## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### Re: Exotic patterns a resume

champagne wrote:do you have the cover for the first one.

7765 [22,221] 45 Candidates,
16 Truths = {1256R4 1256R7 1256C4 1256C7}
16 Links = {47n1 7n2 4n3 13n4 13n7 1b68 2b59 5b59 6b68}
7 Eliminations --> r3c7<>79, r7c1<>48, r1c4<>4, r3c4<>8, r4c1<>7

Note : after 2 HP in B6 and B8
JC Van Hay

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### Re: Exotic patterns a resume

JC Van Hay wrote:Loops in 7765 giving the same eliminations ...

Base : 16 Truths = {1256R4 1256R7 1256C4 1256C7}
OR
Base : 16 Truths = {5689N4 47N5 47N6 5689N7 47N8 47N9}
OR
Base : 12 Truths = {4789B5 79B6 48B8 4789B9}

I reversed the order of the first two, here and in subsequent posts. This puts the three forms in the same order in recent posts.
ronk-Moderator
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### Re: Exotic patterns a resume

JC Van Hay wrote:
champagne wrote:do you have the cover for the first one.

7765 [22,221] 45 Candidates,
16 Truths = {1256R4 1256R7 1256C4 1256C7}
16 Links = {47n1 7n2 4n3 13n4 13n7 1b68 2b59 5b59 6b68}
7 Eliminations --> r3c7<>79, r7c1<>48, r1c4<>4, r3c4<>8, r4c1<>7

Note : after 2 HP in B6 and B8

I identified the bug that could affect other forms of multi fish searched by my solver.
It comes from the minimum of potential required in the multi floors analysis

Thanks again

After the fix, I'll re run the entire file to have an idea of the global effect
champagne
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### Re: Exotic patterns a resume

champagne wrote:My solver finds all SK loops using a specific process, so I have difficulties to follow you when you state that my solver does not find some of them.

I didn't say your solver couldn't find some of them! What is confusing is when you sometimes report them as multi-fish and sometimes SK loops depending on the process you used.
champagne wrote:Unhappily, I never worked on that [MSLS] concept, so I can not follow your explanations. Have you a link to a thread giving the basic knowledge of that logic.

I've looked up the references for Multi-Sector Locked Sets which have also been called Disjoint Locked Sets and Distributed Locked Sets before, but none of them make easy reading for someone with English as a second language. I'll therefore try to explain the concept myself...

To repeat my previous diagram:
Code: Select all
`     v                            v       v          v      v  *----------------------*-----------------------*-----------------------*  |  123-4 249    1349   | 2349   5       6      |  1237-9  8      179   |  >| #2345  4589-2 7      | 1     #238    #2349   | #2369   #239    569   |< 23  |  6     2589   13589  | 2389   237-8   237-9  |  4       123-9  159   |   *----------------------*-----------------------*-----------------------*  |  127-4 2467   146    | 2369   1237-6  8      |  5       137-49 1479  |  >| #1457  3      4568-1 | 569   #167    #1579   | #1789   #1479   2     |< 17  |  9     2578   158    | 235    4       1237-5 |  137-8   6      178   |   *----------------------*-----------------------*-----------------------* >| #345   1      4569-3 | 7     #2368   #2345   | #2689   #249    4689  |< 23 >| #457   4569-7 2      | 4568  #168    #145    | #16789  #1479   3     |< 17  |  8     467    346    | 2346   9       123-4  |  127-6   5      1467  |   *----------------------*-----------------------*-----------------------*     ^                            ^        ^         ^     ^     45                           68       459      689    49`

To satisfy the marked rows we need 2 (1)s, 2 (2)s, 2 (3)s and 2 (7)s ............ }
To satisfy the marked columns we need 3 (4)s, 2 (5)s, 2 (6)s, 2 (8)s and 3 (9)s } = total 20
The 20 # cells can't contain any further digits other than those shown for their respective rows and columns. So, if one of the exclusions shown was assigned, it would reduce the total number of digits needed but would NOT reduce the number of # cells. Therefore one cell would eventually be left empty however the remaining digits were assigned. This makes it a MSLS.

My point is that however we identify multi-fish eliminations, effectively we are locating a MSLS – something that is common to all viewpoints.
A distinguishing multi-fish feature is that there are two families of houses, one which must be satisfied for a focus digit set (1237) and the other for the complementary set (45689), and the digits in these sets are never mixed.
David P Bird
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### Re: Exotic patterns a resume

Thank you very much, david.

Going through your diagram with these fresh explanations, it sounded familiar to me.

What you describe is clearly a rank 0 logic. I had no problem to put it in XSUDO and get the eliminations.

73 Candidates,
20 Truths = {2N15678 5N15678 7N15678 8N15678}
20 Links = {1r58 2r27 3r27 7r58 4c168 5c16 6c57 8c57 9c678}
17 Eliminations --> r3c68<>9, r4c18<>4, r1c1<>4, r1c7<>9, r2c2<>2, r3c5<>8, r4c5<>6, r4c8<>9,
r5c3<>1, r6c6<>5, r6c7<>8, r7c3<>3, r8c2<>7, r9c6<>4, r9c7<>6,

This is clearly not in the field my solver is exploring, but we have seen many times that each rank 0 form can have multiple other complementary ones.

What is not 100% clear for me is
is that true for all MSLS ?
champagne
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### Re: Exotic patterns a resume

[Withdrawn:]
Last edited by daj95376 on Mon Sep 03, 2012 3:05 am, edited 2 times in total.
daj95376
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### Re: Exotic patterns a resume

[Withdrawn:]
Last edited by daj95376 on Mon Sep 03, 2012 3:06 am, edited 1 time in total.
daj95376
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### Re: Exotic patterns a resume

daj95376 wrote:So, I claim that you've only found an instance where the Xsudo image for a multi-fish looks surprisingly similar to the Xsudo image for an SK-loop.

As facts are facts, I am more cautious.

If ronk (and JV Van Hay) are right, what seems to be, each puzzle having a sk loop must have a mix (2 rows 2 columns) base multi fish.

This was not the fact in my statistic file, but at least for one puzzles, a bug has been discovered.

I am waiting for a free core to re run the test after the fix, but I expect a verification of the theoretical approach.

On the other way, my solver finds that multi fish for puzzles that don"t have the sk loop, so, that mix multi fish is likely not a signature for a sk loop.
champagne
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### Re: Exotic patterns a resume

[Withdrawn:]
Last edited by daj95376 on Mon Sep 03, 2012 3:06 am, edited 1 time in total.
daj95376
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### Re: Exotic patterns a resume

champagne wrote:On the other way, my solver finds that multi fish for puzzles that don"t have the sk loop, so, that mix multi fish is likely not a signature for a sk loop.

I'd like to see a few of those "mix" (2-row/2-col) multi-fish that are not signatures for an sk-loop.
ronk
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### Re: Exotic patterns a resume

champagne wrote:Some statistics out of the last update of my file of "potential hardest"

in that file

2013 puzzles have an SK loop
2012 with one or more multi fish patterns
1695 with a row based multi fish
1693 with a column based multi fish
1931 with a mix 2 rows 2 columns multi fish

The mix (2 rows 2 columns) multi fish pattern has been found in 3681 puzzles.
I guess but this should be analysed that most of these puzzles not having the SK loop have a "quasi" SK loop.

Just for history, it is for sure one of the diagram proposed by Allan Barker to explain eliminations in the SK loop that pushed me to study the Mix mode

this means that you can expect 3681 - 1931 = 1750 of them in the data base as a minimum*
I'll extract some examples to-day
champagne
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### Re: Exotic patterns a resume

Dear Ronk

When I posted the 3 puzzles above, I was hoping that someone could come up with a multifish with a row only based truth set. However, only 2row 2column truth set solutions have been given. You hinted my goal might be achieved using the central box for box links. Try as I may I haven't achieved it. Any chance you could put me out of my misery?

Phil
pjb
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### Re: Exotic patterns a resume

I find the following multifish patterns for pjb's three puzzles as follows:

;9698;TkP;3952

Multifish 1.1: 20 Truths = {1R1379 3R1379 4R1379 5R1379 8R1379 } 20 Links = { 3c2 5c8 8c28 1b28 3b2 4b28 5b28 8b8 1n17 3n39 7n17 9n39 }
Multifish 2.1: 19 Truths = {1C1379 3C1379 4C1379 5C137 8C1379 } 19 Links = { 1r8 4r2 5r2 8r8 1b4 3b46 4b6 5b4 8b46 1n17 3n39 7n17 9n39 }

;9681;TkP;3642

Multifish 1.1: 20 Truths = {2R1379 3R1379 4R1379 5R1379 7R1379 } 20 Links = { 2c8 3c8 5c2 7c2 2b28 3b2 4b28 5b28 7b8 1n17 3n39 7n19 9n37 }
Multifish 2.1: 19 Truths = {2C137 3C1379 4C1379 5C1379 7C1379 } 19 Links = { 2r2 4r8 5r2 7r8 2b4 3b46 4b6 5b46 7b4 1n17 3n39 7n19 9n37 }

;9650;TkP;5008

Multifish 1.1: 20 Truths = {2R1379 4R1379 5R1379 7R1379 9R1379 } 20 Links = { 2c8 4c2 5c8 7c2 2b28 4b8 5b2 7b28 9b28 1n17 3n39 7n17 9n39 }
Multifish 2.1: 19 Truths = {2C1379 4C1379 5C1379 7C137 9C1379 } 19 Links = { 2r8 5r2 7r8 9r2 2b46 4b46 5b6 7b4 9b4 1n17 3n39 7n17 9n39 }

Leren
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### Re: Exotic patterns a resume

Congratulations leren
I am happy to see that some have developed the search on deeper criteria than my own

Here the first mixed base (2 rows 2 columns) for a puzzle having no SK loop

The 2 next have a similar pattern

Hidden Text: Show
..1...5...2.4...6.3....7....6.28........9..2.......4.65.....1...9.8...4...7.....3;54;col;H2

Code: Select all
`46789 478    1     |369   236    23689  |5    3789   24789 789   2      589   |4     135    13589  |3789 6      1789  3     458    45689 |1569  1256   7      |289  189    12489 ----------------------------------------------------------1479  6      3459  |2     8      1345   |379  13579  1579  1478  134578 3458  |13567 9      13456  |378  2      1578  12789 13578  23589 |1357  1357   135    |4    135789 6     ----------------------------------------------------------5     348    23468 |3679  23467  23469  |1    789    2789  126   9      236   |8     123567 12356  |267  4      257   12468 148    7     |1569  12456  124569 |2689 589    3     `

19 Truths = {1R28 1C28 3R28 3C28 5R28 5C28 7R28 7C28 6N456 }
19 Links = {1r6 1b37 3r6 3b37 5r6 5b19 7r6 7b139 2n56 4n8 5n2 8n56 }

EDIT
It seems that most of the puzzles have the same pattern : 2row 2columns + cells of a mini row/column
Exploring manually the entire file is a big task
Last edited by champagne on Mon Sep 03, 2012 9:03 am, edited 1 time in total.
champagne
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### Re: Exotic patterns a resume

so far, my new solver looks for the following patterns

a) row based (+ optional cells) and columns + cells cover
b) columns based (+ optional cells) and rows + cells cover
c) 2 row + 2 cells and box cover + cells cover
d) a pattern describing one special solution you gave in that thread, but I have only one example of that pattern, so I forgot it exists.

I confirm that I don't study boxes in a pure row base or a pure column base

To anticipate remarks, I omitted in point c) to add (+ optional cells)
In all my search for multi fish, the truths can include additional cells
champagne
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