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I'm stuck on a supposedly "easy" sudoku.

Code: Select all

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

Any tip?

Thanks in advance.

As you didn't post a pencilmark grid, I'll assume you aren't using them. To solve it without pm's, you'll need some kind of short chain, so let's first make some observations:

Code: Select all

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

r1c8 may only be 6 or 9.
r5c8 may only be 4 or 9.
In row 4, digit 6 must be in column 7 or 8.

So what can we read from this?

Either r5c8=4, or r5c8=9 => r1c8=6 => r4c7=6

In both cases r4c7<>4.

Another way to look at it: If r4c7=4 => r5c8=9 => r1c8=6 => no 6 in row 4 => r4c7<>4.

The rest should be easy.

RW

Thank you.

I'm actually using pencil mark. If you have a solution using them, I'll be glad to know about it.

Thanks again in advance.

It's always good to post your current pms if you are using them, so other people know how much you have already been able to eliminate. In your grid, there's first two x-wings and after them you get here:

Code: Select all

 *--------------------------------------------------*
 | 67   5    2    | 8    1    4    | 3    69   79   |
 | 8    4    3    | 6    9    7    | 5    1    2    |
 | 9    67   1    | 5    2    3    | 47   8    46   |
 |----------------+----------------+----------------|
 | 5    12   9    | 14   7    8    | 46+2 26+4 3    |
 | 17   3    6    | 14   5    2    | 8    49   79   |
 | 4    27   8    | 9    3    6    | 27   5    1    |
 |----------------+----------------+----------------|
 | 26   9    5    | 7    4    1    | 26   3    8    |
 | 3    8    4    | 2    6    9    | 1    7    5    |
 | 12   16   7    | 3    8    5    | 9    24   46   |
 *--------------------------------------------------*

This is a BUG+2 grid, the extra candidates are separated with '+'. If this is an unique puzzle, then either r4c7=2 or r4c8=4. From this immediately follows that r4c7<>4 and r4c8<>2.

Of course, even with pms you may use the chain in my first post to get around the x-wings and not have to assume uniqueness. But the BUG cannot really be used without pms.

RW

Once again, there is a nice solution without uniqueness assumption.

After the x-wings:

Code: Select all

 *--------------------------------------------------*
 | 67   5    2    | 8    1    4    | 3    69   79   |
 | 8    4    3    | 6    9    7    | 5    1    2    |
 | 9    67   1    | 5    2    3    | 47   8    46   |
 |----------------+----------------+----------------|
 | 5   @12   9    | 14   7    8    | 246 #246  3    |
 |-17   3    6    | 14   5    2    | 8    49   79   |
 | 4    27   8    | 9    3    6    | 27   5    1    |
 |----------------+----------------+----------------|
 | 26   9    5    | 7    4    1    | 26   3    8    |
 | 3    8    4    | 2    6    9    | 1    7    5    |
 |@12  -16   7    | 3    8    5    | 9   #24   46   |
 *--------------------------------------------------*

On c8 you have a strong link of 2 in r49c8 (one of these must be 2).
In the mean time r4c2 and r9c1 are both 1|2.
The 2 on c8 will force one of these two cells to be 1.
So any cell seeing r4c2 and r9c1 simultaneously must not be 1.
As a result, you can eliminate 1 from r5c1 and r9c2.

This technique is called a Y-wing/W-wing/semi-remote-pair (different people call it by different names ).

Why go through all the trouble with the x-wings if you wish to make eliminations by focusing on those cells?

After the locked candidates:

Code: Select all

 *--------------------------------------------------*
 | 67   5    2    | 8    1    4    | 3    69   679  |
 | 8    4    3    | 6    9    7    | 5    1    2    |
 | 9    67   1    | 5    2    3    | 467  8    467  |
 |----------------+----------------+----------------|
 | 5   *12   9    | 14   7    8    | 246 -246  3    |
 |#17   3    6    | 14   5    2    | 8    49   479  |
 | 4    27   8    | 9    3    6    | 27   5    1    |
 |----------------+----------------+----------------|
 | 26   9    5    | 7    4    1    | 26   3    8    |
 | 3    8    4    | 2    6    9    | 1    7    5    |
 |#126  16   7    | 3    8    5    | 9   *246  46   |
 *--------------------------------------------------*

There's a strong link of 1 in r59c1 and a strong link of 2 in r9c18.

[r4c2]-1-[r5c1]=1=[r9c1]=2=[r9c8]
(If r4c2=1 => r9c1=1 => r9c8=2)

If r4c2<>2, then r9c8=2. Any cell that can see both r4c2 and r9c8 must not be 2.

RW

Code: Select all

 *--------------------------------------------------*
 | 67   5    2    | 8    1    4    | 3    69   679  |
 | 8    4    3    | 6    9    7    | 5    1    2    |
 | 9    67   1    | 5    2    3    | 467  8    467  |
 |----------------+----------------+----------------|
 | 5    12   9    | 14   7    8    | 246  246  3    |
 | 17   3    6    | 14   5    2    | 8    49   479  |
 | 4    27   8    | 9    3    6    | 27   5    1    |
 |----------------+----------------+----------------|
 | 26   9    5    | 7    4    1    | 26   3    8    |
 | 3    8    4    | 2    6    9    | 1    7    5    |
 | 126  126  7    | 3    8    5    | 9    246  46   |
 *--------------------------------------------------*


Suppose r4c8 is not 6. Then we would have:

1) [r6c7]-2-[r7c7]-6-[r4c78]-2-[r6c7]
2) [r6c7]-7-[r5c89]-4-[r4c8]-2-[r9c8]=2=[r7c7]=6=[r7c1]-6-[r1c1]=6=
=[r3c2]=7=[r6c2]-7-[r6c7]

Therefore, r4c8 must be 6 and the puzzle is solved.

asdf007 wrote:I'm stuck on a supposedly "easy" sudoku.

Code: Select all

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

Any tip?

Thanks in advance.

I'd like to see the original. The posted position is too far from easy to be credible.

After simple stuff and a couple of X Wings:

Code: Select all

 
 *--------------------------------------------------*
 | 67   5    2    | 8    1    4    | 3    69   79   |
 | 8    4    3    | 6    9    7    | 5    1    2    |
 | 9    67   1    | 5    2    3    | 47*  8   (4)6  |
 |----------------+----------------+----------------|
 | 5    12   9    | 14   7    8    | 246  246  3    |
 | 17   3    6    | 14   5    2    | 8    49   79   |
 | 4    27   8    | 9    3    6    | 27^  5    1    |
 |----------------+----------------+----------------|
 | 26   9    5    | 7    4    1    | 26^  3    8    |
 | 3    8    4    | 2    6    9    | 1    7    5    |
 | 12   16   7    | 3    8    5    | 9    24   46*  |
 *--------------------------------------------------*


The XY chain: 4-(r3c7)-7-(r6c7)-2-(r7c7)-6-(r9c9)-4
eliminates the 4 in r3c9 because either r3c7 or r9c9 must be a 4, and r3c9 sees both. It's all singles from there.

Above, the ends of the chain are marked with "*", the other cells in the chain are marked with "^", and the candidate to be excluded has () around it.

As a nice loop:

[r3c9]-4-[r3c7]-7-[r6c7]-2-[r7c7]-6-[r9c9]-4-[r3c9] => r3c9<>4