## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### Re: Exotic patterns a resume

David P Bird wrote:
1) IMO the only difference between the SK loop and the "V" loop is the constraint added by "ronk" to have 2 unknown cells in the boxes not belonging to the loop to qualify it of "sk loop".

2) If you consider that a sk loop must verify the "ronk constraint" to have 2-2-2 unknown cells in each row/column of the loop, then we have one example of a "V" loop that does not verify that constraint.

An example map would help me considerably as none of the 9 examples I've looked at seem to fit either description.

I'm sorry to bother you but I'm just trying to tidy these issues up because every so often the debate is re-opened and no-one can define what a V-loop is.

David

Sorry David, I thought both definitions would be clear for you.

The very first posts (Vloop definition) should answer to your point. Here is a copy paste of the text

This puzzle that I name VS (virus loop Sample) has been published first on a French forum. It is a relatively easy puzzle where usually the "V loop" is not searched.
The start is easy and the puzzle becomes difficult in that point

Code: Select all
`.........1....72...7..84.6...8....93.6..4..7.93....6...9.73..8...59....2......... VS puzzle    24568 2458 2469  |1256 12569 3     |145789 145 145789    1     458  3469  |56   569   7     |2      345 4589       235   7    239   |125  8     4     |1359   6   159       -----------------------------------------------------    457   145  8     |1256 12567 1256  |145    9   3         25    6    12    |3    4     9     |158    7   158       9     3    147   |8    157   15    |6      2   145       -----------------------------------------------------    246   9    1246  |7    3     1256  |145    8   1456       34678 148  5     |9    16    168   |1347   134 2         23678 128  12367 |4    1256  12568 |13579  135 15679  `

the V Loop is not hard to see, although finding the sequence of common digits requires attention

Code: Select all
`r3c13 r3c79 r12c8 r89c8 r7c79 r7c13 r89c2 r12c225   39    15    34    15    46    12    48    25    `

so the "V" loop is in rows 3;7 columns 2;8 boxes 1;3;7;9

the "ronk constraint" would require 2 unknown cells in each group r3c456 c8r456 r7c456 r2c456

this is not at all the case here
champagne
2017 Supporter

Posts: 7178
Joined: 02 August 2007
Location: France Brittany

### Re: Exotic patterns a resume

A graphic reminder as to the difference between an "sk-loop" and a "v-loop." Perhaps it would be better if these popular but oft misused terms were replaced with their "native" language equivalents, a hidden-pair-loop (HPL) and a naked-pair-loop (NPL), respectively.

Code: Select all
`     sk-loop                       v-loop hidden-pair loop               naked-pair-loop  (in 24 cells)                 (in 16 cells)`

_____ _____ (clickable images)

Code: Select all
`The HPL truth set:     16 Truths = {1269R28 1269C28}     16 Links = {56n2 2n4 28n5 8n6 45n8 1b19 2b19 6b37 9b37}The NPL truth set:      16 Truths = {28N1379 1379N28}     16 Links = {5r28 8r28 4c8 7c2 8c28 1b19 2b19 6b37 9b37}Eliminations the same in both cases:     13 Eliminations --> r2c45<>5, r2c45<>8, r5c28<>8, r8c56<>5, r45c8<>4, r4c8<>8, r5c2<>7, r8c5<>8,`
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

David P Bird wrote:Alternative Loop
(7=689)r79c2 - (689 =5)r8c13 - (5=128)r8c79 - (128=4)r79c8 -
(4=689)r13c8 - (689=5)r2c79 - (5=128)r2c13 - (128=7)r13c2 - Loop
=> 15 Eliminations: (8)r1c3, (8)r1c7, (5)r2c4, (5)r2c5, (8)r3c1, (8)r3c9, (4)r4c8, (7)r5c2, (4)r5c8, (8)r7c1, (8)r7c9, (5)r8c5, (5)r8c6, (8)r9c3, (8)r9c7
Like the SK loop this is not a pure AIC as the triplet terms are considered true when they contain two truths and false when they contain one truth (the minimum they must hold). Two successive triplets will together hold all three digits allowing them to be eliminated from any other cells in the same house.

Very nice find David! In a normalized "symmetric" pattern, that's three weak links in each corner box and one weak link in each side box. Has this pattern been posted and pointed out before? I sure don't recall it.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

Thanks for the responses gentlemen which are now clearing the way for me.

Champagne, the example you've posted (thank you) definitely should not be called an SK Loop as it is far away from the standard pattern. However you seem to be calling everything that employs SK Loop logic a V-loop which is being too safe! It shows that my analysis of the 9 examples was unnecessary, because they were all SK loops with extra twists.

Ronk, as I've admitted before, I've formulated a spreadsheet grid to perform a truth balance on patterns which have MSLSs which I use to handle SK loops. This works much like the XSudo program except that I can only enter weak inference sets (link sets) for different houses. It does mean that I haven't cared too much about which way round the strong and weak links have been when I've reported them as SK loops.

SK loops need two AICs to represent them using (a&b ^ c|d) in one and (a|b ^ c&d) in the other where ^ indicates a conjugate (XOR) link.
If both chains have true left hand terms (a&b) are true, if both right hand terms are true (c&d) are true and if they have different hands true one digit from each pair is true. If the links were considered weak they would be classed as AAHidden Pairs and if they were considered strong they would be classed as AANakedPairs so it depends on how they are viewed. I therefore suggest that we should drop the Hidden Pair and Naked Pair descriptions and simply call them Locked Pair Loops to cover both viewpoints and stop needless bickering. I appreciate that there are some finer points that could be considered but think this broad-brush approach would be preferable.

This would mean that SK loops would be Locked Pair Loops which have a signature pattern of 4 tell-tale givens in 4 boxes and V-Loops are Locked Pair Loops in other situations.

Champagne, the term "V-Loop" causes trouble with the forum's search engine and could be improved. It would be better to use 'Virus' in full if you decide to continue using it.

I still have some other unanswered questions outstanding:
1) Can SK loops exist with 5 tell-tale digits?
2) What degenerate (partially solved) SK loops can exist?
3) Elimination possibilities for Almost SK Loop patterns?
I would be grateful for any puzzles that demonstrate any of these situations after basic eliminations have been made.

DPB
.
David P Bird
2010 Supporter

Posts: 1043
Joined: 16 September 2008
Location: Middle England

### Re: Exotic patterns a resume

ronk wrote:Very nice find David! In a normalized "symmetric" pattern, that's three weak links in each corner box and one weak link in each side box. Has this pattern been posted and pointed out before? I sure don't recall it.

I haven't seen it before but it's similar to the chain I first proposed for Obi-Wahn's puzzle two pages back that was trumped by Blue.

I don't rate it as anything special because, as you know, once a multi-fish or similar pattern has been found there will be many ways to compose truth and link sets to provide identical eliminations once those from simple follow-on steps are included.
.
David P Bird
2010 Supporter

Posts: 1043
Joined: 16 September 2008
Location: Middle England

### Re: Exotic patterns a resume

David P Bird wrote: I still have some other unanswered questions outstanding:
1) Can SK loops exist with 5 tell-tale digits?
2) What degenerate (partially solved) SK loops can exist?
3) Elimination possibilities for Almost SK Loop patterns?
I would be grateful for any puzzles that demonstrate any of these situations after basic eliminations have been made.

I posted an "sk-loop puzzle" with 5-digits and 20 truths back in 2010. See here.

Unfortunately I didn't then first apply basic steps, so I repost below after applying two hidden pairs (28)b1 and (78)b9. There is another "5 sk-digit puzzle" posted recently in this thread which may not have an opening basic step.

Code: Select all
`100000009040002080006000300000403070000060000020508000009000100080700040500000006 # Pattern Game 119/gsf/11.3/11.3/3.4+--------------------------+--------------------------+--------------------------+| 1       7(35)     28     | 368     34578     4567   | 247-56  2(56)     9      || 7(39)   4         7(35)  | (1369)  -7(1359)  2      | 7(56)   8         7(15)  || 28      7(59)     6      | 189     145789    14579  | 3       2(15)     247-15 |+--------------------------+--------------------------+--------------------------+| 689     (1569)    158    | 4       129       3      | 25689   7         1258   || 34789   -7(1359)  134578 | 129     6         179    | 24589   -2(1359)  123458 || 34679   2         1347   | 5       179       8      | 469     (1369)    134    |+--------------------------+--------------------------+--------------------------+| 247-36  7(36)     9      | 2368    23458     456    | 1       2(35)     78     || 2(36)   8         2(13)  | 7       -2(1359)  (1569) | 2(59)   4         2(35)  || 5       7(13)     247-13 | 12389   123489    149    | 78      2(39)     6      |+--------------------------+--------------------------+--------------------------+20 Truths = {13569R28 13569C28}20 Links = {45n2 2n4 28n5 8n6 56n8 1b37 3b179 5b139 6b37 9b19}12 Eliminations --> r1c7<>56, r3c9<>15, r7c1<>36, r9c3<>13, r2c5<>7, r5c8<>2, r5c2<>7, r8c5<>2, `

There exists a complementary 4-digit AHS loop in boxes with only 12 truths.

Code: Select all
`+----------------------------+----------------------+----------------------------+| 1         35(7)   (28)     | 368    34578   4567  | -56(247)  56(2)   9        || 39(7)     4       35(7)    | 1369   1359-7  2     | 56(7)     8       15(7)    || (28)      59(7)   6        | 189    145789  14579 | 3         15(2)   -15(247) |+----------------------------+----------------------+----------------------------+| 689       1569    158      | 4      129     3     | 25689     7       1258     || 34789     1359-7  134578   | 129    6       179   | 24589     1359-2  123458   || 34679     2       1347     | 5      179     8     | 469       1369    134      |+----------------------------+----------------------+----------------------------+| -36(247)  36(7)   9        | 2368   23458   456   | 1         35(2)   (78)     || 36(2)     8       13(2)    | 7      1359-2  1569  | 59(2)     4       35(2)    || 5         13(7)   -13(247) | 12389  123489  149   | (78)      39(2)   6        |+----------------------------+----------------------+----------------------------+12 Truths = {27B1379 4B37 8B19}12 Links = {2r8 7r2 2c8 7c2 37n1 19n3 19n7 37n9}12 Eliminations --> r1c7<>56, r3c9<>15, r7c1<>36, r9c3<>13, r2c5<>7, r5c8<>2, r5c2<>7, r8c5<>2,`
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

Just for fun I ran Ronk's puzzle through my MSLS code to see if I could reproduce his results.

The interesting thing was that there were two independent patterns, one which matched Ronk's 12 eliminations and a second one which produced 12 more eliminations.

Producing PM's for these moves would have been too painful, so I've attached an Excel spreadsheet which reproduces my solver's output.

Leren
Leren

Posts: 4013
Joined: 03 June 2012

### Re: Exotic patterns a resume

Ronk, thanks for locating this puzzle for me. I vaguely remember seeing one of these oddities before (which wouldn't have been this one) but am clueless where it may be buried.

1.......9.4...2.8...6...3.....4.3.7.....6.....2.5.8.....9...1...8.7...4.5.......6 # Pattern Game 119/gsf/11.3/11.3/3.4

Code: Select all
`      *-----------------------*-----------------------*-----------------------*      | <1>    357    28      | 368    34578  4567    | 247-56 256    <9>     | (359)b1 (7)r2 | 379    <4>    357     | 1369   1359-7 <2>     | 567    <8>    157     |       | 28     579    <6>     | 189    145789 14579   | <3>    125    247-15  | (156)b2      *-----------------------*-----------------------*-----------------------*      | 689    1569   158     | <4>    129    <3>     | 25689  <7>    1258    |       | 34789  1359-7 134578  | 129    <6>    179     | 24589  1359-2 123458  |       | 34679  <2>    1347    | <5>    179    <8>     | 469    1369   134     |       *-----------------------*-----------------------*-----------------------*      | 247-36 367    <9>     | 2368   23458  456     | <1>    235    78      | (136)b7 (2)r8 | 236    <8>    123     | <7>    1359-2 1569    | 259    <4>    235     |       | <5>    137    247-13  | 12389  123489 149     | 78     239    <6>     | (359)b9      *-----------------------*-----------------------*-----------------------*               (7)c2                                           (2)c8`

As a loop:
(7=136)r79c2 - (136=2)r8c13 - (2=359)r79c8 - (359=2)r79c8 -
(2=157)r13c8 - (157=7)r2c79 - (7=359)r2c13 - (359=7)r13c2 - Loop
=> 12 Eliminations: (56)r1c7, (7)r2c5, (15)r3c9, (7)r5c2, (2)r5c8, (36)r7c1, (2)r8c5, (13)r9c3

Again the triplet terms are true when they hold two truths and false when they hold one truth.
This makes all the eliminations from the MSLS and would make eliminations in b1 & b9 if their hidden pairs were unresolved.

Looking at how the four cells in each box are still being considered as two pairs, I currently consider that this should also qualify as a Locked Pair Loop even though the division of the digits being considered is different from the common form. This would then also stretch to the loop in Obi-Wahn's puzzle.

If we choose to accept Obi-Wahn's loop as a Locked Pair Loop then I wouldn't favour us calling either of these cases an SK Loop because it would make the SKL definition over-complicated. I'm only part way through my search for the other example your remember in the Hardest Sudokus thread though which may also have an impact on our deliberations.

DPB
.
David P Bird
2010 Supporter

Posts: 1043
Joined: 16 September 2008
Location: Middle England

### Re: Exotic patterns a resume

Leren wrote:Just for fun I ran Ronk's puzzle through my MSLS code to see if I could reproduce his results.

The interesting thing was that there were two independent patterns, one which matched Ronk's 12 eliminations and a second one which produced 12 more eliminations.

This suggests that you found 12 additional eliminations - is that true?

DPB
.
David P Bird
2010 Supporter

Posts: 1043
Joined: 16 September 2008
Location: Middle England

### Re: Exotic patterns a resume

Leren wrote:Just for fun I ran Ronk's puzzle through my MSLS code to see if I could reproduce his results.

The interesting thing was that there were two independent patterns, one which matched Ronk's 12 eliminations and a second one which produced 12 more eliminations.

Producing PM's for these moves would have been too painful, so I've attached an Excel spreadsheet which reproduces my solver's output.

The combination of the 2-row/2-col loop with an all-row-loop (Allan Barker's term) doesn't look all that painful.

Code: Select all
`1.......9.4...2.8...6...3.....4.3.7.....6.....2.5.8.....9...1...8.7...4.5.......6 # Pattern Game 119/gsf/11.3/11.3/3.4     24 Truths = {13569R28 19R46 13569C28}     26 Links = {1c35 9c5 45n2 2n4 28n5 8n6 56n8 1b367 3b179 5b139 6b37 9b1469}     24 Eliminations --> r3c59<>1, r5c39<>1, r5c17<>9, r9c35<>1, r39c5<>9, r1c7<>56, r7c1<>36,      r2c4<>3, r2c5<>7, r3c9<>5, r4c2<>5, r5c8<>2, r5c2<>7, r6c8<>3, r8c5<>2, r8c6<>5, r9c3<>3,`

The different count for the Truths and Links is probably due to intersecting shared Truths, although I've not identified the precise cause. By its behavior, i.e., the large elimination count, this TLG must be an "effective 0-rank" logic pattern.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

David P Bird wrote:Ronk, thanks for locating this puzzle for me. I vaguely remember seeing one of these oddities before (which wouldn't have been this one) but am clueless where it may be buried.

For a second example, I was referring to what you are calling the Obi-Wahn puzzle, a puzzle I posted back in 2012.

Too bad I didn't switch to this normalized diagonal-symmetric morph way back then.

Code: Select all
`..1.....2.3...4.5.6.....7......49.3....86.....9.3.1.....8.....1.4.5...9.7.....6..  # 7658;GP;H1521 ..1|...|..2 .3.|..4|.5. 6..|...|7.. ---+---+--- ...|.49|.3. ...|86.|... .9.|3.1|... ---+---+--- ..8|...|..1 .4.|5..|.9. 7..|...|6.. `

[edit: Morph was not minimal; r4,r5 swapped; c4,c5 swapped]
Last edited by ronk on Thu Nov 19, 2015 3:16 pm, edited 1 time in total.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

ronk wrote:
David P Bird wrote:Ronk, thanks for locating this puzzle for me. I vaguely remember seeing one of these oddities before (which wouldn't have been this one) but am clueless where it may be buried.

For a second example, I was referring to what you are calling the Obi-Wahn puzzle, a puzzle I posted back in 2012.

Right! So we don't have a third one in sight as yet. I think the one I may be recalling may have been in my exchanges with Blue on the programmers forum. I'm pretty sure he composed a degenerate example too.

My computer had an automatic Windows 7 update this morning after which I lost my internet connection. It may have been a coincidence or not, I don't know, but eventually I was able to get back on line.

So I've now managed to complete my trawl of the featured puzzles on the Hardest thread but only found this Almost SK Loop which is made to balance by adding the extra cover set in c5.

........4.1...3.9.6...9.8.....3.5.....71......3...2.1...4...7...9.5...2.8.......6 # tarek_Pearly_#3298
Code: Select all
`       *--------------------------*--------------------------*--------------------------*       | 2359-7  2578    2359-8   | 2678    125-678 1678     | 1235-6  3567    <4>      | (478)b1(35)r2 | 2457    <1>     258      | 4678-2  245678  <3>      | 256     <9>     257      |        | <6>     2457    235      | 247     <9>     147      | <8>     357     1235-7   | (67)b3        *--------------------------*--------------------------*--------------------------*       | 1249    468-2   12689    | <3>     4678    <5>      | 2469    4678    2789     |        | 2459    468-25  <7>      | <1>     468     4689     | 234569  468-35  23589    |        | 459     <3>     5689     | 46789   4678    <2>      | 4569    <1>     5789     |        *--------------------------*--------------------------*--------------------------*       | 1235    256     <4>      | 2689    123-68  1689     | <7>     358     1359-8   | (67)b7 (13)r8 | 137     <9>     136      | <5>     134678  4678-1   | 134     <2>     138      |        | <8>     257     1235     | 2479    123-47  1479     | 1359-4  345     <6>      | (48)b9        *--------------------------*--------------------------*--------------------------*                (25)c2                     (4678)c5                    (35)c8`

MS-NS:(25)r2,(13)r8,(25)c2,(4678)c5,(35)c8,(478)b1,(67)b3,(67)b7,(48)b9
=> 20 Eliminations:7r1c1, 8r1c3, 678r1c5, 6r1c7, 2r2c4, 7r3c9, 2r4c2, 25r5c2, 35r5c8, 68r7c5, 8r7c9, 1r8c6, 47r9c5, 4r9c7

DPB
.
David P Bird
2010 Supporter

Posts: 1043
Joined: 16 September 2008
Location: Middle England

### Re: Exotic patterns a resume

Leren wrote:The interesting thing was that there were two independent patterns, one which matched Ronk's 12 eliminations and a second one which produced 12 more eliminations.

Producing PM's for these moves would have been too painful, so I've attached an Excel spreadsheet which reproduces my solver's output.

I just recently noticed the 2nd sheet of your Excel spreadsheet. If your MSLS #2 is applied to the original pencilmarks, there are actually 16 exclusions. The 12 exclusions comes about when MSLS #2 is applied to the pencilmarks remaining after the application of MSLS #1.

When switching to AAHS in rows only, I was surprised to find that the three layers for digits <169> is sufficient.

Code: Select all
`     12 Truths = {169R2468}     12 Links = {1c359 6c17 9c157 4n2 2n4 8n6 6n8}     16 Eliminations --> r3c59<>1, r5c39<>1, r5c17<>9, r9c35<>1, r39c5<>9, r1c7<>6, r2c4<>3,      r4c2<>5, r6c8<>3, r7c1<>6, r8c6<>5,`
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

Regarding the puzzle: 100000009040002080006000300000403070000060000020508000009000100080700040500000006 # Pattern Game 119/gsf/11.3/11.3/3.4,
my program found the variant loop described by David above, and also the "multifish" which appears the same as Ronks above:

12 Truths = {169R2, 169R4, 169R6, 169R8}
12 Links = { 69c1, 1c3, 19c5, 69c7, 1c9, 2n4, 4n2, 6n8, 8n6}
16 Eliminations: 24<>3, 42<>5, 68<>3, 86<>5, 17<>6, 35<>1, 35<>9, 39<>1, 51<>9, 53<>1, 57<>9, 59<>1, 71<>6, 93<>1, 95<>1, 95<>9

Phil
pjb
2014 Supporter

Posts: 2263
Joined: 11 September 2011
Location: Sydney, Australia

### Re: Exotic patterns a resume

ronk wrote: I just recently noticed the 2nd sheet of your Excel spreadsheet.

Thanks, without that I would never have found the concealed worksheet tab for Leren's second multi-fish.

I now realise that there are two multi-fish using different sets of base digits (13569) and (169) which I didn't before – I stopped looking after I'd found the first of these, so that's a lesson learnt.

When two multi-fish patterns make identical eliminations I guess Obi-Wahn transforms can be used to convert one to the other (described towards the end of < this post >). These transformations work because they progress through complementary digit sets. It would then be possible to list all possible combinations of truth and link sets that would produce the same eliminations. (I suppose therefore there would be a way to identify which of these could be taken to be canonical form.)

Leren's sets are essentially different though and can't be transformed one into the other in this way. Where the two sets produce common eliminations it needn't be because there are common truth sets, it could be because in each multi-fish the digit concerned is shown to be locked a different group of cells both of which see the elimination cell.

.
David P Bird
2010 Supporter

Posts: 1043
Joined: 16 September 2008
Location: Middle England

PreviousNext

Return to Advanced solving techniques