The New Sudoku Players' Forum

[kurbads]

A 1 in yellow 17 makes the green 18>8, 128>2 and 129>9 leaving the yellow 19 no numbers left to put making 17>7.

What is the rule behind it? Chain or wing or fish?

[P.O.]

the logic can be written as a contradiction chain, in the notation i use:

Code: Select all

1r5c9 => r5c3 <> 1,9
 r5c9=1 - r4c7{n1 n8} - r5c7{n18 n2} - r5c5{n12 n9} => r5c9 <> 1


some call this technique nishio:
https://www.sudoku9x9.com/nishio.php

[Hajime]

In SiSeSuSo I implemented this as a forcing net
1 Pick an unsolved cell C
2 Pick a candidate k as a solve of this cell C
3 Solve as much of the puzzle
4 if this leads to
4a a unsolved cell with no candidates or
4b a region where some candidate p is not a solution or not further present in that region
Then C cannot be k.

Cell C needs not to be bivalue as the link states.
It is very near guessing.

[P.O.]

in the link provided although the illustration of the technique uses a bivalue cell, the definition of the technique doesn't assume that only bivalue cells can be used: ’Suppose an undetermined cell is digit "k" say. If this assumption leads to a contradiction, then we can confirm that this assumption is incorrect’.
there is no guessing at all, the candidate is known to be contradictory before it is eliminated, the chain proves it.

[Leren]

Code: Select all

*-----------*
|145|972|368|
|236|481|759|
|978|3..|412|
|---+---+---|
|.52|...|...|
|.6.|5.4|.3.|
|..3|...|5..|
|---+---+---|
|684|...|..5|
|327|6..|9..|
|5..|24.|6.3|
*-----------*

1459723682364817599783..412.52.......6.5.4.3...3...5..684.....53276..9..5..24.6.3

It's a WXYZ Wing, which is described here, or more generally, an ALS-XZ Rule, which is described here.

Code: Select all

*--------------------------------------------*
| 1   4   5  | 9    7    2    | 3   6   8    |
| 2   3   6  | 4    8    1    | 7   5   9    |
| 9   7   8  | 3    56   56   | 4   1   2    |
|------------+----------------+--------------|
| 478 5   2  | 178  1369 3679 |a18  49  1467 |
| 78  6  b19 | 5   b129  4    |b128 3   7-1  |
| 478 19  3  | 178  1269 679  | 5   249 1467 |
|------------+----------------+--------------|
| 6   8   4  | 17   39   39   | 12  27  5    |
| 3   2   7  | 6    15   58   | 9   48  14   |
| 5   19  19 | 2    4    78   | 6   78  3    |
*--------------------------------------------*

To explain it as an ALS-XZ in words, you have two sets : a; a single cell containing 1 & 8 and b; 3 cells containing 128&9. Both sets contain 1 more candidate value than the number of cells, and there is one candidate value, 8, that is common to both sets, and all the 8's in both sets can see each other.

So, if r4c7 is not 1, it must be 8. That removes the 8 from set b, which would then be a locked set 189. So either r4c7 is 1 or r5c357 contains 1. Since r5c9 can see all those 1's it can't be 1.

Leren

[denis_berthier]

A 1 in yellow 17 makes the green 18>8, 128>2 and 129>9 leaving the yellow 19 no numbers left to put making 17>7.

What is the rule behind it? Chain or wing or fish?

Following the same order of cells as you, you have a whip[4]: r4c7{n1 n8} - r5c7{n8 n2} - r5c5{n2 n9} - r5c3{n9 .} => r5c9 ≠ 1
Contrary to other chains or nets, this is a continuous chain: each candidate is linked to the previous one.
It is a special case of a whip[4], in rc-space, i.e. a whip-rc[4].
As usual in my notation, z- and t- candidates are not written (they don't belong to the chain).

Same elimination by another whip[4]:
r5c3{n1 n9} - r5c5{n9 n2} - r5c7{n2 n8} - r4c7{n8 .} => r5c9 ≠ 1

BTW, the "General" section is not the place to post such questions. It should be in the "Help" section.

[StrmCkr]

Code: Select all

*--------------------------------------------*
| 1   4   5  | 9    7    2    | 3   6   8    |
| 2   3   6  | 4    8    1    | 7   5   9    |
| 9   7   8  | 3    56   56   | 4   1   2    |
|------------+----------------+--------------|
| 478 5   2  | 178  1369 3679 |a18  49  1467 |
| 78  6  b19 | 5   b129  4    |b128 3   7-1  |
| 478 19  3  | 178  1269 679  | 5   249 1467 |
|------------+----------------+--------------|
| 6   8   4  | 17   39   39   | 12  27  5    |
| 3   2   7  | 6    15   58   | 9   48  14   |
| 5   19  19 | 2    4    78   | 6   78  3    |
*--------------------------------------------*

ALS a) r4c7 (18)
ALS b) r5c357 (1289)
RCC x: 8
non RCC Z: 1
=> r5c9 <> 1

how it works is that 8 is in either set or in none: called the Restricted common candidate
which makes both sets potential locked set
the non Restricted common candidate{s} of both sets are locked regardless of the 8's position or lack of one.
then any cell that can see these candidates may be excluded in this case r5c9 <> 1

with the cell count and digit count being the same these end up classed under barns as size 4: which is a wxyz - wing

another example of the rule for als-xz : is the xy- wing {size 3 barn}
als a)r5c19 (178)
als b)r4c7 (18)
RCC x: 1
nRCC z: 8
=> r5c7,r4c1 <> 8

Code: Select all

+--------------+-----------------+-----------------+
| 1     4   5  | 9    7     2    | 3     6    8    |
| 2     3   6  | 4    8     1    | 7     5    9    |
| 9     7   8  | 3    56    56   | 4     1    2    |
+--------------+-----------------+-----------------+
| 47-8  5   2  | 178  1369  3679 | (18)  49   1467 |
| (78)  6   19 | 5    129   4    | 12-8  3    (17) |
| 478   19  3  | 178  1269  679  | 5     249  1467 |
+--------------+-----------------+-----------------+
| 6     8   4  | 17   39    39   | 12    27   5    |
| 3     2   7  | 6    15    58   | 9     48   14   |
| 5     19  19 | 2    4     78   | 6     78   3    |
+--------------+-----------------+-----------------+