The New Sudoku Players' Forum

[jiesushang]

Hey，guys。As the picture shows，I design a question。All of the interrelated cells are colored。Now，please find all candidates which can be deleted。

[yzfwsf]

This post for jiesushang
This post is for my friend jiesushang posted, because he is a newly registered user, posting needs to be reviewed, and now the forum seems to have no one to review or review is very untimely.

Code: Select all

,---------------------------------,---------------------------------,---------------------------------,
| 12456789#  123456789  123456789 | 123456789  123456789  789#      | 689#       123456789  12456789# |
| 12456789#  123456789  123456789 | 123456789  123456789  789#      | 89#        123456789  12456789# |
| 123456789  35#        123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 12456789#  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  12456789# |
| 12456789#  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  12456789# |
| 123456789  45#        123456789 | 123456789  34#        123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123#      | 123#       123456789  123456789 | 1236#      123456789  123456789 |
| 123456789  123456789  123#      | 123#       123456789  1237#     | 123456789  123456789  123456789 |
| 12456789#  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  12456789# |
'---------------------------------'---------------------------------'---------------------------------'

Assuming that the puzzle has a unique solution, you can use the UR technique to find all the eliminations under the current PM.

[jiesushang]

Hey，guys，I am the questioner of this training。
The picture links here --> https://ibb.co/WB8xddq

[m_b_metcalf]

My program finds multiple solutions. Here is one of them:

Code: Select all

  7  8  1  4  2  5  6  3  9
  2  4  6  1  3  9  7  5  8
  3  5  9  7  6  8  4  1  2
  1  2  3  8  4  6  5  9  7
  9  7  5  2  1  3  8  4  6
  4  6  8  5  9  7  3  2  1
  8  9  2  6  5  4  1  7  3
  6  1  4  3  7  2  9  8  5
  5  3  7  9  8  1  2  6  4

It would help if you could post sukakus also in 729-string format.

Thanks,

Mike

[yzfwsf]

This puzzle is not standard sukaku, it is just assumed to be the unique solution (actually multiple solutions, the assumption of the unique solution is just to use UR techniques) and then discusses the eliminations of the current structure.

Code: Select all

123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789

[Leren]

Here is my first attempt at a solution to your puzzle as I understand it.

Code: Select all

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

I only used a few basics, lots of Uniqueness moves and a few manual placements to avoid UR threats or complete a UR solution. The solution is not unique in that 8 and 9 can be interchanged.

Leren

[m_b_metcalf]

The solution is not unique in that 8 and 9 can be interchanged.

This sukaku has at least 1,318,841 solutions (that's where I stopped counting).

Mike

[marek stefanik]

Hi jiesushang,
Welcome to the forum.

We can make some quick progress using the URs 12r78c34 and 89r12c67 (provided all candidates of the URs would be present in a state with a unique solution).
My first few steps are available at the beginning, with all of their eliminations mentioned (which leads to a big overlap).

9 truths: 3c19 + r3c2, r6c25, r7c34, r8c34 (lime and blue)
9 links: [3](UR 12r78c34), 3r3678, 4r6, 5c2

eliminations: Show

–3r3c345678, –3r6c34678, –3r7c25678, –3r8c25678,
–4r6c1346789,
–5r1245789c2

15 truths: 3c19 + r1c67, r2c67, r3c2, r6c25, r7c347, r8c346 (all marked truths)
15 links: 1r78, 2r78, 3r3678, 4r6, 5c2, 6c7, 7c6, [3](UR 89r12c67)

eliminations: Show

–1r7c125689, –1r8c125789,
–2r7c125689, –2r8c125789,
–3r3c345678, –3r6c34678, –3r7c2568, –3r8c2578,
–4r6c1346789,
–5r1245789c2,
–6r345689c7,
–7r345679c6

We can eliminate some extra 3s, I tried to avoid repeating truths and links, but it doesn't look very pretty:
6L A = ([3](UR 12r78c34), 3r6, 3c16, 3b578 + r7c34, r8c34) / 2

Diagram and short explanation: Show

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . 3 | . . . |
| . . . | . . 3 | . . . |
| 3 . . | 3 3 3 | . . . |
+-------+-------+-------+
| 3 .123|123. 3 | . . . |
| 3 .123|123. 3 | . . . |
| 3 . . | . . 3 | . . . |
+-------+-------+-------+

Each marked candidate is part of at least two of the sublinks:
[3](UR 12r78c34), 3r6, 3c16, 3b578 + r7c34, r8c34
Therefore if 7 of them were true, you would in some sense place 14 true candidates into what amounts to 13 links.

9 truths: 3c16 + r3c2, r6c25, r7c34, r8c34
9 links: [6]A, 3r3, 4c6, 5c2

eliminations: Show

–3r3c345789,
–4r6c1346789,
–5r1245789c2

The only "new" elimination is -3r3c9 (allowing pointing candidates 3b3\c8).

After steps 1 and 3 (i.e. not using the 89 UR), we arrive here:

Code: Select all

,--------------------------------,---------------------------------,---------------------------------,
| 12456789   12346789  123456789 | 123456789  123456789  789       | 689        123456789  12456789  |
| 12456789   12346789  123456789 | 123456789  123456789  789       | 89         123456789  12456789  |
| 123456789 a35        12456789  | 12456789   12456789   12456789  | 12456789   12456789   12456789  |
:--------------------------------+---------------------------------+---------------------------------:
| 12456789   12346789  123456789 | 123456789 d123456789  123456789 | 123456789  123456789  12456789  |
| 12456789   12346789  123456789 | 123456789 d123456789  123456789 | 123456789  123456789  12456789  |
| 12356789  b45        1256789   | 1256789   c34         1256789   | 1256789    1256789    12356789  |
:--------------------------------+---------------------------------+---------------------------------:
| 123456789  1246789   123       | 123        12456789   12456789  | 126        12456789   123456789 |
| 123456789  1246789   123       | 123        12456789   127       | 12456789   12456789   123456789 |
| 12456789   1246789–3 123456789 | 123456789 e123456789  123456789 | 123456789  123456789  12456789  |
'--------------------------------'---------------------------------'---------------------------------'

3b3\c8 => –3r459c8
3r3\b1 => –3b1p2356
(3=5)r3c2 – (5=4)r6c2 – (4=3)r6c5 – 3r45c6 = 3r9c6 => –3r9c2

Adding the eliminations from the 89 UR (step 2), we end up here:

Code: Select all

,--------------------------------,--------------------------------,-------------------------------,
| 12456789   1246789   12456789  | 123456789  123456789  789      | 689       123456789  12456789 |
| 12456789   1246789   12456789  | 123456789  123456789  789      | 89        123456789  12456789 |
| 123456789  35        12456789  | 12456789   12456789   1245689  | 1245789   12456789   12456789 |
:--------------------------------+--------------------------------+-------------------------------:
| 12456789   12346789  123456789 | 123456789  123456789  12345689 | 12345789  12456789   12456789 |
| 12456789   12346789  123456789 | 123456789  123456789  12345689 | 12345789  12456789   12456789 |
| 12356789   45        1256789   | 1256789    34         125689   | 125789    1256789    12356789 |
:--------------------------------+--------------------------------+-------------------------------:
| 3456789    46789     123       | 123        456789     45689    | 126       456789     3456789  |
| 3456789    46789     123       | 123        456789     127      | 45789     456789     3456789  |
| 12456789   1246789   123456789 | 123456789  123456789  12345689 | 12345789  12456789   12456789 |
'--------------------------------'--------------------------------'-------------------------------'

I didn't find any way to get more eliminations (or get other eliminations using only the 89 UR).

Marek

[yzfwsf]

Hi Mike:
His original intention is that there is a large Dynamic Nice Loop (containing UR nodes and fish nodes) with many eliminations under the current PM, find these eliminations.Or there is a Rank 0 structure.

YZF

[jiesushang]

Hi，Marek,thanks for your answer.
Actually，if we take the Rank as the angle of view，there are no more eliminations.
However，let's think over the 89UR carefully.From the Rank=0，we should fill in three 89s in R12C67.Then，taking the notice of R2C7=89，we can eliminate extra 89s.
Extra eliminations：-89 R2C89

Then，there's an elimination that I'm not able to find by myself.Actually，we can eliminate 3R8C3.But，I can't use Rank theory to explain it.If you want to know the reason，I suggest you finding the contradiction by substitution.

The standard answer links here --> https://ibb.co/5j5vXCr

Welcome to discuss with me.

jiesushang

[marek stefanik]

Ah, those are nice. The 89 restricts 12r8 to r8c346. Then you can get -3r8c3 like this:

8 truths: 1r8, 2r8, 3c19 + r3c2, r6c25, r7c4
9 links: 1b8, 2b8, 3r3678, 4r6, 5c2 + r8c3
=> –3r8c3

Marek

[jiesushang]

You are right.I didn't think more deeply.Thanks for opening a new perspective about Rank.

jiesushang

[denis_berthier]

This puzzle is not standard sukaku, it is just assumed to be the unique solution (actually multiple solutions, the assumption of the unique solution is just to use UR techniques) and then discusses the eliminations of the current structure.

Given a sukaku known as having multiple solutions, you want to use the assumption of uniqueness? What's the purpose of this nonsense?
.