How do I solve this Sudoku without Guessing?

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How do I solve this Sudoku without Guessing?

Postby hiprakhar » Mon Dec 10, 2018 4:53 pm

How do I solve this Sudoku without Guessing? I have filled the pencil marks.
Screenshot_20181210-035604.jpg
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hiprakhar
 
Posts: 2
Joined: 08 December 2018

Re: How do I solve this Sudoku without Guessing?

Postby SpAce » Tue Dec 11, 2018 12:52 am

Hi hiprakhar. Quite a few patterns/techniques would work here. Are you familiar with Skyscrapers, Empty Rectangles, Remote Pairs, W-Wings, Sashimi X-Wings, or Simple Coloring for example? Any of them would solve the bottleneck, after which it's just singles to the end.

The simplest pattern I see is Skyscraper in 4s. It would eliminate 4r3c3:

Code: Select all
.----------------.---------------.-------------.
|   67   78  1   | 48    5   2   | 9    3   46 |
| a(4)8  5   9   | 1     3   6   | 48   2   7  |
|   2    3   6-4 | 9   d(4)8  7  | 468  5   1  |
:----------------+---------------+-------------:
|   1    2   38  | 5     6   348 | 34   7   9  |
|   9    6   37  | 27    1   34  | 5    8   24 |
|   5    4   378 | 27    9   38  | 36   1   26 |
:----------------+---------------+-------------:
|  b48   1   2   | 6    c48  5   | 7    9   3  |
|   3    9   456 | 48    7   1   | 2    46  58 |
|   67   78  456 | 3     2   9   | 1    46  58 |
'----------------'---------------'-------------'

Skyscraper: (4)r2c1 = r7c1 - r7c5 = (4)r3c5 => -4 r3c3; stte

The pattern proves that at least one of r2c1 or r3c5 must be 4; therefore r3c3 (which sees both) can't be.

That pattern can also be seen as a Sashimi X-Wing. The same elimination is also available with a Remote Pair (48), or an Empty Rectangle. There are also several W-Wings that would solve the puzzle. If you're not familiar with those techniques, you can study them here, for example.
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
SpAce
 
Posts: 793
Joined: 22 May 2017


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