## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### solving puzzle 10

As an example of another possible path to the solution of puzzle 10, as well as for any other puzzle containing a Loop, ...

Using here only "basics" (elimination of all the candidates not in the solutions of each unit and each digit), out of the 16 remaining possible combinations of the bilocals 69B19+24B37,
15 lead to a contradiction and 1 gives the solution : [9r2c1+6r3c2]+[4r1c8+2r2c7]+[6r8c7+9r9c8]+[2r7c2+4r8c1]
JC Van Hay

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### Re: solving puzzle 10

JC Van Hay wrote:As an example of another possible path to the solution of puzzle 10, as well as for any other puzzle containing a Loop, ...

Using here only "basics" (elimination of all the candidates not in the solutions of each unit and each digit), out of the 16 remaining possible combinations of the bilocals 69B19+24B37,
15 lead to a contradiction and 1 gives the solution : [9r2c1+6r3c2]+[4r1c8+2r2c7]+[6r8c7+9r9c8]+[2r7c2+4r8c1]

I have also a code investigating that possibility, but so far, it is compiling all possible permutations within the SK loop, and this is not very exciting. A version reducing the permutations accounting the SK loop constraints would be more attractive.

Using the process based on permutations within the sk loop, I solved all puzzles having a SK loop

The process applied here (or a similar one) should solve many puzzles having an exocet pattern with the same set of rules.
champagne
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### Re: Exotic patterns a resume

champagne, on your web page you have given the wrong puzzle in your first line!

This is a notation of the SK loop that shows the linking pairs must contain one truth each:

(69-24)r2c46 = (24)r2c79 - (24)r13c8 = (24-69)r45c8 = (69)r79c8 - (69)r8c79 =
(69-24)r8c46 = (24)r8c13 - (24)r79c2 = (24-69)r56c2 = (69)r13c2 - (69)r2c13 = Loop

The UR threat is given by the four cells listed at the start of the opening and continuation lines.
It's then easy to see that if the odd terms (on the left of the weak links) have two truths it will hold a (69)UR and if the even terms have two truths it will hold a (24)UR

With (2)r5c5 being given, the cells in boxes 4 & 6 also show that the odd terms can't hold two truths as then r5c2 and r5c8 would both have to hold (4). If the givens in boxes 2 and 8 were offset in the same way, this would apply to the even terms too, which is what happens in the Easter Monster.

 typo in the loop
Last edited by David P Bird on Thu Sep 20, 2012 7:19 am, edited 1 time in total.
David P Bird
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### Re: Exotic patterns a resume

David P Bird wrote: on your web page you have given the wrong puzzle in your first line!

thanks, I'll update the file to-day this is a copy-paste bad effect

David P Bird wrote:With (2)r5c5 being given, the cells in boxes 4 & 6 also show that the odd terms can't hold two truths as then r5c2 and r5c8 would both have to hold (4). If the givens in boxes 2 and 8 were offset in the same way, this would apply to the even terms too, which is what happens in the Easter Monster.

for sure, the proof that the main belts are not valid can be done in several ways. My solver did not show it through the UR threat. I change the proof to focus on that UR potential also used in the 2 next (an key for the process used) eliminations.

Up to now, we have no clue to tell whether the main belts must be false in a SK loop structure.

To come back to JC Van Hay approach, If I am right, I found at least one puzzle where I was left with more than one scenario at the end using only basic rules to prove it false, but the puzzle was solved using eliminations common to both remaining scenarios.
champagne
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### Re: solving puzzle 10

JC Van Hay wrote:As an example of another possible path to the solution of puzzle 10, as well as for any other puzzle containing a Loop, ...

Using here only "basics" (elimination of all the candidates not in the solutions of each unit and each digit), out of the 16 remaining possible combinations of the bilocals 69B19+24B37,
15 lead to a contradiction and 1 gives the solution : [9r2c1+6r3c2]+[4r1c8+2r2c7]+[6r8c7+9r9c8]+[2r7c2+4r8c1]

I tried to implement that process to prepare a revision of the coding.
I did not try to stay within basic rules, but at least for one scenario, I could not prove it false without using an XWing derived pattern.

I put the corresponding path in the page
puz10 path as of JC Van Hay[/quote]

the first path remains at the same place (wrong puzzle replaced by the right one)

puz10 path[/quote]

I find the result very impressive, although a manual work can include errors.

The next step will be to adjust the code.
champagne
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### Re: solving puzzle 10

JC Van Hay wrote:As an example of another possible path to the solution of puzzle 10, as well as for any other puzzle containing a Loop, ...

Using here only "basics" (elimination of all the candidates not in the solutions of each unit and each digit), out of the 16 remaining possible combinations of the bilocals 69B19+24B37,
15 lead to a contradiction and 1 gives the solution : [9r2c1+6r3c2]+[4r1c8+2r2c7]+[6r8c7+9r9c8]+[2r7c2+4r8c1]

I implemented that process and had a surprise showing an error in the manual solution pointed above.
Here is the problem, with a possible misunderstanding of what JC Van Hay is doing

With the following scenario (always in puzzle 10)

9r1c2 6r2c3 4r2c9 2r3c8 2r7c2 6r7c8 4r8c1 9r8c9

and the set of rules I am using, I am locked here

Code: Select all
2    9    137  |14   345   34    |58   78   6
37   5    6    |29   8     29    |37   1    4
8    13   4    |16   3567  367   |9    2    35
------------------------------------------------
59   7    28   |3    469   1     |26   49   58
35   46   13   |8    2     469   |15   49   7
19   46   28   |7    469   5     |26   3    18
------------------------------------------------
137  2    9    |5    37    8     |4    6    13
4    8    37   |26   1     26    |37   5    9
6    13   5    |49   3479  3479  |18   78   2

No problem to continue with 37 r2c17 r8c37 establishing 7r2c1 7r8c3, and showing quickly the contradiction, but we are far beyond the basic rules. I already used derived pairs, hidden pairs and derived XW to come to that point.

Question to JC Van Hay:

What do you do with that scenario (how do you conclude it is false)
champagne
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### Re: solving puzzle 10

champagne wrote:Question to JC Van Hay:
What do you do with that scenario (how do you conclude it is false)

The XW is not necessary, but well the Skyscraper 7C38 :=> -7r8c7 -> contradiction using only singles.

Complementary informations :

1. To write it again in another way, I use "basics" = Locked Subsets + all single digit techniques.
2. I solved in the same way the puzzles 68, 73, 83, 87, 88, 89 and 90 here. Puzzle 73 is somewhat special as 5 cases need more than singles and 3 cases need an XYChain after "basics".
JC Van Hay

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### Re: solving puzzle 10

JC Van Hay wrote:
champagne wrote:Question to JC Van Hay:
What do you do with that scenario (how do you conclude it is false)

The XW is not necessary, but well the Skyscraper 7C38 :=> -7r8c7 -> contradiction using only singles.

Complementary informations :

1. To write it again in another way, I use "basics" = Locked Subsets + all single digit techniques.
2. I solved in the same way the puzzles 68, 73, 83, 87, 88, 89 and 90 here. Puzzle 73 is somewhat special as 5 cases need more than singles and 3 cases need an XYChain after "basics".

Thank you very much, it's clear now.

I have also UR's in my nset of rules, but not more so far than XW and pairs. I 'll add in priority skyscrapers and kites.
In that specific situation, after assignment of candidates common to both remaining scenarios, the puzzle is solved with not more than a dynamic process (rating below 9)

I'll adjust later the posted solution to the path seen by my solver with that scenario using the skyscraper.

BTW, the link "here" points on a thread mute since 2008 and your first entry is 2010
Does it mean that the puzzle numbers are coming out of that thread or are your numbers related to the list of potential hardest
champagne
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### Re: solving puzzle 10

champagne wrote: I solved in the same way the puzzles 68, 73, 83, 87, 88, 89 and 90 here.
...
BTW, the link "here" points on a thread mute since 2008 and your first entry is 2010
Does it mean that the puzzle numbers are coming out of that thread or are your numbers related to the list of potential hardest
They are coming from that thread : first post "Last edited by Eioru on Sat Oct 11, 2008 3:45 am, edited 86 times in total."
I only identified : [number SER : name of the puzzle, number in 01 file 1 ]
68 96 : ?,
73 101 : ?,
83 111 : St Patrick 16, 4032
87 115 : OW0801008,
88 116 : Easter Monster, 78
89 117 : OW081006,
90 118 : ?,
JC Van Hay

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### Re: Exotic patterns a resume

I applied JC VAN Hay strategy to the entire file of puzzles having the SK loop of my data base

My set of rules is limited to SE dynamic plus rule + UR's + kites and sky scrappers.

I have still one bug to identify and fix, but I am left in the last test with 20 unsolved puzzles only.

I do not intend to introduce in the extended dynamic plus set of rules the chains (this is the field of nested chains in Sudoku Explainer), but I have still to implement some effects of the non valid scenario? I'll then see if the resisiting puzzles are still there;

In the first resisting puzzle (number 60), one scenario ended with a PM containing only pairs. This could be an extension of the dynamic plus rules.
champagne
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### Re: Exotic patterns a resume

I finished the coding of the solution for puzzles having a sk loop using JC Van Hay strategy (partly).
The last step was to deliver to the standard process the results of the scenario analysis

I have now 9 puzzles resisting to the current code as it is in the google project.
Analysis of these 9 puzzles could take time although they seem to be very close and likely share the same property explaining why they resisted to the code.

Most of them belong of seem to be derived from tarek's pearly collection

Code: Select all
..8...5...6...3.7.4.......1.7..32......9.5......67..2.5.......4.2.3...6...1...8..;7654;TkP;3138
9.......1.3...4.7...6...2...5.3.2.......6........78.5...2...6...4.7...3.1.......9;8400;tax;tarek-ultra-0204
98.7.....7.6.......54...7..4..6..9......5..3......2..1..94..6......1..5......3..2;8402;GP;H2040
1....6.8....7....2....3.5.....5....7.6...4.1.....2.3...14..8...6.2....4.89.......;8405;elev;H235
1.....9...3...7.4...5.....2.....6.7.....1.....4.3.8...9.......5.7.8...3...2...1..;8668;tax;tarek071223170000- 95895
..7...9...3...5.4.6.......8.4..51......7.2......34..1.9.......6.1.5...3...8...7..;9712;TkP;3164
..2...3...7...1.5.6.......8.4...5......43.......1.7.4.8.......2.5.7...1...3...6..;9717;TkP;3101
..9...7...4...1.2.8.......5.2...3......9.6.......12.3.7.......8.3.1...4...5...9..;9762;TkP;3715
..1...2...3...4.5.6.......7.....3.8.....1.....4.9.8...7.......1.5.8...4...2...6..;38022;ig;champagne
champagne
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### death of an old conjecture

Here is an interesting puzzle published on a French forum.

.........1....72...7..84.6...8....93.6..4..7.93....6...9.73..8...59....2.........

after easy moves, we come to that PM
Code: Select all
A     B    C     |D    E     F     |G      H   I
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

we can then see the SK loop

Code: Select all
r3c13 r3c79 r12c8 r89c8 r7c79 r7c13 r89c2 r12c2
25   39    15    34    15    46    12    48    25

As noticed JC Van Hay, the solution is one of the 2 main belts, killing an old conjecture telling that the 2 main belts should always be false.
champagne
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### Re: death of an old conjecture

champagne wrote:... killing an old conjecture telling that the 2 main belts should always be false.

Agreed. Assuming I correctly understand what you mean by "main belt" (ugh), it's rather easy to generate minimal puzzles with an sk-loop with this property.
ronk
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### Re: death of an old conjecture

ronk wrote:Agreed. Assuming I correctly understand what you mean by "main belt" (ugh), it's rather easy to generate minimal puzzles with an sk-loop with this property.

Interesting

I never believed in that conjecture, but I have no idea about a process to generate such puzzles.

We have seen thousands of puzzles having the SK loop, that one is the first I identified with one of the main belts being the solution for the puzzle.

PS main belt is one on the 2 complete potential solutions along the SK loop . This is always the start of any solution I show for a sk loop containing puzzle
champagne
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### Re: Exotic patterns a resume

Champagne wrote:
Here is an interesting puzzle published on a French forum.
.........1....72...7..84.6...8....93.6..4..7.93....6...9.73..8...59....2.........

I agree this is a very unusual one. With the many SK loops I have studied there is a corresponding 4 digit rank zero row based multifish, whose base set corresponds to the digits in the pairs of linking digits in the boxes of the SK loop. Here we only have the 3 digits: 125. So far I can't construct a complementary multifish. Any thoughts?

Phil
pjb
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