Sudoku Players' Forum (clone)

DonM,
What I've a problem with is your opinion on rules (not "methods" that you've never tried to use. You deliberately ignore all the indications I give you (extended sudoku board; progressive use: xyt, hxyt, ...; Sudoku-factory exemples of human solving). You've not changed: you had the same behaviour one year ago on Eureka.

Can you tell me where you can find any indication on how to use your preferred AICs? What you can find is drawings of AICs. But nothing about how to find them.

denis_berthier wrote:DonM,
What I've a problem with is your opinion on rules (not "methods" that you've never tried to use. You deliberately ignore all the indications I give you (extended sudoku board; progressive use: xyt, hxyt, ...; Sudoku-factory exemples of human solving). You've not changed: you had the same behaviour one year ago on Eureka.

I ignore them because they are of no use to me in learning a new method or 'rule'...whatever. No I haven't changed nor apparently has anyone else since presently no one here or there (Eureka) is solving using your rules or methods...whatever. And since it has been more than a year that you have been on the two main forums and no one on them has applied your rules to actual solving, apparently you haven't changed either. Have you ever considered that you may be missing something?

denis_berthier wrote:Can you tell me where you can find any indication on how to use your preferred AICs? What you can find is drawings of AICs. But nothing about how to find them.

Examples using graphics is one of the best ways to teach the use of sudoku methods. When perspective human solvers see patterns expressed in graphics, whether the simpler, such as X-Wings or the more complicated, such as AICs or AAICs, and see practical manually-derived examples, they are more likely to be able to both find the patterns described and apply the use of them to real puzzles.

If you take a close look at the various on-line sudoku tutorials (or even A. Stuart's 'The Logic of Sudoku'), none of them have much in the way of how to actually find the patterns they describe because it is almost impossible to describe how humans find patterns in practice, but they do describe the construct of the patterns and they do give graphics-based examples of the patterns from actual puzzles. They sometimes also give practical examples for one to try. That's what tutorials do. Most people need some handholding; probably a few don't (perhaps such as those on the Sudoku-Factory forum). This is also why I try to use graphics-based examples whenever possible in explaining an advanced concept to newer solvers: in sudoku, a picture really is worth a thousand words.

Once one sees and understands the practical application of patterns or methods, then the 'finding' part comes naturally. Take my experience with learning AAICs for example: While Steve K gave some information on how to find them, it was the many graphics-based examples of his manually-derived solutions that gave me the main information as to how to find them. The fact that his solutions were manually derived was particularly important- if he could find them (AAICs that is) then maybe I could too. If it had been just computer solver output, I wouldn't have been so sure.

What visual clues are you speaking of? Can you give examples? Do you know any computer program that uses such clues?

there is thousands of exampls of visual clues that both a huma player and a solver produce.

a human can spot naked and hidden singles counting the rows for occurances of a given clue and realize its a single.

a program counts the clues and find the same clue that a player does.

a x wing occurs in the same manner find a row column pair and aplly restrictions of the single digit

pairs: you can visually see them expessed as a pair. or they are hidden and found by seeing the number of clues combinatins.


the diffrence in visual is did i find them all?

a player will miss many diffrent objects.

a program will not miss them. unless its programed to ignor a set of rules.

not the most advanced move needed" but "the length of the longest chain needed in any resolution path

same thing. a more advance move requires a longer chain.

But I have no global rigid solving method

seems to me you do actually. your relying on computer generated out put and siting it as applicable to what a human player applies to a puzzle and from what i read on see here is that it does not even come close to replicating what a human does.

why is the defult only short chains?

why are you not incorperating other solving methods and demenstaring how they are identical to which your method does.

you keep saying resolution rules. there is only 1 rule. the end result is candiate is or is not placed.
how it is detained is what you keep saying is human replicable and applied by everone that follows your rules even if they don;t know they are.

if it is easily findable by humans then

demenstarte it with clear manually found moves.
on any random puzzle.

DonM,

So you agree: no one has ever produced any method to find any AIC. What you need is examples with graphics, nice colours and all that. I have no time to do this.
So, if you are not interested, I suggest you just stop reading my stuff.

StrmCkr,
Thanks for the examples about Singles and Pairs. They are excellent counter examples of your statements and of DonM's.
In my extended Sudoku Board, all the Hidden sets and fish appear as naked subsets. Is this not a better visual clue than your counting?

Concerning the rest of your post, I suggest you read my previous answers.

they are still found in the same mannerism.

and how do u justify them as counter examples you asked for a visual cue that people find. i gave them,

found by counting or verifying quantem states of the grid or sub grid.(pm)s

i use counting as its the easiest to show how to find a single.

or even a sum of 45 minus the clues given = missing clues sum per cell.

in the case of singles it shows the single missing.

i am stating that a program will find they all. a human may miss them in the first place but instead utilize something else to accomplish the same move.

where are you showing the diffrence.

regarding a AIC how to find.

it is a alingment of paired sets. spanning many given boxes but connect via line of sight.

for example .
25 + 29 (is 2 diffrent sets)

so that cells a = 25 b = 29 and cells c = 59

given the constraint of alingment say

A (box 1)

B (box 2) - C(box 2)

a restiction of similar clues applyies to box A.
Restriction of 5 in all other cells in line of sight to C & A

this is a simple AIC (or APE extension) can also be written as a XY wing.

StrmCkr wrote:i use counting as its the easiest to show how to find a single.

Even though I'm a mediocre player, I need no counting to find a single.

StrmCkr wrote:regarding a AIC how to find.
it is a alingment of paired sets. spanning many given boxes but connect via line of sight.
for example .
25 + 29 (is 2 diffrent sets)
so that cells a = 25 b = 29 and cells c = 59
given the constraint of alingment say
A (box 1)
B (box 2) - C(box 2)
a restiction of similar clues applyies to box A.
Restriction of 5 in all other cells in line of sight to C & A
this is a simple AIC (or APE extension) can also be written as a XY wing.

Very instructive. Apart from you, who uses counting to find AICs?

Some guys like counting, others like tagging everything. I've no objection if that's what they like. But don't tell me that many players want to do any of this. Or explain to me why variants of Sudoku based on sums of cells have never raised much interest?
What I like is logic. For me, Sudoku is a logic game and it should be solved using well defined logic rules. You like it or not, but I've always been very clear on this. All the known rules can be written in my first order logic framework and can be used in free combination with my own rules. The difference is that my formalised approach allows me to prove things that the previous informal framework didn't even allow you to think of.

sudoku
is a mathmaticall problem of cover sets, its a diffrent apporach. involving subset sums of given arangment of cells active or not active.

sum set sum equations.
(they have raised intrest check out disjoited subset)
or
Sum45 - another approach to easy puzzles.

i program with it.
i find tripless, pairs, quads, quintouples easily with it. aics basically everything and some things not covered by other eliminaions as well.

there is alternative approaches to the same concepts of logic, its a question of what you can understand. or apply the theory. mnay of them are well defined as well.

Even though I'm a mediocre player, I need no counting to find a single.

i do agree that you can find a single in a grid with out counting what is or isnt given. but the point is they are still one and the same thing.
diffrent view. only.

take
pythagorm theorm i know 500+ diffrent proofs. they all prove the same thing all with diffrent approaches.

StrmCkr,
There are lots of approaches to Sudoku. The question you raised was about visual clues; I don't yet see anything about this in your posts.

visual clues

are what a person percieves to be given and not given.

logic and reasoning is only derived by what you can comprehend.

i showed what a person could see via example method "counting".

i also told you a person will actually not see every "simple" move.

instead they may find a "pair" triple etc to identify a single digit placement of restriction they perhaps over looked.

ie its limited by what they comprehend.

i am questioning your approach that you say is "human players" by identifing all simple moves in order of application.

when this is not the case: they is more then one way to make the same ellimination.

how many ways are there.
there is a strict limitation of the applications some are very complex. and a player may find the most ellaborte one and miss the "single"

this is visual.

a computer doesnt rely on what they scan and find. its a limit of what they are program to find in order of operations.

bascially i am saying you should list out.
at each step.

perhaps all possible steps in diffrent ranges of difficulty. or via similarity to show that a range of people with diffrent skills could apply many approaches to solving each step even if they miss something else.

this was a clear point in my thread on rating as well.

StrmCkr wrote:i am questioning your approach that you say is "human players" by identifing all simple moves in order of application

Then, what you're criticising is not "my approach" but SudoRules default strategy. I've always been clear that this is only one of many possible strategies and I've always said that human players use more opportunistic strategies (if they use any strategy at all). See e.g. the "strategy level" thread.
What is human player oriented in my approach is not SudoRules default strategy but:
- the general logic framework,
- the basic factual concepts used,
- the Extended Sudoku Board,
- the progressive approach of chain rules: xy, hxy, xyt, ..... nrczt-chains or whips, nrczt-braids
- ....

Then, what you're criticising is not "my approach" but SudoRules default strategy

true and false. i do realize its a defualt strategy i would like to see that it is written that is so and not labled as a human strategy.

i am also pointing out that more common practiced and applyed stragaties are also similar if not identical to techniques you are describing.

only they are viewed in a diffrent manner by your self.

i would like to see your approach tie into other approaches
so they are accepted as one and the same. i don't see any clear relevance to this case.

StrmCkr wrote:i would like to see that it is written that is so and not labled as a human strategy.

This thread is about nrczt-chains, not about strategies. I've opened a thread about strategies. Your question is answered there.

StrmCkr wrote:i am also pointing out that more common practiced and applyed stragaties are also similar if not identical to techniques you are describing.

What are you speaking of? Strategies or resolution rules?

StrmCkr wrote:i would like to see your approach tie into other approaches
so they are accepted as one and the same.

Resolution rules are definitely not the same thing as cover sets or tagging algorithms (which are anyway not "more common approaches" and they are not the same thing as the "inference level" stuff.

On the conceptual side: my patterns are at the "factual level". They are therefore globally not the same thing as what is looked for in "the inference level" credo that came with the substitution of AICs to NLs - and that I've always pointed to as a very misleading notion. Of course, my patterns can be used to prove elimination theorems, but they are not bits of inferences, they are patterns of candidates visible on the grid (after some effort to find them).

On the practical side, as I've already said many times:
My xy-chains are merely another view of what everyone calls xy-chains.
My nrc-chains are merely another view of basic Nice Loops (i.e. NLs built only on bivalue or bilocation) - or basic AICs, as AICs are just another name for NLs.
All my chains are straightforward (although very powerful) extensions of these basic xy and nrc chains. But the t- and z- extensions do not correspond to any other known chains.
I've also proven subsumption theorems, such as: nrcz-chains subsume broken wings; nrczt-chains subsume almost all Naked, Hidden and Super-Hidden (fish) subsets - including most finned fish.
I've proven the equivalence in scope of nrczt-braids with what everyone calls T&E.
So, I think I've already shown many links with knwon rules or techniques.

Examples of braids

WARNING:
As almost any puzzle with SER ≤ 9.3 can be solved with nrczt-whips (i.e. chains or lassos) and as I'm very reluctant to rely on nets (even braids, which are a very special form of nets) when a chain is available, any interesting example of a braid will be obtained for a puzzle with SER > 9.3.
As a result, the solution to such a puzzle will require long chains and braids and it will seem very complex.
In the following, one should therefore not forget that any such puzzle is likely to be beyond normal human solving. I'm just giving an example of braids, I'm not stating that such complex puzzles should be proposed for human solving.

Contrary to the solutions I usually give with chains, I can't guarantee here that the braids used are the shortest ones available. (The contrary is very likely, didn't even try to optimise their length.) The only purpose is to show a few cases of how a braid can look.


The puzzle I'll use is #3263 in gsf's list of 8152 hardest:
20627, 094, 0640, 100800002003400050060005700000090040000006000009040000020000100700000006005080030, gsf-2007-05-24-0753, 0, 49.00s, C21.m/F10135.16143/N12760.27297/P3.33.6422.13.22.20618.18.4.2.230/M2.69.190/V2, C21.m/F15.57/N10.22/B8.18.18/H2.4.2/X2.3/Y1.30/K1.1.8.0.0.1/O1.1/G11.0.1/M1.27.1

Code: Select all

+-------+-------+-------+
| 1 . . | 8 . . | . . 2 |
| . . 3 | 4 . . | . 5 . |
| . 6 . | . . 5 | 7 . . |
+-------+-------+-------+
| . . . | . 9 . | . 4 . |
| . . . | . . 6 | . . . |
| . . 9 | . 4 . | . . . |
+-------+-------+-------+
| . 2 . | . . . | 1 . . |
| 7 . . | . . . | . . 6 |
| . . 5 | . 8 . | . 3 . |
+-------+-------+-------+


How did I proceed? As rules for braids are not (yet) defined in SudoRules, I used the following procedure (half manual):

Code: Select all

Input puzzle
Loop until solution found:
       Run SudoRules from the current state with the usual rules for chains.
       When no rule is applicable, make ONE elimination with a braid.
End loop


***** SudoRules version 13.7wB *****
100800002003400050060005700000090040000006000009040000020000100700000006005080030
hidden-single-in-a-row ==> r1c2 = 5
interaction column c4 with block b8 for number 6 ==> r7c5 <> 6
hidden-pairs-in-a-block {n3 n4}{r1c7 r3c9} ==> r3c9 <> 9
hidden-pairs-in-a-block {n3 n4}{r1c7 r3c9} ==> r3c9 <> 8
hidden-pairs-in-a-block {n3 n4}{r1c7 r3c9} ==> r3c9 <> 1
hidden-pairs-in-a-block {n3 n4}{r1c7 r3c9} ==> r1c7 <> 9
hidden-pairs-in-a-block {n3 n4}{r1c7 r3c9} ==> r1c7 <> 6

At this point, the PM is:

Code: Select all

+-------------------------+-------------------------+-------------------------+
|1       5       47       |8       367     379      |34      69      2        |
|289     789     3        |4       1267    1279     |689     5       189      |
|2489    6       248      |1239    123     5        |7       189     34       |
+-------------------------+-------------------------+-------------------------+
|23568   1378    12678    |12357   9       12378    |23568   4       13578    |
|23458   13478   12478    |12357   12357   6        |23589   12789   135789   |
|23568   1378    9        |12357   4       12378    |23568   12678   13578    |
+-------------------------+-------------------------+-------------------------+
|34689   2       468      |35679   357     3479     |1       789     45789    |
|7       13489   148      |12359   1235    12349    |24589   289     6        |
|469     149     5        |12679   8       12479    |249     3       479      |
+-------------------------+-------------------------+-------------------------+


Now comes a special case of an nrczt-braid, in rc-space: an yxzt-braid.

For easier reading, all the cells are numbered: C1 to C18. Each branch is written in a different line. The cell of the branching points (always an rlc or *) are recalled before the links (as C5 in "C5 ------- C8:{n3 n7 n6#1}r1c5"; "*" is the target.
As usual, #k after a candidate means it is justified by the rlc of cell Ck; * means it is justified by the target.
Remember that the ordering of the candidates is essential and that, in a braid, any t-candidate is still justified by the target or a PREVIOUS right-linking candidate (rlc) wrt to this ordering.

xyzt-braid[18]
* ------- C1:{n9 n6}r1c8 - C2:{n6 n8 n9*}r2c7 - C3:{n8 n7 n9*}r2c2 - C4:{n7 n4}r1c3 - C5:{n4 n3}r1c7 - C6:{n3 n4}r3c9 - C7:{n4 n7 n9*}r9c9 -
C5 ------- C8:{n3 n7 n6#1}r1c5 -
* ------- C9:{n9 n2 n8#2}r2c1 - C10:{n2 n8 n4#6}r3c3 - C11:{n8 n1 n4#4}r8c3 - C12:{n4 n6 n8#10}r7c3 -
C10 ------- C13:{n8 n9 n2#9 n4#6}r3c1 - C13:{n9 n4 n6#12}r9c1 - C15:{n4 n9 n1#11}r9c2 - C16:{n9 n2 n4#14}r9c7 - C17:{n2 n1 n4#14 n7#7 n9#15}r9c6 - C18{n1 . n2#9 n6#1 n7#8}r2c6
==> r2c9 <> 9

As in any chain, the llc of C1 is nrc-linked to the target.
But, contrary to a chain:
- the left-linking candidate of C9 is linked to the target instead of to the right-linking candidate of C8,
- the left-linking candidate of C8 is linked to the right-linking candidate of C5 instead of to the right-linking candidate of C7,
- the left-linking candidate of C13 is linked to the right-linking candidate of C10 instead of to the right-linking candidate of C12.


nrczt-whip-rn[11] n9{r1c8 r2c7} - n9{r2c2 r9c2} - n9{r7c1 r3c1} - n9{r3c4 r7c4} - n6{r7c4 r9c4} - n1{r9c4 r9c6} - n7{r9c6 r9c9} - {n7 n8}r7c8 - n8{r3c8 r2c9} - {n6 n1}r2c5 - {n6r2c5 .} ==> r8c8 <> 9


Alternative path:
the above braid and whip could have been replaced by the two whips below:
nrczt-rl-lasso[12] n9{r1c8 r1c6} - n9{r3c4 r3c1} - n9{r2c2 r9c2} - n9{r9c4 r7c4} - n6{r7c4 r9c4} - n1{r9c4 r9c6} - n7{r9c6 r9c9} - {n7 n8}r7c8 - n8{r3c8 r3c3} - n2{r3c3 r2c1} - {n2 n7}r2c6 - {n7 n9}r2c2 ==> r8c8 <> 9
nrczt-rl-lasso[14] n1{r2c9 r3c8} - n8{r3c8 r2c7} - n6{r2c7 r1c8} - n9{r1c8 r1c6} - n9{r3c4 r3c1} - n8{r3c1 r3c3} - n4{r3c3 r1c3} - {n4 n6}r7c3 - n6{r7c4 r9c4} - {n6 n4}r9c1 - {n4 n1}r8c3 - n1{r9c2 r9c6} - n1{r2c6 r2c5} - n6{r2c5 r2c7} ==> r2c9 <> 9
But I wanted to give an example of an xyzt-braid.
End alternative path.


At this point, the PM is:

Code: Select all

+-------------------------+-------------------------+-------------------------+
|1       5       47       |8       367     379      |34      69      2        |
|289     789     3        |4       1267    1279     |689     5       18       |
|2489    6       248      |1239    123     5        |7       189     34       |
+-------------------------+-------------------------+-------------------------+
|23568   1378    12678    |12357   9       12378    |23568   4       13578    |
|23458   13478   12478    |12357   12357   6        |23589   12789   135789   |
|23568   1378    9        |12357   4       12378    |23568   12678   13578    |
+-------------------------+-------------------------+-------------------------+
|34689   2       468      |35679   357     3479     |1       789     45789    |
|7       13489   148      |12359   1235    12349    |24589   28      6        |
|469     149     5        |12679   8       12479    |249     3       479      |
+-------------------------+-------------------------+-------------------------+


Now comes our second braid, an nrczt-braid which uses the four types of 2D cells (rc, rn, cn and bn):

nrczt-braid-cn[14]
* ------- C1:n8r3{c1 c8 c3*} - C2:{n8 n2}r8c8 -
* ------- C3:n7{r2c2 r1c3} - C4:n4r1{c3 c7} - C5:{n4 n9 n2#2}r9c7 - C6:{n9 n7 n8#1}r7c8 - C7:{n7 n4 n9#5}r9c9 - C8:{n4 n1 n9#5}r9c2 -
C7 ------- C9:{n4 n6 n9#5}r9c1 -
C2 ------- C10:{n8 n6 n9#5}r2c7 - C11:{n6 n9}r1c8 - C12:{n9 n1 n2#2 n7#6 n8#1}r5c8 - C13:n1{r5c3 r4c3 r4c2#8 r5c2#8 r6c2#8} - C14:n6{r4 . r7#9}c3
==> r2c2 <> 8

Here again, we have a non-first left-linking candidate (in C3) which is linked to the target instead of the pevious right-linking candidate; and two left-linking candidates (in C9 and C10) which are linked to a right-linking candidate that is not the immediately previous one.

nrczt-whip-rc[11] {n4 n7}r1c3 - {n7 n9}r2c2 - {n9 n1}r9c2 - {n1 n8}r8c3 - {n8 n2}r3c3 - n4{r3c3 r3c1} - n8{r3c1 r3c8} - n9{r3c8 r1c8} - n6{r1c8 r6c8} - n1{r5c3 r5c8} - {n1r5c3 .} ==> r7c3 <> 4
nrczt-whip-rc[14] n8{r2c1 r3c3} - {n8 n6}r7c3 - n6{r7c4 r9c4} - n6{r9c1 r6c1} - n5{r6c1 r5c1} - n3{r5c1 r7c1} - n8{r7c1 r8c2} - {n8 n2}r8c8 - n2{r9c7 r9c6} - n1{r9c6 r9c2} - n9{r9c2 r9c1} - n4{r9c1 r8c3} - n4{r1c3 r1c7} - {n4r9c7 .} ==> r4c1 <> 8
nrczt-whip-rc[14] n8{r2c1 r3c3} - {n8 n6}r7c3 - n6{r7c4 r9c4} - n6{r9c1 r4c1} - n5{r4c1 r5c1} - n3{r5c1 r7c1} - n8{r7c1 r8c2} - {n8 n2}r8c8 - n2{r9c7 r9c6} - n1{r9c6 r9c2} - n9{r9c2 r9c1} - n4{r9c1 r8c3} - n4{r1c3 r1c7} - {n4r9c7 .} ==> r6c1 <> 8


At this point, the PM is:

Code: Select all

+-------------------------+-------------------------+-------------------------+
|1       5       47       |8       367     379      |34      69      2        |
|289     79      3        |4       1267    1279     |689     5       18       |
|2489    6       248      |1239    123     5        |7       189     34       |
+-------------------------+-------------------------+-------------------------+
|2356    1378    12678    |12357   9       12378    |23568   4       13578    |
|23458   13478   12478    |12357   12357   6        |23589   12789   135789   |
|2356    1378    9        |12357   4       12378    |23568   12678   13578    |
+-------------------------+-------------------------+-------------------------+
|34689   2       68       |35679   357     3479     |1       789     45789    |
|7       13489   148      |12359   1235    12349    |24589   28      6        |
|469     149     5        |12679   8       12479    |249     3       479      |
+-------------------------+-------------------------+-------------------------+


Now comes a braid with two left-linking candidates (in C15 and C19) branching off the same right-linking candidate (in C12).

nrczt-braid-cn[23]
* ------- C1:{n9 n7}r2c2 - C2:{n7 n4}r1c3 - C3:{n4 n3}r1c7 - C4:{n3 n4}r3c9 -
* ------- C5:n3{r8c2 r7c1} - C6:n4r7{c1 c6 c9#4} - C7:n4r8{c6 c7 c2*} - C8:n5{r8c7 r7c9} - C9:{n5 n7 n3#5}r7c5 - C10:{n7 n6 n3#3}r1c5 - C11:{n6 n9}r1c8 - C12:{n9 n8 n7#9}r7c8 - C13:{n8 n2}r8c8 - C14:{n2 n9 n4#7}r9c7 -
C12 ------- C15:{n8 n1 n9#11}r3c8 - C16:{n1 n8}r2c9 -
C12 ------- C17:{n8 n6}r7c3 - C18:{n6 n4 n9#14}r9c1 - C19:{n4 n1 n9#14}r9c2 - C20:{n1 n8 n4#18}r8c3 - C21:{n8 n2 n4#4}r3c3 - C22:{n2 n9 n8#16}r2c1 - C23:n9{r2 . r1#11 r8* r9#14}c6
==> r8c2 <> 9


At this point, the PM is:

Code: Select all

+-------------------------+-------------------------+-------------------------+
|1       5       47       |8       367     379      |34      69      2        |
|289     79      3        |4       1267    1279     |689     5       18       |
|2489    6       248      |1239    123     5        |7       189     34       |
+-------------------------+-------------------------+-------------------------+
|2356    1378    12678    |12357   9       12378    |23568   4       13578    |
|23458   13478   12478    |12357   12357   6        |23589   12789   135789   |
|2356    1378    9        |12357   4       12378    |23568   12678   13578    |
+-------------------------+-------------------------+-------------------------+
|34689   2       68       |35679   357     3479     |1       789     45789    |
|7       1348    148      |12359   1235    12349    |24589   28      6        |
|469     149     5        |12679   8       12479    |249     3       479      |
+-------------------------+-------------------------+-------------------------+


nrczt-whip-rn[9] n9{r9c2 r2c2} - n9{r3c1 r3c8} - {n9 n6}r1c8 - n6{r2c7 r2c5} - n7{r2c5 r2c6} - n7{r9c6 r9c9} - {n7 n8}r7c8 - {n8 n6}r7c3 - {n6r9c1 .} ==> r9c4 <> 9
nrczt-whip-rc[11] n3{r3c9 r1c7} - n4{r1c7 r1c3} - n7{r1c3 r2c2} - n9{r2c2 r9c2} - n9{r9c9 r7c9} - n5{r7c9 r8c7} - n4{r8c7 r9c7} - {n4 n7}r9c9 - {n7 n8}r7c8 - n6{r9c1 r7c3} - {n6r9c1 .} ==> r5c9 <> 3
nrczt-whip-rc[12] n9{r3c8 r2c7} - n9{r2c1 r3c1} - n9{r9c1 r9c2} - {n9 n7}r2c2 - {n7 n4}r1c3 - n4{r1c7 r3c9} - {n4 n7}r9c9 - {n7 n8}r7c8 - {n8 n2}r8c8 - {n2 n4}r9c7 - {n4 n6}r9c1 - {n6r7c3 .} ==> r5c8 <> 9
nrczt-whip-rc[12] n9{r1c6 r1c8} - n9{r3c8 r3c1} - n9{r9c1 r9c2} - {n9 n7}r2c2 - {n7 n4}r1c3 - n4{r1c7 r3c9} - {n4 n7}r9c9 - {n7 n8}r7c8 - {n8 n2}r8c8 - {n2 n4}r9c7 - {n4 n6}r9c1 - {n6r7c3 .} ==> r2c6 <> 9
nrczt-whip-rc[13] n9{r1c6 r1c8} - n6{r1c8 r1c5} - n3{r1c5 r1c7} - {n3 n4}r3c9 - n4{r1c7 r1c3} - n7{r1c3 r2c2} - n9{r2c2 r9c2} - {n9 n7}r9c9 - {n7 n8}r7c8 - {n8 n2}r8c8 - {n2 n4}r9c7 - {n4 n6}r9c1 - {n6r7c3 .} ==> r1c6 <> 7
nrczt-whip-rn[11] {n3 n4}r3c9 - n4{r1c7 r1c3} - n7{r1c3 r1c5} - {n7 n5}r7c5 - n5{r7c9 r8c7} - n4{r8c7 r9c7} - n2{r9c7 r8c8} - {n2 n1}r8c5 - n1{r8c2 r9c2} - {n7 n9}r2c2 - {n7r2c2 .} ==> r3c5 <> 3


Nothing remarkable in the sequel.

Hi Denis,
As reference…!
Above puzzle I found SK loop for (27 & 16) at start as beloow:

Code: Select all

*-----------------------------------------------------------------------------*
 | 1       5       47A     | 8       367     379     | 34      69J     2       |
 | 289M    789M    3       | 4       1267L   1279L   | 689K    5       189K    |
 | 2489    6       248A    | 1239    123     5       | 7       189J    34      |
 |-------------------------+-------------------------+-------------------------|
 | 23568   1378    12678B  | 12357   9       12378   | 23568   4       13578   |
 | 23458   13478   12478B  | 12357   12357   6       | 23589   12789H  135789  |
 | 23568   1378    9       | 12357   4       12378   | 23568   12678H  13578   |
 |-------------------------+-------------------------+-------------------------|
 | 34689   2       468C    | 35679   357     3479    | 1       789G    45789   |
 | 7       13489   148C    | 12359   1235    12349   | 24589   289G    6       |
 | 469D    149D    5       | 12679E  8       12479E  | 249F    3       479F    |
 *-----------------------------------------------------------------------------*

=> r3c2<>2, r4c3<>8, r5c3<>48, r9c4<>9, r9c6<>49, r6c8<>8, r5c8<>89, r2c6<>9, r7c1<>6, r8c2<>1, r8c7<>2, r7c9<>7.

ttt