## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### Re: Exotic patterns a resume

David P Bird wrote:
ronk wrote:an embedded impossible loop ... (1-3)r4c2 = 3r2c2 — 3r3c1 = 1r3c9 — 1r1c8 = 1r6c8 ... impossible because it contradicts the exocet assumption that produced it.

Isn't this contradiction just another way of showing that (1) can't be a member of the base set?

I was tempted by that conclusion as well, but it's invalid. Traveling in the opposite direction, and using the (13)r57c46 AUR instead, in the same manner we have ...

(3-1)r4c2 = 1r9c2 - 1r7c1 = 3r7c7 - 3r9c8 = 3r6c8

... but (3) is ultimately a member of the base set.

____ (thumbnail only)
details: Show
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`+-------------------------+-------------------------+-----------------------+| 2458    2467     245678 | 126789   16789  1678    | 24589   248(1)  3     || 2348    247(3)   1      | 23789    3789   5       | 6       248     249   || 258(3)  9        2568   | 268(13)  4      68(13)  | 258     7       25(1) |+-------------------------+-------------------------+-----------------------+| 12348   246(13)  2468   | 13678    13678  9       | 2347    5       12467 || 7       246      2469   | (13)     5      (13)    | 249     246     8     || 1389    5        689    | 4        13678  2       | 379     6(13)   1679  |+-------------------------+-------------------------+-----------------------+| 45(1)   8        457    | 67(13)   2      467(13) | 457(3)  9       4567  || 249     247      3      | 5        6789   4678    | 1       2468    2467  || 6       247(1)   24579  | 13789    13789  13478   | 234578  248(3)  2457  |+-------------------------+-------------------------+-----------------------+     12 Truths = {13R37 13C28 5N46 1B37}     14 Links = {13r5 13c46 4n2 37n46 6n8 3b19}     AUR points {aur 3r3c4 1r5c6 3r7c4 }`
ronk
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### Re: Exotic patterns a resume

David P Bird wrote:I tested my alternative proof with Platinum Blonde

Code: Select all
` *----------------------*----------------------*----------------------* | 35678  34589  34679  | 4679   5689   4578   | 679 #  1      2      |  | 15678  14589  4679   | 124679 125689 124578 | 679 #  56789  3      | >| 15678  1589   2      | 3      15689  1578   | 4      56789  6789   | <   *----------------------*----------------------*----------------------*>| 237    2349   1      | 8      236    234    | 23679  234679 5      | <  | 235    6      349    | 124    7      12345  | 8      2349   149    |  | 23578  23458  347    | 1246   12356  9      | 12367  23467  1467   |  *----------------------*----------------------*----------------------*>| 1236   123    8      | 5      1239   1237   | 123679 234679 14679  | <  | 9      123    36     | 127    4      12378  | 5      23678  1678   |  | 4      7      5      | 129    12389  6      | 1239   2389   189    |  *----------------------*----------------------*----------------------*   67     9                      69     7 `

"abi" loop in that case to eliminate 67 r12c7

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`  6r8c3    7r6c3                         UR r12c37           7r4c1  6r4c5                  ALS r4c12457                   6r6c4   7r8c4          UR r12c47  6r7c1                   7r7c6          ALS r7c12567`

Code: Select all
`6r7c1 - 6r8c3 = 7r6c3 - 7r4c1 = 6r4c5 - 6r6c4 = 7r8c4 - 7r7c6 = 6r7c1 loopeither 7r4c1;7r7c6 =>7r3c89 conflictor     6r4c5;6r7c1 =>6r3c89 conflict`

similar pattern for 69
champagne
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### Re: Exotic patterns a resume

ronk wrote:
David P Bird wrote:
ronk wrote:an embedded impossible loop ... (1-3)r4c2 = 3r2c2 — 3r3c1 = 1r3c9 — 1r1c8 = 1r6c8 ... impossible because it contradicts the exocet assumption that produced it.

Isn't this contradiction just another way of showing that (1) can't be a member of the base set?

I was tempted by that conclusion as well, but it's invalid. Traveling in the opposite direction, and using the (13)r57c46 AUR instead, in the same manner we have ...

(3-1)r4c2 = 1r9c2 - 1r7c1 = 3r7c7 - 3r9c8 = 3r6c8

... but (3) is ultimately a member of the base set.

Yes, I considered that point far too quickly.

Abi's loops take each pair of digits in turn and assume they are in the base set so when a resultant chain produces a contradiction it demonstrates the starting premise can't be true. Nothing can be inferred about a single digit that's involved in the contradiction.

That said, I've yet to find the Abi loops for (69) and (79) in Platinum Blonde.
David P Bird
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### Re: Exotic patterns a resume

David P Bird wrote:
That said, I've yet to find the Abi loops for (69) and (79) in Platinum Blonde.

Code: Select all
`*----------------------*----------------------*----------------------* | 35678  34589  34679  | 4679   5689   4578   | 679 #  1      2      | | 15678  14589  4679   | 124679 125689 124578 | 679 #  56789  3      |>| 15678  1589   2      | 3      15689  1578   | 4      56789  6789   | <  *----------------------*----------------------*----------------------*>| 237    2349   1      | 8      236    234    | 23679  234679 5      | < | 235    6      349    | 124    7      12345  | 8      2349   149    | | 23578  23458  347    | 1246   12356  9      | 12367  23467  1467   | *----------------------*----------------------*----------------------*>| 1236   123    8      | 5      1239   1237   | 123679 234679 14679  | < | 9      123    36     | 127    4      12378  | 5      23678  1678   | | 4      7      5      | 129    12389  6      | 1239   2389   189    | *----------------------*----------------------*----------------------*`

if you have a quick look at the PM, the ABI loop does not exist for 79 . they are in the same box in the UR columns

But you have it for 69
you have just to replace the '7' candidates by the appropriates '9' candidates in the ABI loop for 67
champagne
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### Re: Exotic patterns a resume

may be on more remark about the ABI loop;

when we have an exocet with 3 digits, we have seen that, usually, the ABI loop will give the right pair to put in the base.

With 4 digits, the best we can hope in the UR columns is to have the 4 digits equally shared in 2 boxes.
In that case, the ABI loop should kill four of the 6 possibilities for the base and keep as possible 2 complementary pairs.

In Golden Nugget, we can only clear 2 possibilities out of the 6.
champagne
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### Re: Exotic patterns a resume

In regard to Exotic Patterns, I've noticed the term 'almost SK-loop', but haven't seen much discussion around eliminations that are associated with it. I take 'almost SK-loop' to mean a SK-loop inwhich in one of the 4 boxes three digits rather than two link the hidden pairs of the row and column linking the box. This situation occurs quite commonly amongst the hardest puzzles. Below are a few I've detected:

Hidden Text: Show
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` 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.;1;GP;champagne dry;;;2BN A3B3;;  .......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7.....;3;tax;Golden-Nugget;;;2BN G1G2;; 1.......7.2.4...6...3...5...9..4........62.4....9..8....5.....3.6.2...8.7....1...;11.50;11.50;10.10;tarekdb;Silver_Plate;163;21  ........1.6...9.3...2.3.7..4..8.5........6....3.9...8...1.....4.5...8.9.7.....2..;cola199 (gsf morph)ED=10.6/1.2/1.2  ........6..3.8..9..4.....85..5.9...8.7...2...1..4.......6.3..5.2....73.....1.....;11.10;1.20;1.20;col;H300;5010;21  ....5..8...67..1.......3..426.9.............19.7...2...3..4..1......8..5..21..6..;92;elev;41;;;2BN A5B5;;G13  1....6.8....7....3....2.4....5.4....6....8.5....3..2....8..1.9..1......796.......;182;elev;L14;1;2;r8c3 r9c3 r1c2 r5c2  ..1.....9.4...1.3.7...8.6.....5.......21.4....1..3..5...6...2...3.8...4.9.......7;9671;TkP;3242;S  .2.4.......7.8...6.....3.5...9.6...1.....23.....5...4...1...8..6...1...797.......;243;elev;258;11.40;11.40;11.30;884  ..34......5...9...7...2...62...7..1..9...5......3....8..1.6...78......21......4..;4024;elev;L406;11.10;11.10;3.40;881  ...45.........9.3.6...375...4....1....8.....29...6..7.3....5.9...2...8...1..7....;620;elev;890;11.30;11.30;10.60;829  ..1...5...2.4...6.3....7....6.28........9..2.......4.65.....1...9.8...4...7.....3;11.70;11.70;2.60;col;H2;54;21  .2.4...8.....8...68....71..2..5...9..95.......4..3.........1..7..28...4.....6.3..;4;elev;3;;;2BN A5A6;;  ..3..6.8....1..2......7...4..9..8.6..3..4...1.7.2.....3....5.....5...6..98.....5.;6;elev;2;;;2BN A8B8;;  1.......9..67...2..8....4......75.3...5..2....6.3......9....8..6...4...1..25...6.;7;elev;15;;;2BN E6F6;;  .2...67..4...8......93........9..57..1...7..2......61.3...4..6...8.......6...5.2.;9;tarekdb;tarx0075;;;2BN I4I6;;`

I compared the patterns to the solved puzzles and found in every case that the eliminations within the 4 boxes were valid, but that in every case the eliminations for one of the rows (or columns) produced an invalid result. Therefore, at least on the basis of this small sample, it seems safe to make the eliminations within the boxes as per normal SK loop, but not in the rows and columns. Has anyone else studied this situation? I apologize if they have, but my searching didn't locate it.

pjb
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### Re: Exotic patterns a resume

pjb wrote:In regard to Exotic Patterns, I've noticed the term 'almost SK-loop', but haven't seen much discussion around eliminations that are associated with it. I take 'almost SK-loop' to mean a SK-loop inwhich in one of the 4 boxes three digits rather than two link the hidden pairs of the row and column linking the box. This situation occurs quite commonly amongst the hardest puzzles. Below are a few I've detected:

SK-loop is a very precise pattern.
A lot of puzzles have some similarities with the SK loop, but I know no logic derived from the SK loop to justify eliminations.

In your list, I have seen puzzles having an exocet pattern, puzzles having a rank 0 logic, Each of these properties leads to some eliminations.

A rank 0 logic gives usually some eliminations very close to what does a SK loop.
I would not say that for exocets, so, if you have a constant coherency in the boxes doing eliminations in a SK loop mode, may be we have missed another property.

misuse of the word SK loop is frequent and started with our friend Allan Barker using the expression (SK loop and not Almost SK loop) for diagrams in XSUDO having the same appearance as the diagram of a true SK loop.

reversely, you can have a "partial exocet". I posted recently that example puzzle 12177

champagne
Last edited by champagne on Thu May 24, 2012 8:13 am, edited 1 time in total.
champagne
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### Re: Exotic patterns a resume

David P Bird wrote:
Code: Select all
` *----------------------*----------------------*----------------------* | 35678  34589  34679  | 4679   5689   4578   | 679 #  1      2      |  | 15678  14589  4679   | 124679 125689 124578 | 679 #  56789  3      | >| 15678  1589   2      | 3      15689  1578   | 4      56789  6789   | <   *----------------------*----------------------*----------------------*>| 237    2349   1      | 8      236    234    | 23679  234679 5      | <  | 235    6      349    | 124    7      12345  | 8      2349   149    |  | 23578  23458  347    | 1246   12356  9      | 12367  23467  1467   |  *----------------------*----------------------*----------------------*>| 1236   123    8      | 5      1239   1237   | 123679 234679 14679  | <  | 9      123    36     | 127    4      12378  | 5      23678  1678   |  | 4      7      5      | 129    12389  6      | 1239   2389   189    |  *----------------------*----------------------*----------------------*   67     9                      69     7 `

(4) Must be true in either r7c8 or r7c9 so there will be one of two JExocets with common cross line candidates in the other stacks

David

As I noticed earlier, this is an interesting point.

I am thinking of adding some code to find it.

I could be interesting to name that "twin Jexocet"

champagne
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### Re: Exotic patterns a resume

pjb when I replied to you <before> you declined to respond, so you can't expect me to elaborate much here.

The Sharks thread I started covered a restricted implementation of multi-fish methods that could be used without needing Xsudo type solvers. As some unrelated posts covering a spat in another thread were inappropriately moved into that thread, and no-one was interested anyway, I abandoned it. I did identify some later refinements to the method, but they take it beyond the scope of what could be expected from a manual player.

See the example in < this post > which covers some of the ground.
David P Bird
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### Re: Exotic patterns a resume

champagne yes that situation is an interesting one, but it must be very rare! The problem with using 'twin' to describe it is that it is easily confused with "double".

The best descriptors I could come up with were "alternative" or "ambiguous" but these are both rather long. So, if no-one else can suggest anything better, "twin" should be OK I suppose.

BTW I'm still in trouble with the ABI loop for (69) in Platinum Blonde. Can you spell out the ALSs you are using please?
David P Bird
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### Re: Exotic patterns a resume

pjb wrote:In regard to Exotic Patterns, I've noticed the term 'almost SK-loop', but haven't seen much discussion around eliminations that are associated with it.
...
I compared the patterns to the solved puzzles and found in every case that the eliminations within the 4 boxes were valid, but that in every case the eliminations for one of the rows (or columns) produced an invalid result. Therefore, at least on the basis of this small sample, it seems safe to make the eliminations within the boxes as per normal SK loop, but not in the rows and columns.

Almost sk-loop simply means the sk-loop is slightly flawed. The puzzle looks very much like an sk-loop, but because of at least one "flaw", it isn't one. For example, in the first of your list, champagne dry, the clue r4c6=5 would be r4c6=4 in an unflawed sk-loop.

An almost sk-loop usually has only a very few of the same exclusions as the pure sk-loop to which it is similar, indeed, often only one exclusion. For the champagne dry, there are no exclusions using just the usual 2-row 2-col strong inference sets ("truths"). Two more truths are required, specifically the r3c12=1234 AALS, to link the <1234>-layers. These two additional truths reduce the k-rank sufficiently to yield an exclusion. You may note this r2c4<>8 exclusion is the same as for the exocet pattern for this puzzle.

[edit: Any additional exclusion(s) would require at least one additional truth.]

___ (clickable image)
Xsudo details: Show
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`980700000700000600006050000040005030007900500000020001008500900000010004000003020     17 Truths = {123R5 1234R7 1234C47 3N12}     21 Links = {1234r3 4r6 1234c1 123c2 2n4 1n7 1b59 2b68 3b59 4b8}`

champagne wrote:A lot of puzzles have some similarities with the SK loop, but I know no logic derived from the SK loop to justify eliminations.
There's one immediately above.

champagne wrote:In your list, I have seen puzzles having an exocet pattern, puzzles having a rank 0 logic, Each of these properties leads to some eliminations.
If you mean a 0-rank almost sk-loop, it would have exactly the same exclusions as the sk-loop.

champagne wrote:...if you have a constant coherency in the boxes doing eliminations in a SK loop mode, may be we have missed another property.
Agreed, but as noted above, more strong inference sets would be required.

champagne wrote:... misuse of the word SK loop is frequent and started with our friend Allan Barker using the expression (SK loop and not Almost SK loop) ...
I would be surprised if that were true, so please provide a link.
Last edited by ronk on Thu May 24, 2012 10:15 pm, edited 1 time in total.
ronk
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### Re: Exotic patterns a resume

david wrote:champagne yes that situation is an interesting one, but it must be very rare! The problem with using 'twin' to describe it is that it is easily confused with "double".

The best descriptors I could come up with were "alternative" or "ambiguous" but these are both rather long. So, if no-one else can suggest anything better, "twin" should be OK I suppose.

"siamois" also can in my mind, but I don't know the equivalent English word and i am not sure it would be a good idea

david wrote:BTW I'm still in trouble with the ABI loop for (69) in Platinum Blonde. Can you spell out the ALSs you are using please?

Let me restart from the 67 loop posted before

Code: Select all
` *----------------------*----------------------*----------------------* | 35678  34589  34679  | 4679   5689   4578   | 679 #  1      2      |  | 15678  14589  4679   | 124679 125689 124578 | 679 #  56789  3      | >| 15678  1589   2      | 3      15689  1578   | 4      56789  6789   | <   *----------------------*----------------------*----------------------*>| 237    2349   1      | 8      236    234    | 23679  234679 5      | <  | 235    6      349    | 124    7      12345  | 8      2349   149    |  | 23578  23458  347    | 1246   12356  9      | 12367  23467  1467   |  *----------------------*----------------------*----------------------*>| 1236   123    8      | 5      1239   1237   | 123679 234679 14679  | <  | 9      123    36     | 127    4      12378  | 5      23678  1678   |  | 4      7      5      | 129    12389  6      | 1239   2389   189    |  *----------------------*----------------------*----------------------*   `

"abi" loop in that case to eliminate 67 r12c7

Code: Select all
`  6r8c3    7r6c3                         UR r12c37           7r4c1  6r4c5                  ALS r4c12567                   6r6c4   7r8c4          UR r12c47  6r7c1                   7r7c6          ALS r7c12567`

first ALS used here is r4c12457.
In that ALS 67 are cleared in r4c7 leaving 7r4c1 6r4c5
No problem to say this is an ALS, the counterpart is a cell in the row 4

Second ALS used is r7c12567
Again no problem to state it is an ALS. r7c89, the counterpart, is clearly an AHS with digit '4' locked.
in that ALS 67 are cleared in r7c7 leaving 6r7c1 7r7c6

We have an identical situation with digits 69 and the table is the following

Code: Select all
`  6r8c3    9r5c3                         UR r12c37           9r4c2  6r4c5                  ALS r4c12567                   6r6c4   9r9c4          UR r12c47  6r7c1                   9r7c5          ALS r7c12567`

edit als r4c12567 and not r4c12457
champagne
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### Re: Exotic patterns a resume

champagne thanks for the elaboration – I wasn't firing on all cylinders last night.

For those that still have trouble understanding the logic of ABI loops:
Each loop is constructed on the premise that the base call hold a particular digit pair which will exclude them from the other cells in the same column and box.

Code: Select all
` *----------------------*----------------------*----------------------* | 35678  34589  34679  | 4679   5689   4578   | 679 #  1      2      |  | 15678  14589  4679   | 124679 125689 124578 | 679 #  56789  3      | >| 15678  1589   2      | 3      15689  1578   | 4      56789  6789   | <   *----------------------*----------------------*----------------------*>| 237    2349   1      | 8      236    234    | 23679  234679 5      | <  | 235    6      349    | 124    7      12345  | 8      2349   149    |  | 23578  23458  347    | 1246   12356  9      | 12367  23467  1467   |  *----------------------*----------------------*----------------------*>| 1236   123    8      | 5      1239   1237   | 123679 234679 14679  | <  | 9      123    36     | 127    4      12378  | 5      23678  1678   |  | 4      7      5      | 129    12389  6      | 1239   2389   189    |  *----------------------*----------------------*----------------------*`

For (69)r7c12 the fully expanded loop is
(6)r7c1 - (6)r8c3 = (6#2)r12c37 –[UR]- (9#2)r12c37 = (9)r5c3 – (9)r4c2 = (9-6)r4c8 =
(6)r4c5 – (6)r6c4 = (6#2)r12c47 –[UR]- (9#2)r12c47 = (9)r9c4 - (9)r7c5 = (49-6)r7c79 = Loop

As this is a closed loop, all the odd or all the even numbered terms will be true. Hence either (6) will be true in r6c1 & r4c5 or (9) will be true in r4c2 & r7c5. One way or another row 3 will be left without a (6) or a (9) creating a contradiction and proving the opening premise must be false.

That's slightly different from your explanation champagne, but if you exclude (69) in the rest of c7, why not do the same in b3 ?
You'll also notice I didn't notate the large almost naked sets but used the smaller complementary almost hidden sets which are easier to follow and less error prone.

When a JExocet exists I still like my method better as I believe that it's quicker.
David P Bird
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### Re: Exotic patterns a resume

David P Bird wrote:For (69)r7c12 the fully expanded loop is
(6)r7c1 - (6)r8c3 = (6#2)r12c37 –[UR]- (9#2)r12c37 = (9)r5c3 – (9)r4c2 = (9-6)r4c8 =
(6)r4c5 – (6)r6c4 = (6#2)r12c47 –[UR]- (9#2)r12c47 = (9)r9c4 - (9)r7c5 = (49-6)r7c79 = Loop

It doesn't bother you that one of the two exocet digits is removed from both exocet targets r4c8 and r7c89

David P Bird wrote:When a JExocet exists I still like my method better as I believe that it's quicker.

I'll be surprised if we see the "abi loop" in a puzzle that doesn't have an exocet.
ronk
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### Re: Exotic patterns a resume

pjb, the above almost sk-loop for champagne dry yields 1 exclusion. Virtually the same logic set (a morphed set with 1 truth added) for platinum blonde yields 20 exclusions. Here, other than for column 7, exclusions potentially occur in 8 cells and 8 units (boxes), the same count as for the hidden-pair-loop form of a pure sk-loop.

Therefore, champagne dry and platinum blonde seem to be good representatives of the two ends of the almost sk-loop spectrum. The uniqueness property is not utilized in either one.

___ (clickable thumbnail)

platinum blonde details (pastable into Xsudo): Show
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`000000012000000003002300400001800005060070800000009000008500000900040500470006000After one hidden single:     18 Truths = {4679R47 4679C34 12N7}     27 Links = {679r12 679c7 4n2 1256n3 12n4 47n8 7n9 479b4 46b5 6b7 79b8}     23 Eliminations --> r125c3<>5, r4c8<>234, r6c57<>6, r6c17<>7, r9c57<>9, r15c3<>3, r2c4<>12,      r7c8<>23, r5c6<>4, r6c2<>4, r7c9<>1, r7c7<>9, r8c6<>7`
ronk
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Joined: 02 November 2005
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