## Interesting SK loop

Advanced methods and approaches for solving Sudoku puzzles

### Interesting SK loop

I came across the following puzzle in the Patterns game posted by Dobrichev on May 19, 2018:

.123.....45.......3.6...7..6..7..4......2...8.....5.9...46..3.......9.5.....8...2

It has an SK loop (or whatever you prefer to call them) of the classic type:

(13=89)r4c56 - (89=14)r56c4 - (14=25)r89c4 - (25=17)r7c56 - (17=89)r7c89 - (89=16)r89c7 - (16=25)r56c7 - (25=13)r4c89 - loop
r4c2 <> 3; r4c3 <> 1; r4c3 <> 3; r7c1 <> 1; r7c1 <> 7; r7c2 <> 7; r2c4 <> 1; r3c4 <> 1; r3c4 <> 4; r1c7 <> 6; r2c7 <> 1; r2c7 <> 6;

However to my surprise it also has in the same cells a loop of the variant kind (one digit link between boxes and 3 within boxes):

(3=189)r4c56 - (189=4)r56c4 - (4=125)r89c4 - (125=7)r7c56 - (7=189)r7c89 - (189=6)r89c7 - (6=125)r56c7 - (125=3)r4c89 - loop
r4c2 <> 3; r4c3 <> 3; r7c1 <> 7; r7c2 <> 7; r3c4 <> 4; r1c7 <> 6; r2c7 <> 6; r5c6 <> 1; r6c5 <> 1; r5c8 <> 1; r6c9 <> 1; r8c5 <> 1; r9c6 <> 1; r8c9 <> 1; r9c8 <> 1

Phil
pjb
2014 Supporter

Posts: 2113
Joined: 11 September 2011
Location: Sydney, Australia

### Re: Interesting SK loop

Hi Phil, also found a Multifish : Truths 18 Base 2589 Rows 12347; Links 18 Cols 5689 Box 1 Cells r1c7 r2c4 r2c7 r3c4 r4c2 r4c3 r7c1 r7c2 which gives the same 12 eliminations as the SK loop.

Also, if I play the SK loop first I get a second Multifish : Truths 20 Base 12589 Rows 4 & 7 Cols 4 & 7; Links 20 Boxes 5, 6, 8 & 9 Cells r2c4 r3c4 r4c2 r4c3 r1c7 r2c7 r7c1 r7c2 => - 1 r59c68, r68c59.

Intriguingly all the SK loop eliminations occur in the pivot loop cells with none in the boxes. Can't say I've ever seen that behaviour before, but then I haven't played an SK loop for years.

Leren
Leren

Posts: 3748
Joined: 03 June 2012

### Re: Interesting SK loop

Leren wrote:Hi Phil, also found a Multifish : Truths 18 Base 2589 Rows 12347; Links 18 Cols 5689 Box 1 Cells r1c7 r2c4 r2c7 r3c4 r4c2 r4c3 r7c1 r7c2 which gives the same 12 eliminations as the SK loop.

Also, if I play the SK loop first I get a second Multifish : Truths 20 Base 12589 Rows 4 & 7 Cols 4 & 7; Links 20 Boxes 5, 6, 8 & 9 Cells r2c4 r3c4 r4c2 r4c3 r1c7 r2c7 r7c1 r7c2 => - 1 r59c68, r68c59.

Intriguingly all the SK loop eliminations occur in the pivot loop cells with none in the boxes. Can't say I've ever seen that behaviour before, but then I haven't played an SK loop for years.

Leren

Hi both,

A skloop has always several corresponding multi fish , the shortest is done of the 16 cells as sets. Normally, if a pattern is "SKloop compatible " many high ratings will have a SK loop. This is often true when the number of clues is small.
champagne
2017 Supporter

Posts: 7033
Joined: 02 August 2007
Location: France Brittany

### Re: Interesting SK loop

pjb wrote:I came across the following puzzle in the Patterns game posted by Dobrichev on May 19, 2018:

.123.....45.......3.6...7..6..7..4......2...8.....5.9...46..3.......9.5.....8...2

It has an SK loop (or whatever you prefer to call them) of the classic type:
However to my surprise it also has in the same cells a loop of the variant kind (one digit link between boxes and 3 within boxes):
Phil

There is a smaller 12/12 rank0 pattern achieving 15 eliminations also:

{ 3R5 3R6 7R8 7R9 4C5 4C6 6C8 6C9 6B5 7B6 3B8 4B9 }
{ 5n6 5n8 6n5 6n9 8n5 8n9 9n6 9n8 4b2 6b3 3b4 7b7 }

You may put this notation directly into the Xsudo solver to view the pattern.
It is no SK-Loop, but looks fine.
Bernd

logel

Posts: 57
Joined: 29 April 2012
Location: Germany

### Re: Interesting SK loop

Thanks for the interest. I've now established that these patterns that have both a standard SK loop and a variant SK loop int the same 16 cells are common and I've listed a number of them in the SK help file at my web site (www.philsfolly.net.au). Leren, with the example I posted the variant SK gives eliminations in all the boxes, while as you say the standard SK gives none. Typically, the eliminations produced by these two types of SK loops are different.

Phil
pjb
2014 Supporter

Posts: 2113
Joined: 11 September 2011
Location: Sydney, Australia

### Re: Interesting SK loop

probably not relevant but fun anyway... {actually it ended up being relevant}

strmckr's 11.4
Code: Select all
`.----------------------.---------------------.----------------------.| 5       137    1467  | 23468  234678  378  | 12     468    9      || 346     2      469   | 1      34689   3589 | 456    7      468    || 1467    179    8     | 24569  24679   579  | 3      456    12     |:----------------------+---------------------+----------------------:| 13678   4      15679 | 389    1389    2    | 5679   35689  3678   || 123678  13789  12679 | 3489   5       1389 | 24679  34689  234678 || 238     3589   259   | 7      3489    6    | 2459   1      2348   |:----------------------+---------------------+----------------------:| 24      157    3     | 2569   12679   1579 | 8      469    1467   || 178     6      157   | 3589   13789   4    | 179    2      137    || 9       178    24    | 2368   123678  1378 | 1467   346    5      |'----------------------'---------------------'----------------------'`

the two sk loops i know that are different one uses almost* hidden locked sets
Code: Select all
`+-------------------------+--------------------------+-------------------------+| 5       17(3)     1467  | 23468   234678    378    | 12     46(8)     9      || 46(3)   2         46(9) | 1       -46(389)  (3589) | 46(5)  7         46(8)  || 1467    17(9)     8     | 24569   24679     579    | 3      46(5)     12     |+-------------------------+--------------------------+-------------------------+| 13678   4         15679 | 389     1389      2      | 5679   -6(3589)  3678   || 123678  -17(389)  12679 | 3489    5         1389   | 24679  -46(389)  234678 || 238     (3589)    259   | 7       3489      6      | 2459   1         2348   |+-------------------------+--------------------------+-------------------------+| 24      17(5)     3     | 2569    12679     1579   | 8      46(9)     1467   || 17(8)   6         17(5) | (3589)  -17(389)  4      | 17(9)  2         17(3)  || 9       17(8)     24    | 2368    123678    1378   | 1467   46(3)     5      |+-------------------------+--------------------------+-------------------------+`

Code: Select all
`[20,236] 44 Candidates      25 Truths = {3589R2 3589R8 3589C2 3589C8 8N4 3B19 5B37 8B37 9B19}     7 Links = {56n2 28n5 2n6 45n8}     9 Eliminations --> r45c8<>6, r2c5<>46, r5c2<>17, r8c5<>17, r5c8<>4, `

and the other type use almost* locked sets
Code: Select all
`+-----------------------+---------------------+-----------------------+| 5       (137)   1467  | 23468  234678  378  | 12     (468)   9      || (346)   2       (469) | 1      389-46  3589 | (456)  7       (468)  || 1467    (179)   8     | 24569  24679   579  | 3      (456)   12     |+-----------------------+---------------------+-----------------------+| 13678   4       15679 | 389    1389    2    | 5679   3589-6  3678   || 123678  389-17  12679 | 3489   5       1389 | 24679  389-46  234678 || 238     3589    259   | 7      3489    6    | 2459   1       2348   |+-----------------------+---------------------+-----------------------+| 24      (157)   3     | 2569   12679   1579 | 8      (469)   1467   || (178)   6       (157) | 3589   389-17  4    | (179)  2       (137)  || 9       (178)   24    | 2368   123678  1378 | 1467   (346)   5      |+-----------------------+---------------------+-----------------------+`

Code: Select all
` [20,236] 48 Candidates,      16 Truths = {28N1 1379N2 28N3 28N7 1379N8 28N9}     16 Links = {46r2 17r8 17c2 46c8 3b19 5b37 8b37 9b19}     9 Eliminations --> r45c8<>6, r2c5<>46, r5c2<>17, r8c5<>17, r5c8<>4, `

where * can be additional "almost" qualities --- ie ( n cells with n+(1+*) digits)
Last edited by StrmCkr on Wed Sep 05, 2018 8:52 am, edited 1 time in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1085
Joined: 05 September 2006

### Re: Interesting SK loop

for example i did a band and stack swap on your original puzzle and found this "hidden" version of an sk loop.

Code: Select all
`+-------------------------+------------------------------+------------------------+| 7          13(9)  13(8) | 6          -3(289)  -13(589) | 4         13(2)  13(5) || 14(9)      2      1346  | 1579       3479     13579    | 16(5)     1367   8     || 14(8)      1346   5     | 1278       23478    1378     | 16(2)     9      1367  |+-------------------------+------------------------------+------------------------+| 3          45679  4678  | 789        1        2        | -6(589)   468    4569  || -1(289)    1679   12678 | 4          5        789      | -16(289)  12368  1369  || -14(2589)  1459   1248  | 3          89       6        | 7         1248   1459  |+-------------------------+------------------------------+------------------------+| 6          17(5)  17(2) | -17(2589)  -7(289)  4        | 3         17(8)  17(9) || 14(2)      1347   9     | 1278       23678    1378     | 16(8)     5      1467  || 14(5)      8      1347  | 1579       3679     13579    | 16(9)     1467   2     |+-------------------------+------------------------------+------------------------+`

Code: Select all
` [22,228] 42 Candidates      24 Truths = {2589R1 2589R7 2589C1 2589C7 2B37 5B37 8B19 9B19}     10 Links = {2r5 2c5 56n1 7n4 17n5 1n6 45n7}     12 Eliminations --> r1c56<>3, r5c17<>1, r7c45<>7, r45c7<>6, r6c1<>14, r1c6<>1, r7c4<>1,         note: a jelly fish picks off the other 8 eliminations after wards.   `

the complementary almost locked set version:
Code: Select all
`+-----------------------+------------------------+----------------------+| 7        (139)  (138) | 6        289-3  589-13 | 4       (123)  (135) || (149)    2      346-1 | 1579     3479   13579  | (156)   367-1  8     || (148)    346-1  5     | 1278     23478  1378   | (126)   9      367-1 |+-----------------------+------------------------+----------------------+| 3        45679  4678  | 789      1      2      | 589-6   468    4569  || 289-1    1679   12678 | 4        5      789    | 289-16  12368  1369  || 2589-14  1459   1248  | 3        89     6      | 7       1248   1459  |+-----------------------+------------------------+----------------------+| 6        (157)  (127) | 2589-17  289-7  4      | 3       (178)  (179) || (124)    347-1  9     | 1278     23678  1378   | (168)   5      467-1 || (145)    8      347-1 | 1579     3679   13579  | (169)   467-1  2     |+-----------------------+------------------------+----------------------+`

Code: Select all
` [22,228] 48 Candidates,      16 Truths = {2389N1 17N2 17N3 2389N7 17N8 17N9}     20 Links = {1r17 3r1 7r7 1c17 4c1 6c7 1b1379 2b37 5b37 8b19 9b19}     20 Eliminations --> r1c56<>3, r2c38<>1, r3c29<>1, r5c17<>1, r7c45<>7, r8c29<>1, r9c38<>1,      r45c7<>6, r6c1<>14, r1c6<>1, r7c4<>1, `

did some more transformation so you can easily see the direct comparison to my puzzle in the first example.
Code: Select all
`+-------------------------+------------------------------+------------------------+| 2      14(9)      1346  | 1579       3479     13579    | 1367   16(5)     8     || 13(9)  7          13(8) | 6          -3(289)  -13(589) | 13(2)  4         13(5) || 1346   14(8)      5     | 1278       23478    1378     | 9      16(2)     1367  |+-------------------------+------------------------------+------------------------+| 45679  3          4678  | 789        1        2        | 468    -6(589)   4569  || 1679   -1(289)    12678 | 4          5        789      | 12368  -16(289)  1369  || 1459   -14(2589)  1248  | 3          89       6        | 1248   7         1459  |+-------------------------+------------------------------+------------------------+| 1347   14(2)      9     | 1278       23678    1378     | 5      16(8)     1467  || 17(5)  6          17(2) | -17(2589)  -7(289)  4        | 17(8)  3         17(9) || 8      14(5)      1347  | 1579       3679     13579    | 1467   16(9)     2     |+-------------------------+------------------------------+------------------------+`
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1085
Joined: 05 September 2006

### Re: Interesting SK loop

StrmCkr wrote:probably not relevant but fun anyway... {actually it ended up being relevant}

strmckr's 11.4
where * can be additional "almost" qualities --- ie ( n cells with n+(1+*) digits)

Maybe also not relevant:
in your first example 25 bases / 7 links can be reduced to 16/16.

The is a smaller pattern with 12 bases and links, not SK but somewhat similar.

Code: Select all
`{ 1N2 2N1 2N3 3N2 7R7 7R9 6C7 6C9 4B3 1B7 1B9 4B9 }{ 4r2 6r2 7n9 1r8 9n7 1c2 7c2 4c8 3b1 9b1 6b6 7b8 } `

The point is, if you look for SK you will find SK only.

logel

Posts: 57
Joined: 29 April 2012
Location: Germany

### Re: Interesting SK loop

The point is, if you look for SK you will find SK only.

that's self explanatory.... Of course if your looking for a specific move set you are only going to find the move type..

Ps the 16/16 reduced link yup speak of uses almost locked sets, and is posted as the 2nd picture... (32) and the hidden set patter of 25/7 is also =32.. It isn't smaller technically they use diffrent data space.

Moreover, SK loops was the stepping stone towards an underlying method for finding more complicated versions

Msls, and muti fish, virus patterns, x2y2belts, sharks, and any other name that was coined during the development time
Between a few contributes including my self.

Any-who I was attempting to show pjb his SK solver presently only finds the almost locked set versions, but not the hidden set version.

Msls is technically a combination of almost hidden and almost locked which is the third type.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1085
Joined: 05 September 2006

### Re: Interesting SK loop

While I appreciate the contributions made above, my personal interest with SK loops is finding patterns that can be represented by a continuous chain. If I wanted to represent the rank zero pattern with truth/link sets then I would be pursuing msls's and multifishes.
Phil
pjb
2014 Supporter

Posts: 2113
Joined: 11 September 2011
Location: Sydney, Australia

### Re: Interesting SK loop

They are all Continous nice loops. Where the links are using 4 almost almost hidden/ locked sets... Good luck writing them as they are atm beyond my writing skill.
best I can do is work out the als/ahs used..

Code: Select all
` my stab at the almost almost hidden set loop +-------------------------+------------------------------+------------------------+| 7          13(9)  13(8) | 6          -3(289)  -13(589) | 4         13(2)  13(5) || 14(9)      2      1346  | 1579       3479     13579    | 16(5)     1367   8     || 14(8)      1346   5     | 1278       23478    1378     | 16(2)     9      1367  |+-------------------------+------------------------------+------------------------+| 3          45679  4678  | 789        1        2        | -6(589)   468    4569  || -1(289)    1679   12678 | 4          5        789      | -16(289)  12368  1369  || -14(2589)  1459   1248  | 3          89       6        | 7         1248   1459  |+-------------------------+------------------------------+------------------------+| 6          17(5)  17(2) | -17(2589)  -7(289)  4        | 3         17(8)  17(9) || 14(2)      1347   9     | 1278       23678    1378     | 16(8)     5      1467  || 14(5)      8      1347  | 1579       3679     13579    | 16(9)     1467   2     |+-------------------------+------------------------------+------------------------+`

Almost Almost hidden set - loop
a) Digits [2589] @ R1C235689
B) Digits [2589] @ C1R235689
C) Digits [2589] @ R7C234589
D) Digits [2589] @ C7R234589

AB RC[8,9] @ R1C23, C1R23
BC RC[2,5] @ R7C23, C1R89
CD RC[8,9] @ R7C89, C7R89
DA RC[2,5] @ R1C89, C7R23

each almost almost hidden set has 6 cells with 4 digits
each is linked to another almost almost hidden set
each set has 2 RC's to either the first set or the 2nd set.
the first and last sector are linked directly.
when any of the rc is applied as true in any of the combined sets the rest is locked as singles. =>> the loop becomes a hidden set.
==> any cells of the sectors used not listed as a RC must only contain the digits of the Digit set from the overlapping sectors.
12 Eliminations --> r1c56<>3, r5c17<>1, r7c45<>7, r45c7<>6, r6c1<>14, r1c6<>1, r7c4<>1,
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1085
Joined: 05 September 2006