Almost hidden set - xz rule:

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Re: Almost hidden set - xz rule:

Postby yzfwsf » Thu Apr 09, 2020 11:50 pm

Do you implement it in your solver? I think the logic of AHS-XZ is more complex than that of ALS-XZ.


StrmCkr wrote:
Code: Select all
+-----------------+------------------+-----------------------+
| 3     158  2458 | 6     458   7    | 9       24    14      |
| 69    7    46   | 49    1     2    | 3       8     5       |
| 2589  158  2458 | 4589  3     4589 | 14(6)   2467  147     |
+-----------------+------------------+-----------------------+
| 7     6    125  | 3     245   145  | 8       9     24      |
| 258   58   9    | 4578  6     458  | 247     1     3       |
| 4     3    128  | 789   278   189  | 27      5     6       |
+-----------------+------------------+-----------------------+
| 168   9    678  | 2     478   3    | 5       467   147(8)  |
| 568   4    5678 | 1     9     58   | (26)    3     7(28)   |
| 158   2    3    | 4578  4578  6    | -4(+1)  47    9       |
+-----------------+------------------+-----------------------+

What's the trues and links? Is it as shown in the picture below?
ahs.png
ahs.png (27.85 KiB) Viewed 1465 times
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Re: Almost hidden set - xz rule:

Postby StrmCkr » Fri Apr 10, 2020 4:12 am

Code: Select all
Do you implement it in your solver? I think the logic of AHS-XZ is more complex than that of ALS-XZ.


its identical

their is two ways to approach it:
"twiddle"
the ALS size ie digits 123 swaps to digits 456789 and you have the als set that is "off"
the sector *Cells[1234] => Cells* 56789 {off}

instead of searching for "on sets" the als is now looking for "off" sets ie the counter part ahs

which used the exact same code as the als engine.

my code completely removes all solve cells in the "pm grid" so the above doesn't work for me.

the 2nd way to do it is a have 2 separate data bases
one that records all digits in each cell for a sector {standard als-xz array}

a second one
that stores the RCB positions for what is active per digit {ahs}

so yes i have ahs sets programed to a degree in my solver {my current program isn't as actuate as my previous, as Ive updating its fundamentals and speed it up 4 fold}

both codes use the same engine:
my elimination routine in my AHS- is the only thing i really had to modify as the eliminations aren't directly correlated to my eliminations storage systems i have atm.
{and this still has some bugs in it, for my rebuild upgrade code i am currently using}

xsudoku:
will cause a lot of issues when trying to discern what the real ahs-xz eliminations are as it cant identify them explicitly as it uses truth links and it tends to add in extra eliminations
when a sector is reduced to 1 cell. {when it used in the links}

AHS
A ) 16 @ R38C7
B) 128 @ R7C9,R8C79
R: R89C7
eliminations:
R9C7 <> 4,
r7C9 <> 1 {missing in my current code from glitches on dual link processing}

which leaves it as a single and from the internal limitation we get the cannibalistic extension eliminations from set A. as set b locks A

Code: Select all
+-------------------+----------------------+-----------------+
| 3       158  2458 | 6       458     7    | 9    24    14   |
| 69      7    46   | 49      1       2    | 3    8     5    |
| 2589    158  2458 | 4589    3       4589 | 146  2467  147  |
+-------------------+----------------------+-----------------+
| 7       6    125  | 3       245     145  | 8    9     24   |
| 258     58   9    | 4578    6       458  | 247  1     3    |
| 4       3    128  | 789     278     189  | 27   5     6    |
+-------------------+----------------------+-----------------+
| 168     9    678  | 2       -8(47)  3    | 5    467   1478 |
| 568     4    5678 | 1       9       58   | 26   3     278  |
| -1(58)  2    3    | (4578)  (4578)  6    | 14   47    9    |
+-------------------+----------------------+-----------------+

ahs

a) 58 @ R7C5,R9C45
b) 47 @ R9C145
R: R9C45, Z: ZR9C45
eliminations:
R9C1 <> 1,
R7C5 <> 8 {missing in my current code from glitches on dual link processing}
Some do, some teach, the rest look it up.
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Re: Almost hidden set - xz rule:

Postby rjamil » Fri Apr 10, 2020 9:39 am

Hi StrmCkr,

Haven't checked but I see two Almost Locked Pair moves in your last example in b8r9 to remove both the eliminations separately.

StrmCkr wrote:
Code: Select all
+-------------------+----------------------+-----------------+
| 3       158  2458 | 6       458     7    | 9    24    14   |
| 69      7    46   | 49      1       2    | 3    8     5    |
| 2589    158  2458 | 4589    3       4589 | 146  2467  147  |
+-------------------+----------------------+-----------------+
| 7       6    125  | 3       245     145  | 8    9     24   |
| 258     58   9    | 4578    6       458  | 247  1     3    |
| 4       3    128  | 789     278     189  | 27   5     6    |
+-------------------+----------------------+-----------------+
| 168     9    678  | 2       -8(47)  3    | 5    467   1478 |
| 568     4    5678 | 1       9       58   | 26   3     278  |
| -1(58)  2    3    | (4578)  (4578)  6    | 14   47    9    |
+-------------------+----------------------+-----------------+

Code: Select all
 +-------------------+----------------------+-----------------+
 | 3       158  2458 | 6       458     7    | 9    24    14   |
 | 69      7    46   | 49      1       2    | 3    8     5    |
 | 2589    158  2458 | 4589    3       4589 | 146  2467  147  |
 +-------------------+----------------------+-----------------+
 | 7       6    125  | 3       245     145  | 8    9     24   |
 | 258     58   9    | 4578    6       458  | 247  1     3    |
 | 4       3    128  | 789     278     189  | 27   5     6    |
 +-------------------+----------------------+-----------------+
 | 168     9    678  | 2       47-8    3    | 5    467   1478 |
 | 568     4    5678 | 1       9       (58) | 26   3     278  |
 | (58)-1  2    3    | (4578)  (4578)  6    | 14   47    9    |
 +-------------------+----------------------+-----------------+
Almost Locked Pair: Row 9 wise 58 @ b8r9c456 r9c1 b8r8c6 => -8 @ r7c5 => -1 @ r9c1
Code: Select all
 +-----------------+----------------------+-----------------+
 | 3     158  2458 | 6       458     7    | 9    24    14   |
 | 69    7    46   | 49      1       2    | 3    8     5    |
 | 2589  158  2458 | 4589    3       4589 | 146  2467  147  |
 +-----------------+----------------------+-----------------+
 | 7     6    125  | 3       245     145  | 8    9     24   |
 | 258   58   9    | 4578    6       458  | 247  1     3    |
 | 4     3    128  | 789     278     189  | 27   5     6    |
 +-----------------+----------------------+-----------------+
 | 168   9    678  | 2       (47)-8  3    | 5    467   1478 |
 | 568   4    5678 | 1       9       58   | 26   3     278  |
 | 158   2    3    | (4578)  (4578)  6    | 1-4  (47)  9    |
 +-----------------+----------------------+-----------------+
Almost Locked Pair: Row 9 wise 47 @ b8r9c456 r9c8 b8r7c5 => -4 @ r9c7 => -8 @ r7c5

R. Jamil
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Re: Almost hidden set - xz rule:

Postby StrmCkr » Fri Apr 10, 2020 7:35 pm

Almost locked Candidates are: ahs+ als: logic which is not what we are discussing
Code: Select all
+-------------------+----------------------+-----------------+
| 3       158  2458 | 6       458     7    | 9    24    14   |
| 69      7    46   | 49      1       2    | 3    8     5    |
| 2589    158  2458 | 4589    3       4589 | 146  2467  147  |
+-------------------+----------------------+-----------------+
| 7       6    125  | 3       245     145  | 8    9     24   |
| 258     58   9    | 4578    6       458  | 247  1     3    |
| 4       3    128  | 789     278     189  | 27   5     6    |
+-------------------+----------------------+-----------------+
| 168     9    678  | 2       47-8    3    | 5    467   1478 |
| 568     4    5678 | 1       9       (58) | 26   3     278  |
| -1(58)  2    3    | 47(58)  47(58)  6    | 14   47    9    |
+-------------------+----------------------+-----------------+

{note that it doesn't use all the digits in r9C45 }
R9 contains the ahs and R7 contains the als set

same thing occurs with this:
Code: Select all
+-----------------+----------------------+-----------------+
| 3     158  2458 | 6       458     7    | 9    24    14   |
| 69    7    46   | 49      1       2    | 3    8     5    |
| 2589  158  2458 | 4589    3       4589 | 146  2467  147  |
+-----------------+----------------------+-----------------+
| 7     6    125  | 3       245     145  | 8    9     24   |
| 258   58   9    | 4578    6       458  | 247  1     3    |
| 4     3    128  | 789     278     189  | 27   5     6    |
+-----------------+----------------------+-----------------+
| 168   9    678  | 2       -8(47)  3    | 5    467   1478 |
| 568   4    5678 | 1       9       58   | 26   3     278  |
| 158   2    3    | 58(47)  58(47)  6    | 1-4  (47)  9    |
+-----------------+----------------------+-----------------+

b8 is the ahs
B9 contains the als
Some do, some teach, the rest look it up.
stormdoku
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Re: Almost hidden set - xz rule:

Postby rjamil » Fri Apr 10, 2020 8:00 pm

Hi StrmCkr,

StrmCkr wrote:Almost locked Candidates are: ahs+ als: logic which is not what we are discussing

Apology for misunderstanding and many thanks for correcting the digits in r9c45.

R. Jamil
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Re: Almost hidden set - xz rule:

Postby rjamil » Sun Apr 26, 2020 5:07 pm

Hi StrmCkr,

Well, its off topic but, is Strong Wing/Ring moves also part of AHS move?

Code: Select all
Strong Wing:
  ---------------+---------------+---------------
    .    /    .  |  .    .    .  |  .    /    .
    /   XY+   /  |  /    /    /  |  /   XZ+   /
    .    /    .  |  .    .    .  |  .    /    .
  ---------------+---------------+---------------
    .    /    .  |  .    .    .  |  .    /    .
    .    /    .  |  .    .    .  |  .    /    .
    .    /    .  |  .    .    .  |  .    /    .
  ---------------+---------------+---------------
    .    /    .  |  .    .    .  |  .    /    .
    /   YZ+   /  |  /    /    /  |  /  +Z-*   /
    .    /    .  |  .    .    .  |  .    /    .
  ---------------+---------------+---------------

  ---------------+---------------+---------------
    /   XY+   /  |  /    /    /  |  /   XZ+   /
    /    /    /  |  .    .    .  |  /    /    /
    /    /   YZ+ |  /    /    /  |  /    /  +Z-*
  ---------------+---------------+---------------
Strong Ring:
  ---------------+---------------+---------------
    .    /    .  |  .    .    .  |  .    /    .
    /  XY-*   /  |  /    /    /  |  /  XZ-*   /
    .    /    .  |  .    .    .  |  .    /    .
  ---------------+---------------+---------------
    .    /    .  |  .    .    .  |  .    /    .
    .    /    .  |  .    .    .  |  .    /    .
    .    /    .  |  .    .    .  |  .    /    .
  ---------------+---------------+---------------
    .    /    .  |  .    .    .  |  .    /    .
    /  WY-*   /  |  /    /    /  |  /  WZ-*   /
    .    /    .  |  .    .    .  |  .    /    .
  ---------------+---------------+---------------

  ---------------+---------------+---------------
    /  XY-*   /  |  /    /    /  |XZ-*   /    /
    /    /    /  |  .    .    .  |  /    /    /
    /    /  WY-* |  /    /    /  |  /  WZ-*   /
  ---------------+---------------+---------------

Note: I have analyzed and found only above mentioned Strong Wing/Ring moves' exemplars. Coded and under rigorous testing phase. At first glance, it seems to me very powerful move as it solves total 491 additional puzzles without guess out of Ruud's 50k specialty puzzles. Similarly, only 13 more puzzles out of 17 clue 49,158 puzzles; 42 out of Mike Metcalf's Patterns Game benchmark file 26,855 puzzles; and 6 more puzzles out of 1to9only's 4,279 unique patterns game puzzles. No matter, how many instances of the same move detected that reduced the steps to solve the puzzles with guess also.

Actually, I am interested to know that how many other moves that are also part of AHS moves? (Let for example, L1/2/3-Wing moves?)

The reason behind is that, I have coded XY-Wing, XYZ-Wing, WXYZ-Wing moves along with all known patterns of 4 cells with 4 clues in total ALS moves. Now, I am thinking about to collect > 4 cells/clues ALS moves counterpart/complementary AHS moves patterns, i.e., up to 4 cells/clues AHS moves patterns.

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Re: Almost hidden set - xz rule:

Postby yzfwsf » Fri Feb 04, 2022 11:32 pm

Double linked AHS-XZ
Code: Select all
.-----------------------.-------------------.------------------------.
| (123)679  4     5     | 67   6789   89    | (2)68   (1)89  (123)89 |
| 2369      2369  269   | 1    45689  4589  | 2568    7      2389    |
| 8         169   1679  | 567  2      3     | 456     1459   149     |
:-----------------------+-------------------+------------------------:
| 23456     2356  246   | 9    358    7     | 1       4568   48      |
| 145679    1569  14679 | 25   158    1258  | 3       45689  4789    |
| 13579     8     179   | 4    135    6     | 57      2      79      |
:-----------------------+-------------------+------------------------:
| 12469     1269  3     | 267  14679  1249  | (278)4  (18)4  5       |
| 12459     7     1249  | 8    1459   12459 | (2)4    3      6       |
| 12456     1256  8     | 3    14567  1245  | 9       (1)4   (127)4  |
'---------------------'-------------------'--------------------------'


Almost AHS-XZ:A=123r1{r1c1789};B=1278b9{b9p12489};X=1r19c8,2r18c7 => r1c1<>679,r1c9<>89,r27c7<>2,r37c8<>1,b9p129<>4
Thank jco for point out the typo.
Last edited by yzfwsf on Sat Feb 05, 2022 12:21 pm, edited 2 times in total.
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Re: Almost hidden set - xz rule:

Postby StrmCkr » Fri Feb 04, 2022 11:47 pm

An RCC of ALS is to make one of the ALS lose a kind of candidate and make it a Locked Set.
And an RCC of AHS-XZ is to make one of the AHS lose a cell and make it a Locked Set.
In this way, there will be two types of RCC of AHS, one type is overlapping cells that
do not contain their common candidates,
and the other is that the cells containing
their common candidates are located in the same House, and these cells cannot contain
any other candidates that make up the AHS.


-- notes from YZF to digest for rebuilding. red scenarios don't work in current code


markups for grids for rebuilding my code

Code: Select all
+-----------------------+-------------------+-------------------------+
| 679(123)  4     5     | 67   6789   89    | 68(2)   9-8(1)  89(123) |
| 2369      2369  269   | 1    45689  4589  | 2568    7       2389    |
| 8         169   1679  | 567  2      3     | 456     1459    149     |
+-----------------------+-------------------+-------------------------+
| 23456     2356  246   | 9    358    7     | 1       4568    48      |
| 145679    1569  14679 | 25   158    1258  | 3       45689   4789    |
| 13579     8     179   | 4    135    6     | 57      2       79      |
+-----------------------+-------------------+-------------------------+
| 12469     1269  3     | 267  14679  1249  | 4(278)  4-1(8)  5       |
| 12459     7     1249  | 8    1459   12459 | 4(2)    3       6       |
| 12456     1256  8     | 3    14567  1245  | 9       14      14(27)  |
+-----------------------+-------------------+-------------------------+


Code: Select all
+-------------------+----------------------+-----------------+
| 3       158  2458 | 6       458     7    | 9    24    14   |
| 69      7    46   | 49      1       2    | 3    8     5    |
| 2589    158  2458 | 4589    3       4589 | 146  2467  147  |
+-------------------+----------------------+-----------------+
| 7       6    125  | 3       245     145  | 8    9     24   |
| 258     58   9    | 4578    6       458  | 247  1     3    |
| 4       3    128  | 789     278     189  | 27   5     6    |
+-------------------+----------------------+-----------------+
| 168     9    678  | 2       -8(47)  3    | 5    467   1478 |
| 568     4    5678 | 1       9       58   | 26   3     278  |
| -1(58)  2    3    | (4578)  (4578)  6    | 14   47    9    |
+-------------------+----------------------+-----------------+



Code: Select all
+-----------------+------------------+----------------------+
| 3     158  2458 | 6     458   7    | 9      24    14      |
| 69    7    46   | 49    1     2    | 3      8     5       |
| 2589  158  2458 | 4589  3     4589 | 4(16)  2467  147     |
+-----------------+------------------+----------------------+
| 7     6    125  | 3     245   145  | 8      9     24      |
| 258   58   9    | 4578  6     458  | 247    1     3       |
| 4     3    128  | 789   278   189  | 27     5     6       |
+-----------------+------------------+----------------------+
| 168   9    678  | 2     478   3    | 5      467   47-1(8) |
| 568   4    5678 | 1     9     58   | (26)   3     7(28)   |
| 158   2    3    | 4578  4578  6    | 4(1)   47    9       |
+-----------------+------------------+----------------------+
Some do, some teach, the rest look it up.
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Re: Almost hidden set - xz rule:

Postby jco » Sat Feb 05, 2022 11:48 am

yzfwsf wrote:Double linked AHS-XZ
Code: Select all
.-----------------------.-------------------.------------------------.
| (123)679  4     5     | 67   6789   89    | (2)68   (1)89  (123)89 |
| 2369      2369  269   | 1    45689  4589  | 2568    7      2389    |
| 8         169   1679  | 567  2      3     | 456     1459   149     |
:-----------------------+-------------------+------------------------:
| 23456     2356  246   | 9    358    7     | 1       4568   48      |
| 145679    1569  14679 | 25   158    1258  | 3       45689  4789    |
| 13579     8     179   | 4    135    6     | 57      2      79      |
:-----------------------+-------------------+------------------------:
| 12469     1269  3     | 267  14679  1249  | (278)4  (18)4  5       |
| 12459     7     1249  | 8    1459   12459 | (2)4    3      6       |
| 12456     1256  8     | 3    14567  1245  | 9       (1)4   (127)4  |
'---------------------'-------------------'--------------------------'

Almost AHS-XZ:A=123r1{r1c1789};B=1278b9{b9p12489};X=1r19c8,2r18c7 => r1c1<>679,r1c9<>89,r27c7<>2,r37c8<>8,b9p129<>4

Interesting! I could get most eliminations [but the -8 r37c8 that has a typo: no 8 at r3c8] with

(ahs) Loop (23-1)r1c19 = (1)r1c8 - (1)r79c8 = (178-2)b9p129 = (2)r8c7 - (2)r1c7 = (23-1)r1c19
=> -679 r1c1, -89 rc9, -2 r27c7, -1 r3c8, -4 b9p129.

I got an additional (seemingly unimportant) elimination (-1 r3c8) in comparison with the (nice!) quoted move.
(I did not apply Firework, but it was the first idea when looking at the grid).
Btw, interesting thread! First time visiting it.
EDIT: After posted I realized that instead of r37c8<>8 (quoted move), the intended elimination is r3c8<>1.
JCO
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Re: Almost hidden set - xz rule:

Postby StrmCkr » Sat Feb 05, 2022 3:00 pm

I did not apply Firework,

fire work is technically an AHS-xz move i do give it that its easy spot when you know how that small space version functions.

ahs-xz are as mentioned a few times in another thread are difficult to wield & perform eliminations compared to their als-xz counter part

which is why this one is a long term back burner project.
that and the general consensus was these are found completely under als-xz

i've mentioned the below comment in the fireworks thread on and listed the older threads its derived from
http://sudopedia.enjoysudoku.com/Almost_Locked_Candidates.html
looks like people started using this old technique and appreciating it with some advancement
aka http://forum.enjoysudoku.com/almost-hidden-set-xz-rule-t32268.html


http://forum.enjoysudoku.com/post313965.html#p313965

p.s thanks ysf for transferring the grid over and applying the better write up for it.
and jco for the correction
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Re: Almost hidden set - xz rule:

Postby jco » Sat Feb 05, 2022 7:20 pm

This is a small improvement on my previous ahs chain (loop)

Code: Select all
.--------------------------------------------------------------------.
| 123-679   4     5     |(67) (6789) (89)   |(268)   (19)-8  123-89  |
| 2369      2369  269   | 1    45689  4589  | 568-2   7      2389    |
| 8         169   1679  | 56*7 2      3     | 456     459-1  149     |
|-----------------------+-------------------+------------------------|
| 23456     2356  246   | 9    358    7     | 1       456-8  48      |
| 145679    1569  14679 | 25   158    1258  | 3       4569-8 4789    |
| 13579     8     179   | 4    135    6     | 57      2      79      |
|-----------------------+-------------------+------------------------|
| 12469     1269  3     | 267  14679  1249  | 7-42*8 (148)   5       |
| 12459     7     1249  | 8    1459   12459 |(24)     3      6       |
| 12456     1256  8     | 3    14567  1245  | 9      (14)    127-4   |
'--------------------------------------------------------------------'

Loop (23-1)r1c19 = (1-9)r1c8 = (956-4)r345c8 = (4)r79c8 - (4=2)r8c7 - (2)r1c7 = (23-1)r1c19
=> -679 r1c1, -89 r1c9, -1 r3c8, -8 r145c8, -4 b9p19, -2 r27c7

The digits pre-marked with * are additional eliminations that the (doubly-linked) als-xz move (using the cells marked with (.) ) get.
It would be nice if a (doubly-linked) ahs-xz could get those additional eliminations as well. It seems that the reason I lose that (-8)r7c7 elimination comes from the way the chain "enters" block 9. But (-7)r3c4 seems out of reach for this chain.
JCO
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Re: Almost hidden set - xz rule:

Postby StrmCkr » Sat Feb 05, 2022 7:57 pm

you would have to scale the first ahs up 2 more digits for the extra elim in box 2
Code: Select all
+--------------------------+---------------------+-------------------------------+
| -9(123-67)  4      5     | (67)  89(67)  89    | 8(26)      9-8(1)    -89(123) |
| 2369        2369   269   | 1     45689   4589  | 568-2      7         2389     |
| 8           169    1679  | 56-7  2       3     | 456        459-1     149      |
+--------------------------+---------------------+-------------------------------+
| 23456       2356   246   | 9     358     7     | 1          456-8     48       |
| 145679      1569   14679 | 25    158     1258  | 3          4569-8    4789     |
| 13579       8      179   | 4     135     6     | 5-7        2         79       |
+--------------------------+---------------------+-------------------------------+
| 12469       1269   3     | 26-7  1469-7  1249  | -4(+7-28)  -4(+8-1)  5        |
| 12459       7      1249  | 8     1459    12459 | 4(2)       3         6        |
| 2456-1      256-1  8     | 3     4567-1  245-1 | 9          4(1)      -4(12-7) |
+--------------------------+---------------------+-------------------------------+
some of the extended eliminations are from how the cells resolve then post clean up or include a more complicated "blr" effect for locked digits.
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Re: Almost hidden set - xz rule:

Postby jco » Tue Jan 31, 2023 10:36 pm

Hi,

I would like to add something on the example below from a post by yzfwsf from last year.
(The subject is ahs-xz and for this reason I am posting here).

Code: Select all
.------------------------------------------------------------------.
| 145    2     1345 |  3459    3459  *[6]9-3|*[7]569 8    *[1]3579 |
| 458    358   7    |  1       234589  369  | 2569   2469  2359    |
| 1458   9     6    |*(3)458 *(3)2458  7    | 25     24   *(13)25  |
|-------------------+-----------------------+----------------------|
| 2578   578   258  |  3589    6       39   | 279    1     4       |
| 3      1     9    |  47      47      2    | 8      5     6       |
| 24578  6     2458 |  589     589     1    | 3      279   279     |
|-------------------+-----------------------+----------------------|
| 12678  78    128  |  679     179     5    | 4      3     2789    |
| 1567   4     135  |  2       1379    8    | 5679   679   579     |
| 9      3578  2358 |  367     37      4    | 1      267   2578    |
'------------------------------------------------------------------'



I see (3)r3c45 = (3-1)r3c9 = (176)r1c679 => -3 r1c6 as the ahs move that should have been found by the engine.
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Re: Almost hidden set - xz rule:

Postby yzfwsf » Sat Dec 02, 2023 8:39 am

I think it's simpler to treat AHS as a weak relationship between non AHS candidate numbers.
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Re: Almost hidden set - xz rule:

Postby yzfwsf » Thu Dec 07, 2023 4:03 am

StrmCkr wrote:
An RCC of ALS is to make one of the ALS lose a kind of candidate and make it a Locked Set.
And an RCC of AHS-XZ is to make one of the AHS lose a cell and make it a Locked Set.
In this way, there will be two types of RCC of AHS, one type is overlapping cells that
do not contain their common candidates,
and the other is that the cells containing
their common candidates are located in the same House, and these cells cannot contain
any other candidates that make up the AHS.


-- notes from YZF to digest for rebuilding. red scenarios don't work in current code

There is another type of RCC in AHS, where all non AHS candidates in two AHS form a strong region.
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