The New Sudoku Players' Forum

[richardberg.rb]

Hi, I am fairly new to Sudoku and stuck on this puzzle. Any hint would be very much appreciated. Thanks, Richard

Code: Select all

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

Starting grid:

Code: Select all

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

[tarek]

Hi Richard and welcome to the forum ...

This puzzle has some techniques that solves it which could be at your level but could be considered advanced for somebody new to sudoku ...

Could you give us an idea of your solving techniques arsenal that you currently use and if you solve using pencilmarks?

Tarek

[Cenoman]

Hi Richard,
It seems that you have run correctly all basic techniques. Hopefully you have seen the NT (Naked Triple) (356)r459c2 and you get also the following PM (Pencil Marks):

Code: Select all

 +-------------------+----------------------+--------------------+
 |  24    1     3    |  5     47      8     |  27   6     9      |
 |  8     79    59   |  167   167     2     |  4    15    3      |
 |  245   47    6    |  9     147     3     |  27   8     15     |
 +-------------------+----------------------+--------------------+
 |  7     56    2    |  4     156     15    |  9    3     8      |
 |  35    356   4    |  68    5689    59    |  1    27    27     |
 |  9     8     1    |  3     2       7     |  5    4     6      |
 +-------------------+----------------------+--------------------+
 |  345   2     59   |  17    13579   6     |  8    157   1457   |
 |  6     49    7    |  18    1589    159   |  3    125   1245   |
 |  1     35    8    |  2     357     4     |  6    9     57     |
 +-------------------+----------------------+--------------------+

At that stage, you need an advanced technique that is called AIC (Alternate Inference Chain)
Alternate because it is a sequence of alternating strong links and weak links.
A Strong Link exists between candidates that can't all be False (at least one is true). Symbol '='
A Weak Link exists that can't simultneously be True (at most one is True). Symbol '-'

Here is an AIC that solve your puzzle: (3)r7c5 = (3-4)r7c1 = (4-9)r8c2 = (9)r7c3 => r7c5<>9; singles to the end.
Strong links: between the 3s at row 7, between the 4s at box 7, between the 9s at box 7.
Weak links: between 3,4 at cell r7c1, between 4,9 at cell r8c2, between the 9s at row 7 and between 3,9 at cell r7c5
(these last two WLs for justification of the inference r7c5<>9)
This chain is called a Wing because it has three strong links, and more precisely an S-wing, but don't worry with such details for the moment.

Another AIC with same result: (3)r7c5 = r7c1 - (3=5)r9c2 - (5=9)r7c3 => r7c5<>9; singles to the end.

Here are some links for you to learn more about AIC's.
Sudopedia
Myth Jellies' historical post Notice the date, 2006 !
David P. Bird teaching document 2017

[Leren]

Code: Select all

*----------------------------------------------*
| 24   1    3  | 5    47     8   | 27 6   9    |
| 8    79   59 | 167  167    2   | 4  15  3    |
| 245  47   6  | 9    147    3   | 27 8   15   |
|--------------+-----------------+-------------|
| 7    56   2  | 4    156    15  | 9  3   8    |
| 35   356  4  | 68   5689   59  | 1  27  27   |
| 9    8    1  | 3    2      7   | 5  4   6    |
|--------------+-----------------+-------------|
|c345  2   a59 | 17  d1357-9 6   | 8  157 1457 |
| 6   b49   7  | 18   1589   159 | 3  125 1245 |
| 1    35   8  | 2    357    4   | 6  9   57   |
*----------------------------------------------*

(9) r7c3 = (9-4) r8c2 = (4-3) r7c1 = (3) r7c5 => - 9 r7c5; stte

From your solved cell position you can easily get to the above PM.

If you follow the short chain I've written out through cells a-b-c-d it shows that if r7c3 is not 9 r7c5 is 3 (and not 9 in particular). It's also obvious that if r7c3 is 9 then r7c5 is not 9.

So, if r7c3 is 9 or is not 9 then r7c5 is not 9. So you can eliminate 9 from r7c5. The puzzle then solves easily with singles from there (that's what the stte notation means at the end of the chain).

Sorry about the complicated looking argument, but there were too many easier moves required to solve the puzzle.

Leren

PS: I see I've parallel posted with two others. Despite the differences in our approaches there are no fundamental differences in what we are all saying.

[eleven]

No chains needed here:

Code: Select all

+----------------------+----------------------+----------------------+
|X24     1      3      | 5      47     8      |Y27     6      9      |
| 8      79     59     | 167    167    2      | 4      15     3      |
|Y245    47     6      | 9      147    3      | 2-7    8      15     |
+----------------------+----------------------+----------------------+
| 7      56     2      | 4      156    15     | 9      3      8      |
| 35     356    4      | 68     5689   59     | 1      27     27     |
| 9      8      1      | 3      2      7      | 5      4      6      |
+----------------------+----------------------+----------------------+
| 345    2      59     | 17     13579  6      | 8      157    1457   |
| 6      49     7      | 18     1589   159    | 3      125    1245   |
| 1      35     8      | 2      357    4      | 6      9      57     |
+----------------------+----------------------+----------------------+

xy-wing r1c1-r1c7-r3c2 eliminates 7r3c7

Code: Select all

+----------------------+----------------------+----------------------+
| 2      1      3      | 5      4      8      | 7      6      9      |
| 8      79     59     | 167    167    2      | 4      15     3      |
| 45     47     6      | 9     Y17     3      | 2      8     X15     |
+----------------------+----------------------+----------------------+
| 7      56     2      | 4      156    15     | 9      3      8      |
| 35     356    4      | 68     5689   59     | 1      27     27     |
| 9      8      1      | 3      2      7      | 5      4      6      |
+----------------------+----------------------+----------------------+
| 345    2      59     | 17     13579  6      | 8      157    1457   |
| 6      49     7      | 18     1589   159    | 3      125    1245   |
| 1      35     8      | 2      35-7   4      | 6      9     Y57     |
+----------------------+----------------------+----------------------+

xy-wing r3c9-r3c5-r9c9 eliminates 7r9c5

Code: Select all

+----------------------+----------------------+----------------------+
| 2      1      3      | 5      4      8      | 7      6      9      |
| 8      79    X59     | 167    167    2      | 4     X15     3      |
|y45     47     6      | 9      17     3      | 2      8     x15     |
+----------------------+----------------------+----------------------+
| 7      56     2      | 4      156    15     | 9      3      8      |
| 35     356    4      | 68     5689   59     | 1      7      2      |
| 9      8      1      | 3      2      7      | 5      4      6      |
+----------------------+----------------------+----------------------+
| 34-5   2     X59     | 17     1379-5 6      | 8     X15    y14-5   |
| 6      49     7      | 18     1589   159    | 3      2      145    |
| 1      35     8      | 2      35     4      | 6      9      7      |
+----------------------+----------------------+----------------------+

x-wing in 5 c38r27 eliminates three 5's in r7
Then xy-wing r3c9-r3c1-r7c9 eliminates 4r7c1, which solves the puzzle

[richardberg.rb]

Thanks a lot for the responses.