The New Sudoku Players' Forum

[RayC333]

Seems that I need more practice! Could someone advise what solving technique I should use to crack the next step of this Sudoku puzzle. As you can see I've progressed quite far, but now hit a brick wall. I've entered my numbers into a Sudoku solver but it can't suggest a hint. I'd prefer not to resort to guessing TIA

[JasonLion]

I would use an XY-Chain next. And then I believe it is singles to the end.

[RayC333]

Thanks JasonLion, I'll persevere looking for that XY chain. I had studied the puzzle for some considerable time but didn't find it and the solver normally identifies them. So frustrating as I thought (along with your previous help) that I fully understood the technique. Clearly I need more practice in actually spotting the pattern in real examples. I will find it!

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 3     6     9      | 7     5     2      | 4     1     8      |
| 5     4     2      | 8     3     1      | 6     9     7      |
| 8     7     1      | 49    6     49     | 25    235   235    |
|--------------------+--------------------+--------------------|
| 6     15    8      | 13    2    a45     | 7     35-4  9      |
| 7     15    4      | 139   19    8      | 25    6     235    |
| 9     2     3      | 45    7     6      | 1     8     45     |
|--------------------+--------------------+--------------------|
| 4     8     7      | 6    c19   b59     | 3     25    12     |
| 1     9     5      | 2     4     3      | 8     7     6      |
| 2     3     6      |d15    8     7      | 9    e45    145    |
*--------------------------------------------------------------*

The XY chain I see is of length 5 in the cells I've marked a-b-c-d-e, which eliminates 4 from r4c8 and the puzzle solves in singles from there.

You seem to be familiar with XY chains, so I won't waste time explaining how this works.

However there is another move that only involves 4 cells.

Code: Select all

*--------------------------------------------------------------*
| 3     6     9      | 7     5     2      | 4     1     8      |
| 5     4     2      | 8     3     1      | 6     9     7      |
| 8     7     1      | 49    6     49     | 25    235   235    |
|--------------------+--------------------+--------------------|
| 6     15    8      | 13    2     45     | 7     345   9      |
| 7     15    4      | 139   19    8      | 25    6     235    |
| 9     2     3      |b45    7     6      | 1     8    a45     |
|--------------------+--------------------+--------------------|
| 4     8     7      | 6     19    59     | 3     25    12     |
| 1     9     5      | 2     4     3      | 8     7     6      |
| 2     3     6      |c15    8     7      | 9     45   d15-4   |
*--------------------------------------------------------------*

This move is called an L3 Wing but I won't bother you with the technicalities of L3 wings, I'll just explain in words how this one works.

Suppose cell a (r6c9) was not 4. Then cell b would have to be 4 (only 2 4's left in Row 6). So it is not 5, so cell c must be 5 (only 2 5's left in Column 4), so it is not 1. So cell d must be 1 (only 2 1's left in Row 9).

So, summarizing this, if cell a is not 4, cell d is 1. In particular it is not 4. But obviously if cell a is 4 then cell d is not 4.

But cell a can only be 4 or not 4, either way cell d is not 4. So you can eliminate 4 from cell d and the puzzle solves in singles from there.

You might think this is a bit obscure, but many would argue that it is a "simpler" move because it only involves three Strong links. The XY chain I saw involves 5 Strong links.

Leren

[JasonLion]

Here is the XY-Chain of length 4 I saw which eliminates 1 from R4C4:

Code: Select all

*-----------------------------------------------------------*
| 3     6     9    |  7     5     2    | 4     1     8      |
| 5     4     2    |  8     3     1    | 6     9     7      |
| 8     7     1    |  49    6     49   | 25    235   235    |
|--------------------+--------------------+-----------------|
| 6    d15    8    |  3-1   2    c45   | 7     345   9      |
| 7     15    4    |  139   19    8    | 25    6     235    |
| 9     2     3    | b45    7     6    | 1     8     45     |
|--------------------+--------------------+-----------------|
| 4     8     7    |  6     19    59   | 3     25    12     |
| 1     9     5    |  2     4     3    | 8     7     6      |
| 2     3     6    | a15    8     7    | 9     45    145    |
*-----------------------------------------------------------*

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 3     6     9      | 7     5     2      | 4     1     8      |
| 5     4     2      | 8     3     1      | 6     9     7      |
| 8     7     1      | 49    6     49     | 25    235   235    |
|--------------------+--------------------+--------------------|
| 6    d15    8      | 3-1   2    c45     | 7     345   9      |
| 7     15    4      | 139   19    8      | 25    6     235    |
| 9     2     3      |b45    7     6      | 1     8     45     |
|--------------------+--------------------+--------------------|
| 4     8     7      | 6     19    59     | 3     25    12     |
| 1     9     5      | 2     4     3      | 8     7     6      |
| 2     3     6      |a15    8     7      | 9     45    145    |
*--------------------------------------------------------------*

There was also a W Wing in Cells a-b-c-d which also eliminates the 1 in r4c4.

The W Wing also has only 3 Strong links and may be more easy to spot because of the signature two bi-value cells with the same two values.

If RayC333 would like to learn about W Wings they are described nicely here.

Leren

[RayC333]

Thanks JasonLion & Leren, I can follow the XY chain and W wing. I'll practice on more examples requiring these techniques.

[Kristoforus]

Hi
Here is many possible continuations. I show you one but profitable:) after this solving is very easy. Starting cell is C4. Here we have 2 candidates: 4 and 9. Lets see what hapen if candidate 4 is false. So if -4C4->4C6->-9C6->9G6->-5G6->5G8->-2G8->2G9->(-2E9 and -2C9)->[E9(3,5) and C9(3,5) naked par]->-5F9->4F9->-4F4 so we have contradiction if 4 is removed from C4 chain implies that must be. 4 is correct value for that cell. Bye