The New Sudoku Players' Forum

[Leren]

I have some questions for yzfwsf about his diagram.

It looks like a genuine Rank 7 construction to me, and the elimination candidate is in the Links 4 times, which is a good start, but it doesn't seem enough to me. However I admit I'm a complete dunce when anything greater than Rank 0 or simple Rank 1 comes along, so feel free to lecture away. Why would I look at the bottom section of the diagram? Well, maybe it could be removed, resulting in a slightly simpler construction, Rank 5 I think, with the elimination digit being in the Links 3 times so maybe a slightly shorter g-whip construction may be possible, but I admit I'm just speculating here. I've got my crash helmet on so I should survive any bombs that come my way.

One small question re the diagram. There is a link 9r2 in the construction but the link line doesn't go up to the 9 in r1c2.

Leren

[SCLT]

Well I'm still confused about StrmCkr's 43 eliminations. Leren's proposed interpretation as a 24x24 Rank-0 has issues (the truths are not covered by the links and the proposed set of links would lead to some inconsistent eliminations anyway for example in c6) so that doesn't help.

I can reproduce 34 of the suggested 43 eliminations. I'm still missing the following eliminations implied by the screenshot. I'd be grateful if anyone could help.

9r1c6, 6r3c6, 6r5c6, 7r7c6, 6r9c6, 8r1c8, 4r2c7, 5r7c2, 2r8c1

[StrmCkr]

lets clean this up a bit:

remove the basics gives this grid

Code: Select all

.----------------------.---------------------.---------------------.
| 7       159    14589 | 1239    13   2459   | 2348   389    6     |
| 469     2      149   | 13679   8    4679   | 347    5      479   |
| 45689   569    3     | 2679    467  245679 | 1      789    24789 |
:----------------------+---------------------+---------------------:
| 2689    1679   12789 | 5       267  3      | 4678   16789  14789 |
| 356     4      157   | 678     9    678    | 3567   2      157   |
| 235689  35679  25789 | 4       267  1      | 35678  36789  5789  |
:----------------------+---------------------+---------------------:
| 2345    357    6     | 12378   13   2478   | 9      178    12578 |
| 239     8      279   | 123679  5    2679   | 267    4      127   |
| 1       579    24579 | 26789   467  246789 | 25678  678    3     |
'----------------------'---------------------'---------------------'

next remove the 1-3 aic loop eliminations {MF 1 & 3} {2 digit sword fish}

Code: Select all

+--------------------------+------------------------+-------------------------+
| 7        59(1)    4589-1 | 29-13      13   2459   | 248-3   89(3)    6      |
| 469      2        49(1)  | -679(13)   8    4679   | 47(3)   5        479    |
| 45689    569      3      | 2679       467  245679 | 1       789      24789  |
+--------------------------+------------------------+-------------------------+
| 2689     679(1)   2789-1 | 5          267  3      | 4678    6789(1)  4789-1 |
| 356      4        157    | 678        9    678    | 3567    2        157    |
| 25689-3  5679(3)  25789  | 4          267  1      | 5678-3  6789(3)  5789   |
+--------------------------+------------------------+-------------------------+
| 245-3    57(3)    6      | 278-13     13   2478   | 9       78(1)    2578-1 |
| 29(3)    8        279    | -2679(13)  5    2679   | 267     4        27(1)  |
| 1        579      24579  | 26789      467  246789 | 25678   678      3      |
+--------------------------+------------------------+-------------------------+

aals [21,235] 16 Candidates,
8 Truths = {1R28 3R28 1C28 3C28}
10 Links = {1r4 3r6 13c4 28n4 1b19 3b37}
19 Eliminations --> r8c4<>2679, r2c4<>679, r1c34<>1, r1c47<>3, r4c39<>1, r6c17<>3, r7c49<>1,
r7c14<>3,

Code: Select all

+---------------------+--------------------+---------------------+
| 7      159    4589  | 29     13   2459   | 248    389    6     |
| 469    2      149   | 13     8    4679   | 347    5      479   |
| 45689  569    3     | 2679   467  245679 | 1      789    24789 |
+---------------------+--------------------+---------------------+
| 2689   1679   2789  | 5      267  3      | 4678   16789  4789  |
| 356    4      157   | 678    9    678    | 3567   2      157   |
| 25689  35679  25789 | 4      267  1      | 5678   36789  5789  |
+---------------------+--------------------+---------------------+
| 245    357    6     | 278    13   2478   | 9      178    2578  |
| 239    8      279   | 13     5    2679   | 267    4      127   |
| 1      579    24579 | 26789  467  246789 | 25678  678    3     |
+---------------------+--------------------+---------------------+

now ill mark stuff on this grid
hidden sk

Code: Select all

+--------------------------+---------------------+--------------------------+
| 7       5(19)     458-9  | 29     13   245-9   | 248     -8(39)    6      |
| 4(69)   2         4(19)  | (13)   8    -4(679) | -4(37)  5         4(79)  |
| 458-69  5(69)     3      | 2679   467  24579-6 | 1       8(79)     248-79 |
+--------------------------+---------------------+--------------------------+
| 2689    (1679)    2789   | 5      267  3       | 4678    -8(1679)  4789   |
| 356     4         157    | 678    9    78-6    | 3567    2         157    |
| 25689   -5(3679)  25789  | 4      267  1       | 5678    -8(3679)  5789   |
+--------------------------+---------------------+--------------------------+
| 245     -5(37)    6      | 278    13   248-7   | 9       8(17)     258-7  |
| -2(39)  8         2(79)  | (13)   5    -2(679) | 2(67)   4         2(17)  |
| 1       5(79)     245-79 | 26789  467  24789-6 | 258-67  8(67)     3      |
+--------------------------+---------------------+--------------------------+

Code: Select all

aals [21,216] 58 Candidates,
     20 Truths = {13679R2 13679R8 13679C2 13679C8}
     45 Links = {1r4 3r6 7r79 9r13 9c3 679c6 7c9 28n1 134679n2 8n3 28n4 28n6 28n7 134679n8 2n9 1b19 3b37 6b19 7b379 9b137}
     24 Eliminations --> (9r1*9c3*9b1) => r1c3<>9, (9r1*9c6) => r1c6<>9, (1n8) => r1c8<>8, (2n6) => r2c6<>4, (2n7) => r2c7<>4, (6b1) =>
     r3c1<>6, (9r3*9b1) => r3c1<>9, (6c6) => r3c6<>6, (7c9*7b3) => r3c9<>7, (9r3*9b3) => r3c9<>9, (4n8) => r4c8<>8, (6c6) =>
     r5c6<>6, (6n2) => r6c2<>5, (6n8) => r6c8<>8, (7n2) => r7c2<>5, (7r7*7c6) => r7c6<>7, (7r7*7c9*7b9) => r7c9<>7, (8n1) =>
     r8c1<>2, (8n6) => r8c6<>2, (7r9*7b7) => r9c3<>7, (9c3*9b7) => r9c3<>9, (6c6) => r9c6<>6, (6b9) => r9c7<>6, (7r9*7b9) =>
     r9c7<>7

naked sk

Code: Select all

+------------------------+--------------------+------------------------+
| 7       (159)   458-9  | 29     13   2459   | 248     (389)   6      |
| (469)   2       (149)  | 13     8    679-4  | (347)   5       (479)  |
| 458-69  (569)   3      | 2679   467  245679 | 1       (789)   248-79 |
+------------------------+--------------------+------------------------+
| 2689    1679    2789   | 5      267  3      | 4678    1679-8  4789   |
| 356     4       157    | 678    9    678    | 3567    2       157    |
| 25689   3679-5  25789  | 4      267  1      | 5678    3679-8  5789   |
+------------------------+--------------------+------------------------+
| 245     (357)   6      | 278    13   2478   | 9       (178)   258-7  |
| (239)   8       (279)  | 13     5    679-2  | (267)   4       (127)  |
| 1       (579)   245-79 | 26789  467  246789 | 258-67  (678)   3      |
+------------------------+--------------------+------------------------+

aals [21,216] 48 Candidates,
16 Truths = {28N1 1379N2 28N3 28N7 1379N8 28N9}
16 Links = {2r8 4r2 5c2 8c8 1b19 3b37 6b19 7b379 9b137}
15 Eliminations --> (9b1) => r1c3<>9, (4r2) => r2c6<>4, (6b1) => r3c1<>6, (9b1) => r3c1<>9, (7b3) => r3c9<>7, (9b3) =>
r3c9<>9, (8c8) => r4c8<>8, (5c2) => r6c2<>5, (8c8) => r6c8<>8, (7b9) => r7c9<>7, (2r8) => r8c6<>2, (7b7) =>
r9c3<>7, (9b7) => r9c3<>9, (6b9) => r9c7<>6, (7b9) => r9c7<>7

hidden & naked skloops side by side.JPG (193.46 KiB) Viewed 567 times

the extra elms on col 6 for digit 6 {for break down}

Code: Select all

+------------------------+---------------------+------------------------+
| 7       59(1)    4589  | 29     13   2459    | 248     89(3)    6     |
| 49(6)   2        49(1) | (13)   8    479(6)  | 47(3)   5        479   |
| 4589-6  59(6)    3     | 2679   467  24579-6 | 1       789      24789 |
+------------------------+---------------------+------------------------+
| 2689    79(16)   2789  | 5      267  3       | 4678    789(16)  4789  |
| 356     4        157   | 678    9    78-6    | 3567    2        157   |
| 25689   579(36)  25789 | 4      267  1       | 5678    789(36)  5789  |
+------------------------+---------------------+------------------------+
| 245     57(3)    6     | 278    13   2478    | 9       78(1)    2578  |
| 29(3)   8        279   | (13)   5    279(6)  | 27(6)   4        27(1) |
| 1       579      24579 | 26789  467  24789-6 | 2578-6  78(6)    3     |
+------------------------+---------------------+------------------------+

[Leren]

Code: Select all

*------------------------------------------------------*
| 7     159  458   | 29    13  2459   | 248  389  6    |
| 469   2    149   | 13    8   679    | 347  5    479  |
| 458   569  3     | 2679  467 245679 | 1    789  248  |
|------------------+------------------+----------------|
| 2689  1679 2789  | 5     267 3      | 4678 1679 4789 |
| 356   4    157   | 678   9   678    | 3567 2    157  |
| 25689 3679 25789 | 4     267 1      | 5678 3679 5789 |
|------------------+------------------+----------------|
| 245   357  6     | 278   13  2478   | 9    178  258  |
| 239   8    279   | 13    5   679    | 267  4    127  |
| 1     579  245   | 26789 467 246789 | 258  678  3    |
*------------------------------------------------------*

Here is where I think you get to after all Rank 0 eliminations are exhausted for me (from the start). Previous material in this and some of my other posts has been removed for clarity reasons.

Leren

<Edit> Added 9 to r2c1. Thanks to SpAce for pointing out the typo. Leren

[SpAce]

Just my two cents. Sorry, I haven't read all previous posts with thought, so there might be nothing new here.

It's pretty clear that StrmCkr's patterns must be Rank 0 (with higher-rank eliminations mixed in) if they work as published, which means that those truths\links counts can't be valid as published. Something like 20 truths with 47 links makes no sense. Their numbers must match to get a Rank 0 pattern. Thus I suspect some of the link combinations are alternate link sets just like in siamese fishes. If so, they should only be counted once. However, I think we've seen it before that XSudo counts them all giving ridiculous link counts. I don't know if it's the case here (or at all, because I don't have XSudo), but it might be.

Anyway, I also get 34 eliminations using both the SK-Loop (20 elims) and StrmCkr's bigger pattern (8 elims) + basics (two hidden pairs, 6 elims) separately. I'm missing the same nine eliminations as SCLT.

Here's StrmCkr's bigger pattern, as I see it:

24x24 {28N134679 134679N28 \ 1r4 1c4 1b19 2r8 3r6 3c4 3b37 4r2 5c2 679r28 679c28 8c8} => 12 elims (4 same as with SK-Loop)

That gives 8 extra eliminations, and 6 more come from basics. I guess those are just superimposed in StrmCkr's full pattern, plus something else to get the nine other eliminations.

2. Looking at StrmCkr's last post, the Naked SK (RH Diagram is OK). The LH diagram Mixed Logic AHS loop, I don't understand yet.

As far as I can tell I get 20 Truths 13679 rc28. For the links I get at least 23 : 9r13, 1r4, 3r6, 7r79, 9c3, 679c6, 7c9, 169b1, 379b37, 167b9. Several cells have links assigned to them. I don't know what to make of that yet.

I gave a working "hidden" SK-Loop using those truths in my first post (it's the MF-version). StrmCkr's version uses much more exotic linksets. I haven't even tried to understand them yet.

[SpAce]

grid: Show

Code: Select all

*------------------------------------------------------*
| 7     15   458   | 29    13  2459   | 248  389  6    |
| 469   2    149   | 13    8   679    | 347  5    479  |
| 458   569  3     | 2679  467 245679 | 1    789  248  |
|------------------+------------------+----------------|
| 2689  1679 2789  | 5     267 3      | 4678 1679 4789 |
| 356   4    157   | 678   9   678    | 3567 2    157  |
| 25689 3679 25789 | 4     267 1      | 5678 3679 5789 |
|------------------+------------------+----------------|
| 245   357  6     | 278   13  2478   | 9    178  258  |
| 239   8    279   | 13    5   679    | 267  4    127  |
| 1     579  245   | 26789 467 246789 | 258  678  3    |
*------------------------------------------------------*

Here is where I think you get to after all Rank 0 eliminations are exhausted for me (from the start). Previous material in this and some of my other posts has been removed for clarity reasons.

How did you eliminate 9r1c2 or is that a typo? Except for that, it's exactly the same pm I got after the 34 eliminations from the four Rank 0 moves (20+8+3+3), the last two being mere hidden pairs.

The simplest option is of course to do the SK-Loop (20), the two Swordfishes (4+4 elims), and the two Hidden Pairs (3+3), or to combine the fishes and pairs into a single move like StrmCkr did (19 elims if before the SK-Loop, 14 if after). Putting them all together with the SK-Loop is just confusing, and mixing in non-rank-0 eliminations makes it incomprehensible. XSudo may be able to do it all as a single move, but it doesn't mean that it has anything to do with human solving.

[SpAce]

Hi StrmCkr,

remove the basics gives this grid

grid after basics: Show

Code: Select all

.----------------------.---------------------.---------------------.
| 7       159    14589 | 1239    13   2459   | 2348   389    6     |
| 469     2      149   | 13679   8    4679   | 347    5      479   |
| 45689   569    3     | 2679    467  245679 | 1      789    24789 |
:----------------------+---------------------+---------------------:
| 2689    1679   12789 | 5       267  3      | 4678   16789  14789 |
| 356     4      157   | 678     9    678    | 3567   2      157   |
| 235689  35679  25789 | 4       267  1      | 35678  36789  5789  |
:----------------------+---------------------+---------------------:
| 2345    357    6     | 12378   13   2478   | 9      178    12578 |
| 239     8      279   | 123679  5    2679   | 267    4      127   |
| 1       579    24579 | 26789   467  246789 | 25678  678    3     |
'----------------------'---------------------'---------------------'

next remove the 1-3 aic loop eliminations {MF 1 & 3} {2 digit sword fish}

move 1: Show

Code: Select all

+--------------------------+------------------------+-------------------------+
| 7        59(1)    4589-1 | 29-13      13   2459   | 248-3   89(3)    6      |
| 469      2        49(1)  | -679(13)   8    4679   | 47(3)   5        479    |
| 45689    569      3      | 2679       467  245679 | 1       789      24789  |
+--------------------------+------------------------+-------------------------+
| 2689     679(1)   2789-1 | 5          267  3      | 4678    6789(1)  4789-1 |
| 356      4        157    | 678        9    678    | 3567    2        157    |
| 25689-3  5679(3)  25789  | 4          267  1      | 5678-3  6789(3)  5789   |
+--------------------------+------------------------+-------------------------+
| 245-3    57(3)    6      | 278-13     13   2478   | 9       78(1)    2578-1 |
| 29(3)    8        279    | -2679(13)  5    2679   | 267     4        27(1)  |
| 1        579      24579  | 26789      467  246789 | 25678   678      3      |
+--------------------------+------------------------+-------------------------+

aals [21,235] 16 Candidates,
8 Truths = {1R28 3R28 1C28 3C28}
10 Links = {1r4 3r6 13c4 28n4 1b19 3b37}
19 Eliminations --> r8c4<>2679, r2c4<>679, r1c34<>1, r1c47<>3, r4c39<>1, r6c17<>3, r7c49<>1,
r7c14<>3,

Here we see the problem I suspected before. 8 Truths and 10 Links would make it a Rank 2 pattern. Obviously it isn't, or those eliminations wouldn't be possible. It's a Siamese pattern with 8 truths and two different linksets with 8 links each. Thus, both of them are Rank 0 patterns separately, and it should be made clear. Listing them like above is extremely confusing and should be avoided like the plague. Here's how I do it:

8x8 {13R28 13C28 \ 1r4 3r6 [13c4|28n4] 1b19 3b37} => 19 elims

That shows clearly (or as clearly as possible) that the two partial linksets 13c4 and 28n4 are alternates (because either one can cover the same candidates) and thus count only as two links, not four. It means that we have a nice 8x8 Rank 0 pattern, or actually two of them. Not Rank 2. Another way to do it is to count the truths and the other links twice to get:

16x16 {13R2288 13C2288 \ 1r44 3r66 13c4 28n4 11b19 33b37} => 19 elims

Obviously that's not valid as Allan Barker's notation, because it doesn't allow duplicate sets. It is valid Obi-Wahn's notation, though. Generally I prefer the latter anyway, because it makes rank calculations easier. However, in siamese cases, like this one, I prefer the previous notation with the alternate sets, because doubling the size of the pattern makes little sense.

hidden sk

incomprehensible move: Show

Code: Select all

+--------------------------+---------------------+--------------------------+
| 7       5(19)     458-9  | 29     13   245-9   | 248     -8(39)    6      |
| 4(69)   2         4(19)  | (13)   8    -4(679) | -4(37)  5         4(79)  |
| 458-69  5(69)     3      | 2679   467  24579-6 | 1       8(79)     248-79 |
+--------------------------+---------------------+--------------------------+
| 2689    (1679)    2789   | 5      267  3       | 4678    -8(1679)  4789   |
| 356     4         157    | 678    9    78-6    | 3567    2         157    |
| 25689   -5(3679)  25789  | 4      267  1       | 5678    -8(3679)  5789   |
+--------------------------+---------------------+--------------------------+
| 245     -5(37)    6      | 278    13   248-7   | 9       8(17)     258-7  |
| -2(39)  8         2(79)  | (13)   5    -2(679) | 2(67)   4         2(17)  |
| 1       5(79)     245-79 | 26789  467  24789-6 | 258-67  8(67)     3      |
+--------------------------+---------------------+--------------------------+

Code: Select all

aals [21,216] 58 Candidates,
     20 Truths = {13679R2 13679R8 13679C2 13679C8}
     45 Links = {1r4 3r6 7r79 9r13 9c3 679c6 7c9 28n1 134679n2 8n3 28n4 28n6 28n7 134679n8 2n9 1b19 3b37 6b19 7b379 9b137}
     24 Eliminations --> (9r1*9c3*9b1) => r1c3<>9, (9r1*9c6) => r1c6<>9, (1n8) => r1c8<>8, (2n6) => r2c6<>4, (2n7) => r2c7<>4, (6b1) =>
     r3c1<>6, (9r3*9b1) => r3c1<>9, (6c6) => r3c6<>6, (7c9*7b3) => r3c9<>7, (9r3*9b3) => r3c9<>9, (4n8) => r4c8<>8, (6c6) =>
     r5c6<>6, (6n2) => r6c2<>5, (6n8) => r6c8<>8, (7n2) => r7c2<>5, (7r7*7c6) => r7c6<>7, (7r7*7c9*7b9) => r7c9<>7, (8n1) =>
     r8c1<>2, (8n6) => r8c6<>2, (7r9*7b7) => r9c3<>7, (9c3*9b7) => r9c3<>9, (6c6) => r9c6<>6, (6b9) => r9c7<>6, (7r9*7b9) =>
     r9c7<>7

That's just way too complicated, probably partly due to the same confusing link count. I don't even try to understand it.

naked sk

move 2: Show

Code: Select all

+------------------------+--------------------+------------------------+
| 7       (159)   458-9  | 29     13   2459   | 248     (389)   6      |
| (469)   2       (149)  | 13     8    679-4  | (347)   5       (479)  |
| 458-69  (569)   3      | 2679   467  245679 | 1       (789)   248-79 |
+------------------------+--------------------+------------------------+
| 2689    1679    2789   | 5      267  3      | 4678    1679-8  4789   |
| 356     4       157    | 678    9    678    | 3567    2       157    |
| 25689   3679-5  25789  | 4      267  1      | 5678    3679-8  5789   |
+------------------------+--------------------+------------------------+
| 245     (357)   6      | 278    13   2478   | 9       (178)   258-7  |
| (239)   8       (279)  | 13     5    679-2  | (267)   4       (127)  |
| 1       (579)   245-79 | 26789  467  246789 | 258-67  (678)   3      |
+------------------------+--------------------+------------------------+

aals [21,216] 48 Candidates,
16 Truths = {28N1 1379N2 28N3 28N7 1379N8 28N9}
16 Links = {2r8 4r2 5c2 8c8 1b19 3b37 6b19 7b379 9b137}
15 Eliminations --> (9b1) => r1c3<>9, (4r2) => r2c6<>4, (6b1) => r3c1<>6, (9b1) => r3c1<>9, (7b3) => r3c9<>7, (9b3) =>
r3c9<>9, (8c8) => r4c8<>8, (5c2) => r6c2<>5, (8c8) => r6c8<>8, (7b9) => r7c9<>7, (2r8) => r8c6<>2, (7b7) =>
r9c3<>7, (9b7) => r9c3<>9, (6b9) => r9c7<>6, (7b9) => r9c7<>7

Nothing weird about that. It's exactly the same MSLS I gave in my first post (with 5 fewer eliminations because of overlap with the previous move). So, move one (8x8) and this (16x16) produce 34 Rank-0 eliminations (19+15, or 20+14 in reverse order) together. I think we all can understand them. The other nine are the question marks. For example, explanations like this don't help much:

the extra elms on col 6 for digit 6 {for break down}

Code: Select all

+------------------------+---------------------+------------------------+
| 7       59(1)    4589  | 29     13   2459    | 248     89(3)    6     |
| 49(6)   2        49(1) | (13)   8    479(6)  | 47(3)   5        479   |
| 4589-6  59(6)    3     | 2679   467  24579-6 | 1       789      24789 |
+------------------------+---------------------+------------------------+
| 2689    79(16)   2789  | 5      267  3       | 4678    789(16)  4789  |
| 356     4        157   | 678    9    78-6    | 3567    2        157   |
| 25689   579(36)  25789 | 4      267  1       | 5678    789(36)  5789  |
+------------------------+---------------------+------------------------+
| 245     57(3)    6     | 278    13   2478    | 9       78(1)    2578  |
| 29(3)   8        279   | (13)   5    279(6)  | 27(6)   4        27(1) |
| 1       579      24579 | 26789  467  24789-6 | 2578-6  78(6)    3     |
+------------------------+---------------------+------------------------+

I have no idea how that should be interpreted. What are the truths and what are the links? What I see is this Rank 1 pattern:

12x13 {136R28 136C28 \ 1r4 1b19 13c4 3r6 3b37 6r46 6c6 6b19} => no elims

That can't eliminate anything. There should be one fewer link or one more truth or overlapping links, but I don't see how to get any of those. Thus, I don't think that pattern works in isolation like that. If it works at all, it must be part of the bigger monster pattern. Or so it seems to me.

--

Added. Either one of these "Alien Obi-fishes" should get the 34 Rank-0 eliminations at once:

32x32 {13R2288 13C2288 28N1379 1379N28 \ 1r44 2r8 3r66 4r2 13c4 5c2 8c8 11169b1 33379b3 33379b7 11167b9 28n4} => 34 elims

36x36 {13R222888 13C222888 679R28 679C28 \ 1r44 3r66 13c4 11169b1 33379b3 33379b7 11167b9 46n28 28n446} => 34 elims

The first one includes the naked SK-Loop and the second has the hidden one. Both are superimposed with the 16x16 Obifish I showed above. To convert into Allan Barker's notation, just remove the duplicates. However, then the counts of truths and links won't match, so it's impossible to see that it's Rank 0.