The New Sudoku Players' Forum

[David P Bird]

ronk, OK, OK, so I remembered the ensuing discussion 5 years ago rather than SKs definition, but I'm not the only one as you were trying to say the SK loops were defined by the location of the givens in four boxes.

However it's still true that in the Easter Monster it's much more economical to use AANSs rather than AAHSs to notate the chain.

As I said, to me, the essence of SK loops is that analysis shows that there are twin AIC loops with three possible ways the truths can be divided instead of two. This covers any chain of AALSs which I believe defines his discovery better than insisting that it only applies to AAHS loops. It would be somewhat ridiculous to call the AANS notation of the Easter Monster pattern a different name to the AAHS one, when they both employ exactly the same logic and make the same eliminations.

I for one won't be using two different terms.

[ronk]

David P Bird, so for you, clue positioning is important for the "JExocet" but not for the SK-loop. The lack of consistency is glaring.

BTW while there are certainly more puzzles like this "french puzzle", I find all the hullabaloo about the one quite ridiculous.

[JC Van Hay]

The "rank 0 logic" of 16 cells (base) in a square of 2x2 boxes so far recognised :

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+----------------+----------------+
| .    d*** d*** | .    d*** d*** |
| a*** .    .    | c*** .    .    |
| a*** .    .    | c*** .    .    |
+----------------+----------------+
| .    b*** b*** | .    b*** b*** |
| a*** .    .    | c*** .    .    |
| a*** .    .    | c*** .    .    |
+----------------+----------------+
Cover : 2 column sets for a,c
        2 row    sets for b,d
        3 box    sets for *** in each box

+----------------+----------------+
| .    gh** gh** | .    gh** gh** |
| ab** .    .    | ef** .    .    |
| ab** .    .    | ef** .    .    |
+----------------+----------------+
| .    cd** cd** | .    cd** cd** |
| ab** .    .    | ef** .    .    |
| ab** .    .    | ef** .    .    |
+----------------+----------------+
Cover : 4 column sets for a,b,e,f
        4 row    sets for c,d,g,h
        2 box    sets for ** in each box

In each case, the candidates in the cover not in the base are eliminated.

Note : as it is already the case for an XY-Ring, one should not expect an as simple description of the complementary multi-fishes!

[champagne]

I find all the hullabaloo about the one quite ridiculous.

agreed and here was the start

I think the most likely answer is this puzzle does not contain an sk-loop.

[ronk]

I find all the hullabaloo about the one quite ridiculous.

agreedandherewasthestart

I think the most likely answer is this puzzle does not contain an sk-loop.

It takes more than one to create a hullabaloo, you could have chosen not to respond.

[champagne]

I find all the hullabaloo about the one quite ridiculous.

agreedandherewasthestart

I think the most likely answer is this puzzle does not contain an sk-loop.

It takes more than one to create a hullabaloo, you could have chosen not to respond.

unhappily, some statements can not be accepted without clarification

Changing the name for the loop should close the discussion and keep things open for other kinds of puzzles having the same loop

[ronk]

Changing the name for the loop should close the discussion and keep things open for other kinds of puzzles having the same loop

So for the sake of one presently known puzzle that has a 16-cell naked-pair-loop, but not a complementary hidden-pair-loop, you're going to abandon the sk-loop term? IMO that won't go on record as one of the brightest sudoku decisions. I guess you just can't see that a pattern based on about 18 clues, trumps a pattern based on about 50+ candidates in 16 cells. Oh well, your decision.

[champagne]

Oh well, your decision.

You locked the system making that the only safe decision.

It would be a pity to loose the potential of the "V" loop for later analysis and it has no added value to fight as here to know whether it is a sk loop.
You stay in the negative position, the potential of the "V" loop is there, I have no example that a super setting property does not replace the sub setting one.

[ronk]

Oh well, your decision.

It would be a pity to loose the potential of the "V" loop for later analysis and it has no added value to fight as here to know whether it is a sk loop

champagne, instead of arguing to redefine the pattern used by Steve Kurzhals when he discovered the hidden-pair-loop, your time would be better spent adding box covers to your program. Then most, if not all, of the puzzles in the "04c multi_fish rank 0.txt" file which show "; ; ;X" fish styles would read ";R;C;X". For example ...

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98.7.....7.6...8......5....4......3..9.6.........24..1.6.9..5......3..4......1..2
;38692;GP;12_07;1;1234; ; ;X; ;;
After SSTS
         X                        R                    C

___ ___ ___ (clickable thumbnails)

Hmm, the column version has an additional 3 exclusions, all cannibalistic.

Xsudo pastable logic sets: Show

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7 row truths + 8 column truths + 3 cell truths
     18 Truths = {123R5 1234R7 1234C4 1234C7 3N123}
     18 Links = {1234r3 1n7 2n4 5n137 7n13 1b59 2b68 3b59 4b8}
     19 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r7c13<>8, r5c1<>58, r1c7<>6, r3c8<>1,
     r3c9<>4, r4c5<>1, r5c7<>7, r7c3<>7, r8c6<>2, r9c5<>4,
     
16 row truths + 3 cell truths
     19 Truths = {1R1257 2R1257 3R1257 4R1257 3N123}
     19 Links = {1c58 2c68 3c69 4c59 1n7 2n4 5n137 7n13 1234b1}
     19 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r7c13<>8, r5c1<>58, r1c7<>6, r3c8<>1,
     r3c9<>4, r4c5<>1, r5c7<>7, r7c3<>7, r8c6<>2, r9c5<>4

19 column truths + 3 cell truths
     22 Truths = {1C12347 2C12347 3C12347 4C2347 3N123}
     22 Links = {1234r3 12r4 3r6 12r8 34r9 1n7 2n4 5n137 7n13 1234b1}
     22 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r7c13<>8, r8c16<>2, r5c1<>58,
     r1c7<>6, r3c8<>1, r3c9<>4, r4c5<>1, r5c7<>7, r7c3<>7, r8c1<>1, r6c1<>3, r9c5<>4


[edit: revised to start after SSTS, add 2-row/2-col ('X') version, add clickable thumbnails]

[David P Bird]

Here's that set of eliminations expressed as a MSLS which shows 8 lines and 1 box being covered.

98.7.....7.6...8......5....4......3..9.6.........24..1.6.9..5......3..4......1..2;38692;GP;12_07;1;1234; ; ;X; ;;

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Rows *-------------------------*-------------------------*-------------------------* Boxes
 56  | 9       8       12345   | 7       146     236     | 1234-6  1256    3456    | 1234  -  -
 59  | 7       12345   6       | 1234    149     239     | 8       1259    3459    | -     .  -
 .   | 123     1234    1234    | 12348   5       689-23  | 1234679 679-12  679-34  | -     -  .
     *-------------------------*-------------------------*-------------------------*
 .   | 4       1257    12578   | 158     789-1   5789    | 267     3       5678    | .     -  -
 578 | 123-58  9       123-578 | 6       178     3578    | 24-7    2578    4578    | -     .  -
 .   | 6       357     3578    | 358     2       4       | 79      5789    1       | -     -  .
     *-------------------------*-------------------------*-------------------------*
 78  | 123-8   6       1234-78 | 9       478     278     | 5       178     378     | .     -  -
 .   | 1258    1257    125789  | 258     3       5678-2  | 1679    4       6789    | -     .  -
 .   | 358     3457    345789  | 458     678-4   1       | 3679    6789    2       | -     -  .
     *-------------------------*-------------------------*-------------------------*
Colms  .       .       .         .       14      23        .       12      34

Multi-sector Locked Set:(56)r1,(59)r2,(578)r5,(78)r7,(14)c5,(23)c6,(12)c8,(34)c9,(1234)b1 (21 cells/confined digits)
19 Eliminations in 12 cells.

A follow on step identifies (58)HS:r89c1 to make the cannibalistic eliminations given for the 2nd truth and link set approach. As these don't include (5)r89c2 this step is still needed, so the point about the extra eliminations is rather academic.

champagne, the collection of cover sets used has similarities with a single digit Franken Fish. As there are no columns covered in stack 1, any if its boxes can be added to cover the (1234) digit set. This may be of help for a redesign of your Multi-fish algorithm.

In the same way as for the truth & link set approach, the MSLS can be converted to its complement to give the same eliminations:
Multi-sector Locked Set:(1234)r3,(12)r4,(3)r6,(12)r8,(34)r9,(58)c4,(679)c7,(578)b4,(5789)b7 (23 cells/confined digits)
There is therefore still a free choice about whether to cover the focus digits by rows or columns.

[JC Van Hay]

98.7.....7.6...8......5....4......3..9.6.........24..1.6.9..5......3..4......1..2 ;38692;GP;12_07;1;1234; ; ;X; ;;

Here are some logics in that puzzle.

As Xsudo doesn't directly give me these logics, I still prefer looking for loops all cells first (which is topologically and visually easier). Furthermore, concerning Xsudo, I am keeping in mind :

1. There is no such a theorem saying that N SIS contain N truths, even if they do not overlap! Therefore, a candidate can be eliminated if it would imply that a base of N SIS has no solution (Illegal Logic in Xsudo). This is equivalent to a proof by contradiction.
2. However, the following is generally preferred : all the solutions of a base of N SIS can lead to the elimination of a candidate outside or inside the base (cannibalism) if they prevent it to be in the solution(s) of the puzzle or, equivalently, if it is "eliminated" by all of them.
3. Each elimination of a base of N SIS doesn't necessarily require the same cover set.
4. A global rank 0 logic is only defined for a base of N non-overlapping SIS having at least one solution.

After "basics" : r6c1=6; LC(9) : -9r4c79; FXW(6C58) : -6r1c79

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1. 22 cell truths - rank 0 logic - cannibalism : -7r5c7 - quasi sk-loop all cells in B5689

   38692 [22,235] 78 Candidates
   22 Truths = {3N1 3N2 3N3 34689N4 57N5 57N6 345689N7 57N8 57N9}
   22 Links = {1234r3 578r5 78r7 58c4 679c7 1b59 2b68 3b59 4b68}
   18 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r7c13<>8, r5c1<>58, r3c8<>1, r3c9<>4,
                       r4c5<>1, r5c7<>7, r7c3<>7, r8c6<>2, r9c5<>4

2. 11 row truths + 8 column truths - Overlapping truths : 2R5C7

   38692 [22,235] 58 Candidates
   19 Truths = {6789R3 123R5 1234R7 1234C4 1234C7}
   19 Links = {1n7 2n4 3n46789 5n137 7n13 1b59 2b68 3b59 4b8}
   18 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r7c13<>8, r5c1<>58, r3c8<>1, r3c9<>4,
                       r4c5<>1, r5c7<>7, r7c3<>7, r8c6<>2, r9c5<>4

3. 23 cell truths - rank 0 Logic - quasi loop all cells in R34689xC2347

   38692 [22,235] 91 Candidates
   23 Truths = {389N1 34689N2 34689N3 34689N4 34689N7}
   23 Links = {1234r3 12r4 3r6 12r8 34r9 5c4 6c7 7c7 8c134 9c7 57b4 579b7}
   18 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r7c13<>8, r5c1<>58, r3c8<>1, r3c9<>4,                  
                       r4c5<>1, r5c7<>7, r7c3<>7, r8c6<>2, r9c5<>4

4. 16 columns truths + 3 cells - Overlapping truths 1234C23 with 3N23

   38692 [22,235] 65 Candidates
   19 Truths = {1C2347 2C2347 3C2347 4C2347 3N123}
   20 Links = {1234r3 12r4 3r6 12r8 34r9 57n3 2n4 15n7 1234b1}
   18 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r8c16<>2, r7c3<>78, r3c8<>1, r3c9<>4,
                       r4c5<>1, r5c7<>7, r8c1<>1, r9c1<>3, r9c5<>4

4' 19 column truths + 3 cells - Overlapping truths 1234C23 with 3N123 - cannibalism : -12r8c1, -3r9c1

   38692 [22,235] 74 Candidates, 456 solutions
   22 Truths = {1C12347 2C12347 3C12347 4C2347 3N123}
   22 Links = {1234r3 12r4 3r6 12r8 34r9 1n7 2n4 5n137 7n13 1234b1}
   21 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r7c13<>8, r8c16<>2, r5c1<>58, r3c8<>1,
                       r3c9<>4, r4c5<>1, r5c7<>7, r7c3<>7, r8c1<>1, r9c1<>3, r9c5<>4

5. 19 columns truths - rank 0 logic - "complementary" of 4'

   38692 [22,235] 69 Candidates
   19 Truths = {6789C5 56789C6 56789C8 56789C9}
   19 Links = {6r1 9r2 578r5 78r7 49n5 348n6 369n8 348n9 5b3}
   18 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r7c13<>8, r5c1<>58, r3c8<>1, r3c9<>4,
                       r4c5<>1, r5c7<>7, r7c3<>7, r8c6<>2, r9c5<>4


6. 16 row truths + 3 cells - rank 0 logic

   38692 [22,235] 66 Candidates
   19 Truths = {1R1257 2R1257 3R1257 4R1257 3N123}
   19 Links = {1c58 2c68 3c69 4c59 1n7 2n4 5n137 7n13 1234b1}
   18 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r7c13<>8, r5c1<>58, r3c8<>1, r3c9<>4,
                       r4c5<>1, r5c7<>7, r7c3<>7, r8c6<>2, r9c5<>4

7. 23 row truths - rank 0 logic - "complementary" of 6.

   38692 [22,235] 87 Candidates
   23 Truths = {5R4689 6R3489 7R34689 8R34689 9R34689}
   23 Links = {5c4 6c7 7c7 8c134 9c7 49n5 348n6 369n8 348n9 57b4 579b7}
   18 Eliminations --> r5c3<>578, r3c68<>2, r3c69<>3, r7c13<>8, r5c1<>58, r3c8<>1, r3c9<>4,
                       r4c5<>1, r5c7<>7, r7c3<>7, r8c6<>2, r9c5<>4

Note : Logics 2,4,4' are not rank 0 logic !

[ronk]

... concerning Xsudo, I am keeping in mind :
1. There is no such a theorem saying that N SIS contain N truths, even if they do not overlap!

Incorrect, independent of Xsudo! If each candidate of N SIS is a member of only one SIS, and if each SIS candidate is covered by one or more of N WIS, there will be exactly N placements, one per SIS and one per WIS.

... concerning Xsudo, I am keeping in mind :
4. A global rank 0 logic is only defined for a base of N non-overlapping SIS having at least one solution.

Also incorrect. The logic sets I posted above are each shown by Xsudo to have effective 0-rank. That the raw rank in the 1st and 3rd instances is also 0-rank is coincidence (I think).

[ronk]

Here's that set of eliminations expressed as a MSLS which shows 8 lines and 1 box being covered.

98.7.....7.6...8......5....4......3..9.6.........24..1.6.9..5......3..4......1..2;38692;GP;12_07;1;1234; ; ;X; ;;

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Rows *-------------------------*-------------------------*-------------------------* Boxes
 56  | 9       8       12345   | 7       146     236     | 1234-6  1256    3456    | 1234  -  -
 59  | 7       12345   6       | 1234    149     239     | 8       1259    3459    | -     .  -
 .   | 123     1234    1234    | 12348   5       689-23  | 1234679 679-12  679-34  | -     -  .
     *-------------------------*-------------------------*-------------------------*
 .   | 4       1257    12578   | 158     789-1   5789    | 267     3       5678    | .     -  -
 578 | 123-58  9       123-578 | 6       178     3578    | 24-7    2578    4578    | -     .  -
 .   | 6       357     3578    | 358     2       4       | 79      5789    1       | -     -  .
     *-------------------------*-------------------------*-------------------------*
 78  | 123-8   6       1234-78 | 9       478     278     | 5       178     378     | .     -  -
 .   | 1258    1257    125789  | 258     3       5678-2  | 1679    4       6789    | -     .  -
 .   | 358     3457    345789  | 458     678-4   1       | 3679    6789    2       | -     -  .
     *-------------------------*-------------------------*-------------------------*
Colms  .       .       .         .       14      23        .       12      34

Multi-sector Locked Set:(56)r1,(59)r2,(578)r5,(78)r7,(14)c5,(23)c6,(12)c8,(34)c9,(1234)b1 (21 cells/confined digits)
19 Eliminations in 12 cells.

The first eight are apparently weak-inference-sets with the sixteen cells at their row/col intersections being the strong-inference-sets of 0-rank logic. So how do you get five more cells from the "intersection" of r1, r2 and b1?

[David P Bird]

So how do you get five more cells from the "intersection" of r1, r2 and b1?

The 5 cells in box 1 that are in the MSLS are r1c3 & r2c2 which are covered by the the combination of the row and box cover sets plus r3c123 which are completely covered by the box cover set.

The same sort of thing can happen just using row and column cover sets when a non-intersection cell contains only candidates belonging to one of the sets.

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My spread sheet colours and counts all the cells that are completely covered but we can't use either [color=#FF0080]colours[/color] or [u]underlines[/u] in "code" boxes in the forum, which is a pity.

[ronk]

So how do you get five more cells from the "intersection" of r1, r2 and b1?

The 5 cells in box 1 that are in the MSLS are r1c3 & r2c2 which are covered by the the combination of the row and box cover sets plus r3c123 which are completely covered by the box cover set.

Using WIS to identify SIS puts things in reverse order for me. To avoid r1c3,r2c2<>5, these two cells must be members of the SIS, which in turn creates the need for 1234b1 WIS. To avoid r3c123<>1234, these three cells must be members of the SIS too.

Better IMO to leave b1 out of the picture and use b3 instead ... 6r1, 9r2, 578r5, 78r7, 14c5, 23c6, 12c8, 34c9, 5b3