The New Sudoku Players' Forum

[Jacky]

Hi

I need help to get the next step of this puzzle.

[Leren]

Hi Jacky, the shortest solution I can find is relatively advanced given that only a handful of cells are unsolved. Anyway here goes the explanation.

Code: Select all

*-----------------------------------------------------*
| 6    4    5     | 1    8    2     | 9    3    7     |
| 2    9    3     | 6    5    7     | 8    1    4     |
| 8    1    7     | 4    9    3     | 26   5    26    |
|-----------------+-----------------+-----------------|
| 1    2    8     | 9    7    4     | 3    6    5     |
| 4    5    9     | 2    3    6     | 1    7    8     |
| 7    3    6     | 8    1    5     | 4    2    9     |
|-----------------+-----------------+-----------------|
| 39   6   a14    | 7    2    8     | 5   b49   3-1   |
| 5    8    2     | 3   d46   19    | 7   c49  e16    |
| 39   7    14    | 5    46   19    | 26   8    1236  |
*-----------------------------------------------------*

(1=4) r7c3 - r7c8 = (4-9) r8c8 = (9-1) r8c6 = (1) r8c9 => - 1 r7c9; stte

The gobbledegook below the diagram is an AIC, which is short for Alternating Inference Chain. It shows that at least one of r7c2 or r8c9 must be 1. Since r7c9 can see both of these cells it can't be 1.

The notation stte means Singles to the End, which is a Sudoku Tragic's howl of triumph (Yee Haaah or some such), because the puzzle solves completely after the solver's brilliant (according to them) move with just a cascade of singles.

Anyway I'll explain the AIC in words in case you are unfamiliar with the AIC notation.

Follow the cells in the diagram in the sequence a-b-c-d-e.

Suppose r7c3 was not 1. Then it must be 4. So r7c8 can't be 4. Since there are only two 4's in Column 8, r8c8 must be 4 and therefore not 9. Since there are only two 9's in Row 8, r8c6 must be 9 and therefore not 1.

Finally, since there are only two 1's in Row 8 r8c9 must therefore be 1.

You can reverse the argument and start by assuming that r8c9 was not 1, and following the cells in the reverse order e-d-c-b-a you would conclude that r7c3 was 1.

What all this proves is that r7c3 and r8c9 cannot be both not 1. So you can remove 1 from r7c9 and the puzzle solves with a cascade of singles from there (Yee Haaah !).

For the benefit of others here is Jacky's puzzle status in line format : 645182937293657814817493.5.128974365459236178736815429.6.7285..5823..7...7.5...8.

Leren

[champagne]

Hi Jacky, the shortest solution I can find is relatively advanced given that only a handful of cells are unsolved. Anyway here goes the explanation.

Code: Select all

*-----------------------------------------------------*
| 6    4    5     | 1    8    2     | 9    3    7     |
| 2    9    3     | 6    5    7     | 8    1    4     |
| 8    1    7     | 4    9    3     | 26   5    26    |
|-----------------+-----------------+-----------------|
| 1    2    8     | 9    7    4     | 3    6    5     |
| 4    5    9     | 2    3    6     | 1    7    8     |
| 7    3    6     | 8    1    5     | 4    2    9     |
|-----------------+-----------------+-----------------|
| 39   6   a14    | 7    2    8     | 5   b49   3-1   |
| 5    8    2     | 3   d46   19    | 7   c49  e16    |
| 39   7    14    | 5    46   19    | 26   8    1236  |
*-----------------------------------------------------*

(1=4) r7c3 - r7c8 = (4-9) r8c8 = (9-1) r8c6 = (1) r8c9 => - 1 r7c9; stte


Leren

Hi leren,

having a look to your PM, I would use the UR r39c79 giving r9c9 13 then the naked pair 13 in r79c9 => 6r8c9 and stte

[Leren]

I see that Champagne has spotted an easier way. There is a Type 1 UR (26) in the four cells I've marked * in this diagram.

Code: Select all

*--------------------------------------------------------------*
| 6     4     5      | 1     8     2      | 9     3     7      |
| 2     9     3      | 6     5     7      | 8     1     4      |
| 8     1     7      | 4     9     3      |*26    5    *26     |
|--------------------+--------------------+--------------------|
| 1     2     8      | 9     7     4      | 3     6     5      |
| 4     5     9      | 2     3     6      | 1     7     8      |
| 7     3     6      | 8     1     5      | 4     2     9      |
|--------------------+--------------------+--------------------|
| 39    6     14     | 7     2     8      | 5     49    13     |
| 5     8     2      | 3     46    19     | 7     49    16     |
| 39    7     14     | 5     46    19     |*26    8    *13-26  |
*--------------------------------------------------------------*

You can remove 26 from r9c9, and the puzzle solves with singles as before. Champagne's suggestion of the naked pair is not actually necessary, as the simplest next move is r3c9 = 2 (only 2 in Column 9).

If you are not familiar with URs let me know and I'll explain further.

Leren

[Leren]

Hi Jacky, I've just noticed that in your puzzle status you have eliminated 1 and 6 from r9c9.

Since the solution has 1 in r9c9 you have made a mistake somewhere, but all of your solved cells can be thought of as clues to a puzzle that has a unique solution. For the record here it is :

Code: Select all

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

Leren

[Jacky]

I'm actually quite confused by all the short hand, since I'm just new to the forum entirely xD.

So I didn't understand the "gobbledegook" as you mentioned. But I could follow the "summary" and that you could solve them in "singles" easily afterward. Essentially, since these are all pairings, I could follow through "if this is 4 then this blah blah blah" and follow through to see okay that doesn't work out. That just doesn't give that professional feel D;

I do not know what "UR" is, but I used the "skyscraper" or sort method you've told me about long before and eliminated 1 from R9C9 and apparently I also eliminated 6 from R9C9... What's a Type 1 UR ?

How do I read this part : " I would use the UR r39c79 giving r9c9 13 then the naked pair 13 in r79c9 => 6r8c9 "

[Leren]

Hi Jacky,

UR's, or Unique Rectangles is a big topic. The best thing I can do at this stage is to point you to a couple of good teaching sites that discuss this topic here and here.

Also, you might be interested in reading about the so-called controversy that surrounds uniqueness moves here.

I think I answered your last question in my second post.

Leren

[Jacky]

Hi Leren,

I read the articles. It's quite interesting, it's just based on the assumption whether or not this Sudoku has a unique solution for these deadly rectangles or URs. I was just wondering why the skyscraper method proves to be invalid when removing the 1 from R9C9 or am I just not using it correctly... (I probably did the same thing removing 6)

[Leren]

Hi Jacky, there were no Skyscrapers that I could see. Perhaps if you explain what you did eliminating the 1 and 6 in r9c9 I can see where you have gone wrong.

Also you can review how Skyscrapers work here, or you can refer to an earlier discussion we had about Skyscrapers here.

Leren

[Jacky]

I could recognize skyscraper, and I could use it correctly, but I assumed and overextended it's use into an incorrect field. And I'm stuck again with a new Sudoku problem. I'll come around to uploading it...

Thanks guys!