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Is there a logical path?

 
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alana



Joined: 21 Mar 2016
Posts: 1
PostPosted: Mon Mar 21, 2016 3:09 am    Post subject: Is there a logical path? Reply with quote
I have found this sudoku which is now at a point in which I cannot find a pure logic step to continue. All the steps until here were made with logic.

At the situation I'm showing in the attached picture, the only thing I have found to continue is like trial and error (which is logic, in the end, but I don't like it). I would like to have a simpler or different thought to continue. Can you point me?

Let me explain my trial and error like step.

First, I will point the sudoku like this:

(1,1) (1,2) ... (1,9)
(2,1) (2,2) ... (2,9)
...
(9,1) (9,2) ... (9,9)

- to start, we try to put 1 at (1,3) - instead of (2,3), the only other possible position for 1 in this box

- with the 1 we said above, we can say that in the right box will have 1 at (3,5) or (3,6)

- with this second 1 we find the 1 of the box (1,9). It is at (2,8).

- now, in the box (4,9), the 1 will be at (4,9) or (6,9). This is the column 9!

- now, for the box (7,9), 1 can only be at (9,7)

- we also find the 9 at (7,7)

- find the 1 at (8,4), the only position left for it in this box

- find the 9 at (8,4). But we have 1 here, so we are wrong from the start with 1 at (1,3)

Oh... I can't attach an image. So, use this url to see it:

http://imgbox.com/KeCS3nyu

I want to find the easiest next step from this point. Which do you think it is best than my trial and error sequence?
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Mon Mar 21, 2016 12:49 pm    Post subject: Reply with quote
Code:
+-------------+-------------+-------------+
| 9   6   14  | 5   2   14  | 7   8   3   |
| 3   2   14  | 7   8   9   | 6   14  5   |
| 7   5   8   | 3   146 146 | 14  2   9   |
+-------------+-------------+-------------+
| 5   3   2   | 16  9   7   | 8   146 146 |
| 4   1   6   | 8   5   2   | 3   9   7   |
| 8   7   9   | 4   3   16  | 2   5   16  |
+-------------+-------------+-------------+
| 1   8   5   | 6   46  3   | 49  7   2   |
| 2   4   3   | 9   7   8   | 5   146 146 |
| 6   49  7   | 2   14  5   | 149 3   8   |
+-------------+-------------+-------------+

There is only one possibility in each of R8C2 and R7C4. The puzzle needs only singles to complete.

Keith
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Clement



Joined: 24 Apr 2006
Posts: 1111
Location: Dar es Salaam Tanzania
PostPosted: Mon Mar 21, 2016 6:22 pm    Post subject: Is there a logical path? Reply with quote
Alana's grid after basics from the url
Code:

+---------+------------+-------------+
| 9 6  14 | 5  2   14  | 7   8   3   |
| 3 2  14 | 7  8   9   | 6   14  5   |
| 7 5  8  | 3  146 146 | c14  2   9   |
+---------+------------+-------------+
| 5 3  2  | g1-6 9   7   | 8   146 146 |
| 4 1  6  | 8  5   2   | 3   9   7   |
| 8 7  9  | 4  3   16  | 2   5   16  |
+---------+------------+-------------+
| 1 8  5  | a69 46  3   | b49  7   2   |
| 2 49 3  | f19 7   8   | 5   146 146 |
| 6 49 7  | 2  e14  5   | d149 3   8   |
+---------+------------+-------------+

Chains are acceptable as logical steps when other strategies are not forthcoming e.g for this puzzle
(6=9)r7c4 - (9=4)r7c7 - (4=1)r3c7 - r9c7 = r9c5 - r8c4 = (1)r4c4 => - 6 r4c4 which solves it.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Mon Mar 21, 2016 9:30 pm    Post subject: Re: Is there a logical path? Reply with quote
Clement wrote:
Alana's grid after basics from the url
Code:

+---------+------------+-------------+
| 9 6  14 | 5  2   14  | 7   8   3   |
| 3 2  14 | 7  8   9   | 6   14  5   |
| 7 5  8  | 3  146 146 | c14  2   9   |
+---------+------------+-------------+
| 5 3  2  | g1-6 9   7   | 8   146 146 |
| 4 1  6  | 8  5   2   | 3   9   7   |
| 8 7  9  | 4  3   16  | 2   5   16  |
+---------+------------+-------------+
| 1 8  5  | a69 46  3   | b49  7   2   |
| 2 49 3  | f19 7   8   | 5   146 146 |
| 6 49 7  | 2  e14  5   | d149 3   8   |
+---------+------------+-------------+

Chains are acceptable as logical steps when other strategies are not forthcoming e.g for this puzzle
(6=9)r7c4 - (9=4)r7c7 - (4=1)r3c7 - r9c7 = r9c5 - r8c4 = (1)r4c4 => - 6 r4c4 which solves it.

There's an XY-Wing , 14-9 pivoted in r9c5=> -9r8c2
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