The New Sudoku Players' Forum

[rjamil]

Hi experts,

I am currently analyzing Almost Locked Candidates move patterns as follows:

Code: Select all

Almost Locked Candidates: (4 exemplars, multiple exclusions)
Almost Locked Pair
  ---------------+---------------+---------------  ---------------+---------------+---------------
01) .    .    .  | XY-*  /    /  |  /    /    /  02) .    .    .  | XY   -XY  -XY | -XY  -XY  -XY
   XY   -XY  -XY |  .    .    .  |  .    .    .     XY-*  /    /  |  .    .    .  |  .    .    .
   -XY  -XY  -XY |  .    .    .  |  .    .    .      /    /    /  |  .    .    .  |  .    .    .
  ---------------+---------------+---------------  ---------------+---------------+---------------
Almost Locked Triple
  ---------------+---------------+---------------  ---------------+---------------+---------------
03) .    .    .  |XYZ-* XYZ-* /  |  /    /    /  04) .    .    .  | XYZ  XYZ -XYZ |-XYZ -XYZ -XYZ
   XYZ -XYZ -XYZ |  .    .    .  |  .    .    .    XYZ-*  /    /  |  .    .    .  |  .    .    .
   XYZ -XYZ -XYZ |  .    .    .  |  .    .    .    XYZ-*  /    /  |  .    .    .  |  .    .    .
  ---------------+---------------+---------------  ---------------+---------------+---------------

Hope that the above mentioned exemplars/patterns are correct and complete for Almost Locked Candidates move.

While checking the January 26, 2020 puzzle, after basic moves, found two Almost Locked Candidates scenario, but both producing same exclusions:

Code: Select all

 +----------------+---------------+---------------+
 | 169   15    3  | 24   45   8   | 7    26   269 |
 | 69    4     67 | 23   37   1   | 5    8    269 |
 | 2     8     57 | 6    57   9   | 1    4    3   |
 +----------------+---------------+---------------+
 | 34    7     1  | 9    8    5   | 6    23   24  |
 | 8     23    9  | 7    6    24  | 34   5    1   |
 | 5     6     24 | 134  134  234 | 8    9    7   |
 +----------------+---------------+---------------+
 | 7     9     24 | 5    134  6   | 234  13   8   |
 | 1346  1235  8  | 134  9    34  | 234  7   a456 |
 | 134-6 13-5 b56 | 8    2    7   | 9    136  456 |
 +----------------+---------------+---------------+

Almost Locked Candidates: Row 8 wise 56 @ r8c9 r9c3 => -6 @ r9c1 -5 @ r9c2
Almost Locked Candidates: Box 9 wise 56 @ r8c9 r9c3 => -6 @ r9c1 -5 @ r9c2

In January 13, 2020 puzzle:

Code: Select all

 +------------------+-----------------+-----------+
 | 19   67     17   | 2    5     3    | 4  8   69 |
 | 249  2468   248  | 189  1468  1468 | 7  5   3  |
 | 5    468    3    | 789  468   4678 | 2  1   69 |
 +------------------+-----------------+-----------+
 | 6    24789  2478 |b78   3     2-78 | 5  49  1  |
 | 3    29     12   | 4    126   5    | 8  69  7  |
 | 14  a478    5    | 178  9     1678 | 3  46  2  |
 +------------------+-----------------+-----------+
 | 7    1      9    | 3    48    48   | 6  2   5  |
 | 8    3      6    | 5    12    12   | 9  7   4  |
 | 24   5      24   | 6    7     9    | 1  3   8  |
 +------------------+-----------------+-----------+

Almost Locked Candidates: Row 6 wise 78 @ r6c2 r4c4 => -78 @ r4c6
Almost Locked Candidates: Box 4 wise 78 @ r6c2 r4c4 => -78 @ r4c6

My question is that, is there any Dual ALC move exists?

In Mystery Puzzle No 1:

Code: Select all

 +-----------------+---------------------+--------------------+
 | 6   a247   1247 | 1579    1579   8    | 2579   1279   3    |
 | 138  9     1278 | 4       1567   357  | 2567   12678  1256 |
 | 138  37    5    | 13679   2      379  | 4      16789  169  |
 +-----------------+---------------------+--------------------+
 | 7    2345 b24   | 569     569    1    | 8      34     26   |
 | 13-4 2346  16-24| 78      78     24   | 39     5      19   |
 | 15-4 8     9    | 56      3      24   | 26     14     7    |
 +-----------------+---------------------+--------------------+
 | 589  567   3    | 5789    4      579  | 1      2679   2569 |
 | 2    57    78   | 135789  15789  6    | 3579   379    4    |
 | 459  1     67-4 | 2       579    3579 | 35679  3679   8    |
 +-----------------+---------------------+--------------------+

Almost Locked Candidates: Column 2 wise 24 @ r1c2 r4c3 => -24 @ r5c3 -4 @ r56c1
Almost Locked Candidates: Box 1 wise 24 @ r1c2 r4c3 => -24 @ r5c3 -4 @ r9c3

Added as on 20200208 (GMT+05:00):
Coded 1st and 2nd exemplars, i.e., Almost Locked Pair. Found very effective in the first place. Solved 11604 (additional 287) out of Ruud 50k specialty puzzles without guess. Also, solved 10904 (additional 239) out of Games Sample PG 26855 puzzles without guess.

Now thinking about 3rd and 4th exemplars, i.e., Almost Locked Triple.

Once got confirmation about dual ability from experts, will start thinking/analyzing about Dual Almost Locked Pair and Dual Almost Locked Triple scenarios.

Further added:
Surprisingly to note that Hodoku and SukakuExplainer v1.15.10 did not programmed for either Almost Locked Candidates move or Almost Locked Pair and Triple moves.
Checked with YZF_Sudoku v607 and found further exclusions from almost locked pair/triple cell, i.e., exclude other values from almost locked pair/triple cell(s). Updated exemplars accordingly.

Coded additional exclusions in to Almost Locked Pair move and added Almost Locked Triple move. Now RJSolBit program solved puzzles without guess as follows:

Code: Select all

Puzzles      Previous  - Addl excl - Add ALT
Ruud's 50K : 11604 287 - 11871 267 - 11970  99
Tarek 6000 : 0         - 0         - 0
PG   26855 : 10904 239 - 10977  73 - 11006 102
17   49158 : 48121  10 - 48140  19 - 48146   6
PG    4279 : 1253   30 - 1261    8 - 1266    5

Please note that, in Advanced solving techniques topic - Collection of solving techniques pinned post of this forum, did not include any reference material for Almost Locked Candidates, Almost Locked Pair and Almost Locked Triple moves.

R. Jamil

[rjamil]

Hi experts again,

Wish to confirm that, I have searched Almost Locked Quad move. Found nothing in this forum but coded successfully with speed compromised. Please note that, by added ALP move, gives additional 287 Ruud 50k specialty puzzles solved without guess. Also, by added ALT move, gives additional 99, and after added ALQ move, only 5 additional puzzles solved without guess.

Code: Select all

Almost Locked Quad
  ---------------+---------------+---------------  ---------------+---------------+---------------
05) .    .    .  |WXYZ-* / WXYZ-*|  / WXYZ-*  /  06) .    .    .  |WXYZ -WXYZ WXYZ|-WXYZ WXYZ -WXYZ
  WXYZ WXYZ -WXYZ|  .    .    .  |  .    .    .      /    / WXYZ-*|  .    .    .  |  .    .    .
 -WXYZ WXYZ -WXYZ|  .    .    .  |  .    .    .    WXYZ-* / WXYZ-*|  .    .    .  |  .    .    .
  ---------------+---------------+---------------  ---------------+---------------+---------------

R. Jamil

[Leren]

For the Jan 13 2020 puzzle I find the following dual pincer ALS moves.

Code: Select all

*-----------------------------------------------*
| 19  67    17   | 2   5     3    | 4     8  69 |
| 249 2468  248  | 189 1468  1468 | 7     5  3  |
| 5   468   3    | 789 468   4678 | 2     1  69 |
|----------------+----------------+-------------|
| 6   24789 2478 |a78  3     2-78 | 5     49 1  |
| 3   29    12   | 4   126   5    | 8     69 7  |
|a14  78-4  5    |b178 9    c1678 | 3    d46 2  |
|----------------+----------------+-------------|
| 7   1     9    | 3   48    48   | 6     2  5  |
| 8   3     6    | 5   12    12   | 9     7  4  |
| 24  5     24   | 6   7     9    | 1     3  8  |
*-----------------------------------------------*

ALS XZ Rule (Loop 1) : ALS 1 r4c4; ALS 2 r6c1468; Z = 7 & 8 => - 78r4c6, - 4 r6c2, and also

Code: Select all

*----------------------------------------------*
| 19  67    17   | 2     5     3     | 4 8  69 |
|b249 2468  248  |c189  c1468 c1468  | 7 5  3  |
| 5   468   3    | 9-78 c468  c4678  | 2 1  69 |
|----------------+-------------------+---------|
| 6   24789 2478 |a78    3     28-7  | 5 49 1  |
| 3   29    12   | 4     126   5     | 8 69 7  |
|b14  478   5    |a178   9     168-7 | 3 46 2  |
|----------------+-------------------+---------|
| 7   1     9    | 3     48    48    | 6 2  5  |
| 8   3     6    | 5     12    12    | 9 7  4  |
|b24  5     24   | 6     7     9     | 1 3  8  |
*----------------------------------------------*

2 Pincer ALS XY Wing: (78=1) r46c4 - (1=9) r269c1 - (9=78) r2c456, r3c56 => - 78 r4c4, - 7 r46c6; stte

For the Jan 26 2020 Puzzle

Code: Select all

*-----------------------------------------------*
| 169    15    3  | 24  45   8   | 7   26  269  |
| 69     4     67 | 23  37   1   | 5   8   269  |
| 2      8     57 | 6   57   9   | 1   4   3    |
|-----------------+--------------+--------------|
| 34     7     1  | 9   8    5   | 6   23  24   |
| 8      23    9  | 7   6    24  | 34  5   1    |
| 5      6     24 | 134 134  234 | 8   9   7    |
|-----------------+--------------+--------------|
| 7      9     24 | 5   134  6   | 234 13  8    |
|b1346  b1235  8  |b134 9   b34  |b234 7   56-4 |
| 134-5  13-6 a56 | 8   2    7   | 9   136 456  |
*-----------------------------------------------*

ALS XZ Rule (Loop 1) : ALS 1 r9c3; ALS 2 r8c12467; Z = 5 & 6 => - 4, r8c9, - 5 r9c1, - 6 r9c2

and for the Mystery Puzzle No 1

Code: Select all

*-----------------------------------------------------------*
| 6     247    1247 | 1579   1579  8    | 2579  1279   3    |
| 138   9      1278 | 4      1567  357  | 2567  12678  1256 |
| 138   37     5    | 13679  2     379  | 4     16789  169  |
|-------------------+-------------------+-------------------|
| 7     35-24 a24   | 569    569   1    | 8     34     26   |
|b134  b2346  b1246 | 78     78    24   |b39    5     b19   |
| 15-4  8      9    | 56     3     24   | 26    14     7    |
|-------------------+-------------------+-------------------|
| 589   567    3    | 5789   4     579  | 1     2679   2569 |
| 2     57     78   | 135789 15789 6    | 3579  379    4    |
| 459   1      467  | 2      579   3579 | 35679 3679   8    |
*-----------------------------------------------------------*

ALS XZ Rule (Loop 1) : ALS 1 r4c3; ALS 2 r5c12379; Z = 2 & 4 => - 24 r4c2, - 4 r6c1

Leren

[rjamil]

Hi Leren,

Many thanks for providing your feedback. Let me compare your ALS moves with mine ALC moves as follows:

For the Jan 13 2020 puzzle I find the following dual pincer ALS moves.
…
ALS XZ Rule (Loop 1) : ALS 1 r4c4; ALS 2 r6c1468; Z = 7 & 8 => - 78r4c6, - 4 r6c2

Almost Locked Candidates: Row 6 wise 78 @ r6c2 r4c4 => -78 @ r4c6
Almost Locked Candidates: Box 4 wise 78 @ r6c2 r4c4 => -78 @ r4c6
Upgraded to:
Almost Locked Pair: Box 4 Row 4 wise 78 @ r4c123 b4r6c2 r4c4 => -78 @ r4c6 => -4 @ r6c2

For the Jan 26 2020 Puzzle
...
ALS XZ Rule (Loop 1) : ALS 1 r9c3; ALS 2 r8c12467; Z = 5 & 6 => - 4, r8c9, - 5 r9c1, - 6 r9c2

Almost Locked Candidates: Row 8 wise 56 @ r8c9 r9c3 => -6 @ r9c1 -5 @ r9c2
Almost Locked Candidates: Box 9 wise 56 @ r8c9 r9c3 => -6 @ r9c1 -5 @ r9c2
Upgraded to:
Almost Locked Pair: Row 8 Box 7 wise 56 @ r8c123 r8c9 b7r9c3 => => -5 @ r9c1 => -6 @ r9c2 => -4 @ r8c9

and for the Mystery Puzzle No 1
...
ALS XZ Rule (Loop 1) : ALS 1 r4c3; ALS 2 r5c12379; Z = 2 & 4 => - 24 r4c2, - 4 r6c1

Almost Locked Candidates: Column 2 wise 24 @ r1c2 r4c3 => -24 @ r5c3 -4 @ r56c1
Almost Locked Candidates: Box 1 wise 24 @ r1c2 r4c3 => -24 @ r5c3 -4 @ r9c3
Upgraded to:
Almost Locked Pair: Row 5 Box 4 wise 24 @ r5c123 r5c6 b4r4c3 => => -24 @ r4c2 => -4 @ r6c1

Maybe searching Almost Locked Pair/Triple/Quad moves are easier than ALS-XZ/XY moves (in terms of both, manual and programming wise), as it simply check less cells (i.e., to check mini-Line cells for the presence of unsolved cell only once).

I have tweaked my Almost Locked Pair/Triple/Quad move search routine, without loosing single instance of detection with added some speed performance increment achieved as follows:
1) For each mini-Line in 27 mini-Rows and 27 mini-Columns;
2) If no unsolved Cell found in mini-Line then go to step 1;

3) For each hp in 6 away Line cells;
4) If no hidden pair found in hp then go to step 3;
5) For each np in 6 away Box cells;
6) If no naked pair found in np then go to step 5;
7) Check if any elimination found in either hp or away Box cells then perform Almost Locked Pair move.

Repeat above step 3 to 7 with away Line cells and away Box cells interchanged.
Similarly, check Almost Locked Triple and Almost Locked Quad after Almost Locked Pair steps for the same mini-Line, then go to step 1.

(Latest, pre-released and stable beta source code of my RJSolBit.c program can be obtained from my GitHub backup site, with only bugs in reporting steps/debugging [#define RJ 3] option.)

R. Jamil

[yzfwsf]

Hi Jamil

2) If no unsolved Cell found in mini-Line then go to step 1;

I think should be "If no two or three unsolved Cells found in mini-Line then go to step 1"

[StrmCkr]

Almost locked Candidate is the weak set version of an already known move type

size 1 -8 -> size 8 -1
als-xz -> AHS xz { aka ALC}

one uses Pencil marks the other use hidden set.

which is why there really isn't much discussed about them.

[rjamil]

Hi yzfwsf and StrmCkr,

Hi Jamil

2) If no unsolved Cell found in mini-Line then go to step 1;

I think should be "If no two or three unsolved Cells found in mini-Line then go to step 1"

Thanks for the tip. I think, you mean that, for ALP, ALT and ALQ, if no one, two or three unsolved Cell(s) found in mini-Line, respectively, then go to step 1?!?!

Almost locked Candidate is the weak set version of an already known move type

size 1 -8 -> size 8 -1
als-xz -> AHS xz { aka ALC}

one uses Pencil marks the other use hidden set.

which is why there really isn't much discussed about them.

You mean that ALC (pair, triple and quad) move is subset of AHS move?

If yes, then:
1) all possible patterns of XY-, XYZ- & WXYZ-Wing moves; and
2) only 4 cells ALS move, not covered in WXYZ-Wing move; and
3) Almost Locked Candidates (pair, triple and quad) move; and
4) only 4 cells AHS move, not covered Almost Locked Quad move,
are sufficient to search for all ALS and AHS moves?

(Just like, searching Naked tuple (pair, triple and quad) and Hidden tuple (pair, triple and quad) are sufficient.)

R. Jamil

[yzfwsf]

Thanks for the tip. I think, you mean that, for ALP, ALT and ALQ, if no one, two or three unsolved Cell(s) found in mini-Line, respectively, then go to step 1?!?!

I mean, the number of empty cells in ERI area must be greater than one.
ALP,ALT,ALQ are virtual naked subset + hidden subset,ERI as a virtual cell. If ERI has only one empty cell ,the virtual hidden subset will turn to locked hidden subset, and the virtual naked subset will turn to locked naked subset in turn.
Actually the virtual hidden subset maybe turn to hidden single.

[StrmCkr]

Size 4 als has a equivalent size 5 ahs
Size 4 ahs has a equivalent size 5 als

So yes in theory a size 4 of each covers all
For xz rule.

Specifically:
Size als = (size - 9) ahs

[rjamil]

Hi,

I mean, the number of empty cells in ERI area must be greater than one.

Well, I have tweaked the same way, i.e., for ALP, ALT and ALQ, empty cells in mini-Line must be greater than one. However, for ALT and ALQ, added check for empty cells in mini-Line must be greater than two; and, for ALQ, added check for empty cells in away-Line and away-Box must be greater than three each.

Size 4 als has a equivalent size 5 ahs
Size 4 ahs has a equivalent size 5 als

So yes in theory a size 4 of each covers all
For xz rule.

Specifically:
Size als = (9 - size) ahs

Thanks for the confirmation. I am doing in right direction.

R. Jamil