9.
If r5c4 = 7 - r7c4 = 2 - r3c4 = 9.
If r5c4 = 3 - r27c4 (2,7) - r3c4 = 9.
Each of these solutions takes you to a kind of “hidden triple”.

Another possible road, which best shows the "hidden triple" is to look only at the r27c4 cells.
The numbers 2,3,7 can only be in these two cells combined with the possible solutions in r56c4.
In this case we obtain -2 in r9c4 and -2-7 in r3c4.
I hope I have been clear, otherwise we resent.

Ciao Gianni
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immpy



Joined: 06 May 2017
Posts: 199

PostPosted: Mon Feb 26, 2018 3:53 pm    Post subject: Reply with quote

Hello Mike,

This is an example of a Type 4 UR. Here are the parameters.

We look for additional candidates in two non diagonal cells again, but this time we ignore those extra candidates and concentrate on the UR candidates themselves: If one of the UR candidates is not possible anymore in any other cell of a house that contains both cells with the extra candidates, the other UR candidate can be eliminated from those UR cells.

In this case the 8s are not possible anywhere else in the house c4 or in the box 5. That means that an 8 must be present in one of those two cells which make up the UR. Since this is true, both of the 6s can be eliminated from r56c4, or else the Deadly Pattern would surface, resulting in two possible solutions to the puzzle.

An interesting side-note to this; an additional candidate (of 8) COULD be present in EITHER house; either row 4 OR box 5...BUT NOT IN BOTH. This is unlikely, but possible.

Hope I shed some light on the Type 4 UR.

cheers...immp

I used the Strong Links on 6 (pairs) to make my next eliminations, as I totally missed this Type 4 UR...but it is a beautiful technique.
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mtharp



Joined: 19 Jun 2006
Posts: 30

PostPosted: Tue Feb 27, 2018 10:52 am    Post subject: Reply with quote

Gianni & immp,

Thanks.

Mike
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