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Very difficult puzzle

 
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peterberg



Joined: 30 May 2013
Posts: 3

PostPosted: Thu May 30, 2013 5:51 pm    Post subject: Very difficult puzzle Reply with quote

Hi Guys,
I was just wondering, is this puzzle solvable without guessing?
http://www.livesudoku.com/en/sudoku.php?puzzle=1317893

I spent a whole lot of time there and got stuck.
Would love to at least know it's possible to solve using reason only...

Thanks.
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Thu May 30, 2013 7:48 pm    Post subject: Reply with quote

How about posting the grid position at which you're stuck?

And yes, it's possible.
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JC Van Hay



Joined: 13 Jun 2010
Posts: 365
Location: Charleroi, Belgium

PostPosted: Thu May 30, 2013 7:59 pm    Post subject: Reply with quote

Single digit "techniques" are only required to solve this puzzle ...
Besides Singles and Locked Candidates, the following is needed : r1c3=1.
There are multiple ways to logically justify this. For example :
Code:
+----------------+-------------------+-------------------+
| 5    2    9(1) | 9(1)    3       8 | 6       7    4    |
| 8    79   3    | 479(1)  479(1)  6 | 2       5    9(1) |
| 179  4    6    | 1279    1279    5 | 89(1)   139  1389 |
+----------------+-------------------+-------------------+
| 349  359  49   | 589(1)  59(1)   7 | 589(1)  2    6    |
| 6    1    8    | 259     259     3 | 59      4    7    |
| 79   579  2    | 589(1)  6       4 | 3       19   189  |
+----------------+-------------------+-------------------+
| 139  39   7    | 6       8       2 | 4       13   5    |
| 2    8    5    | 347     47      1 | 79      6    39   |
| 134  6    4-1  | 357     57      9 | 7(1)    8    2    |
+----------------+-------------------+-------------------+
Either r1c3=1 or r1c4=1, r2c9=1 and r4c5=1, r9c7=1 :=> r9c3#1 :=> r1c3=1.
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Thu May 30, 2013 8:11 pm    Post subject: Reply with quote

After basics:
Code:
+----------------+----------------+----------------+
| 9    1    45   | 45   8    7    | 2    6    3    |
| 7    56   8    | 3456 3456 2    | 1    9    45   |
| 456  3    2    | 1456 1456 9    | 457  458  4578 |
+----------------+----------------+----------------+
| 358  589  35   | 4579 459  6    | 4579 1    2    |
| 2    4    7    | 159  159  8    | 59   3    6    |
| 56   569  1    | 4579 2    3    | 8    45   457  |
+----------------+----------------+----------------+
| 458  58   6    | 2    7    1    | 3    48   9    |
| 1    7    9    | 368  36   4    | 56   2    58   |
| 348  2    34   | 689  69   5    | 46   7    1    |
+----------------+----------------+----------------+

Nice puzzle! I had a W-wing and a bunch of XY-wings.

Keith
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JC Van Hay



Joined: 13 Jun 2010
Posts: 365
Location: Charleroi, Belgium

PostPosted: Thu May 30, 2013 9:08 pm    Post subject: Reply with quote

The same with Keith's grid but on the digit 4 (r1c3=4) Very Happy !
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Thu May 30, 2013 9:35 pm    Post subject: Reply with quote

What is going on here? Keith's and JC's grids are different and when I click the link I get a puzzle that doesn't match either of theirs. And clicking the link repeated times gets me a different puzzle each time.
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JC Van Hay



Joined: 13 Jun 2010
Posts: 365
Location: Charleroi, Belgium

PostPosted: Thu May 30, 2013 9:42 pm    Post subject: Reply with quote

Marty R. wrote:
What is going on here? Keith's and JC's grids are different and when I click the link I get a puzzle that doesn't match either of theirs. And clicking the link repeated times gets me a different puzzle each time.

Idem Very Happy The puzzles are identical up to a permutation of the digits 1 to 9 Wink
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Thu May 30, 2013 10:02 pm    Post subject: Reply with quote

JC Van Hay wrote:
Marty R. wrote:
What is going on here? Keith's and JC's grids are different and when I click the link I get a puzzle that doesn't match either of theirs. And clicking the link repeated times gets me a different puzzle each time.

Idem Very Happy The puzzles are identical up to a permutation of the digits 1 to 9 Wink


Talk to me like I'm eight years old; I don't understand. Embarassed
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JC Van Hay



Joined: 13 Jun 2010
Posts: 365
Location: Charleroi, Belgium

PostPosted: Thu May 30, 2013 10:24 pm    Post subject: Reply with quote

Marty R. wrote:
JC Van Hay wrote:
Marty R. wrote:
What is going on here? Keith's and JC's grids are different and when I click the link I get a puzzle that doesn't match either of theirs. And clicking the link repeated times gets me a different puzzle each time.

Idem Very Happy The puzzles are identical up to a permutation of the digits 1 to 9 Wink


Talk to me like I'm eight years old; I don't understand. Embarassed

Marty, you get Keith's grid by replacing 123456789 by 418392675 respectively in the grid I posted. To get an idea of the number of equivalent grids, the number of permutations of the digit 1 to 9 is equal to 9.8.7.6.5.4.3.2.1=362880 (9 possibilities for a first digit times 8 possibilities for a second digit times 7 possibilities for a third digit ...) !

JC
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Thu May 30, 2013 11:53 pm    Post subject: Reply with quote

I guess I'm hopeless. About 100 years ago I studied permutations and combinations, but I can't get through my thick skull what's going on here. It sounds like Peter is stuck on a particular puzzle and I don't have a clue as to what's going on.

No need to respond; I'm ready to move on. Embarassed
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Fri May 31, 2013 4:55 am    Post subject: Reply with quote

Marty,

Go to the link:

http://www.livesudoku.com/en/sudoku.php?puzzle=1317893

You will see a puzzle.

Now, press F5 to refresh the page. You will see what I think is the same puzzle, except some of the digits are transposed. 4 may become 2 and so on. Press F5 over and over, you get the idea.

Curious.

Keith
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peterberg



Joined: 30 May 2013
Posts: 3

PostPosted: Fri May 31, 2013 7:42 am    Post subject: Reply with quote

Very Happy
I see I started a whole new discussion.
Yes the same puzzle has different arrangement every time it loads.
It is I believe because of the scoring system. They measure times and have a high score system so it helps avoid cheating
Anyway thanks for the help, I'm rather new to the whole terminology but I'm starting to learn now, is was solving the easier puzzles till now and they didn't require special skills.
The thing I enjoy the most is the multiplayer option on this website but I'm not as fast as the good players they have in there so I usually lose but still it makes the game a lot more interesting.
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Fri May 31, 2013 4:57 pm    Post subject: Reply with quote

Quote:
Now, press F5 to refresh the page. You will see what I think is the same puzzle, except some of the digits are transposed. 4 may become 2 and so on. Press F5 over and over, you get the idea.


OK, I can see that the number of givens stays the same and so is the symmetry. Given that, does that mean each version is of equal difficulty and has a similar solution path?
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Fri May 31, 2013 8:41 pm    Post subject: Reply with quote

Marty R. wrote:
Quote:
Now, press F5 to refresh the page. You will see what I think is the same puzzle, except some of the digits are transposed. 4 may become 2 and so on. Press F5 over and over, you get the idea.


OK, I can see that the number of givens stays the same and so is the symmetry. Given that, does that mean each version is of equal difficulty and has a similar solution path?

It's the same puzzle, only the symbols (numbers) are interchanged.

Keith
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