Solving Hardest Puzzles

Advanced methods and approaches for solving Sudoku puzzles

Solving Hardest Puzzles

Postby champagne » Wed Jul 28, 2010 9:41 am

I open this new thread using gif files .
the corresponding html file is available on my website at that point
http://gpenet.pagesperso-orange.fr/UM/U ... s/HP__.htm

note : links are not working in the gif file

Image
Last edited by champagne on Wed Jul 28, 2010 9:44 am, edited 1 time in total.
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Re: Solving Hardest Puzzles

Postby champagne » Wed Jul 28, 2010 9:41 am

Last edited by champagne on Wed Jul 28, 2010 9:50 am, edited 1 time in total.
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Re: Solving Hardest Puzzles

Postby champagne » Wed Jul 28, 2010 9:42 am

next gif text can be seen here
http://gpenet.pagesperso-orange.fr/UM/U ... s/HP04.htm
the file containing puzzles of game 112 having the sk loop is here
http://gpenet.pagesperso-orange.fr/downloads/KL_G112


Image
Last edited by champagne on Sat Jul 31, 2010 4:33 pm, edited 2 times in total.
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Re: Solving Hardest Puzzles

Postby champagne » Thu Jul 29, 2010 3:02 pm

locked for post 4 typical solutions among hardest
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Re: Solving Hardest Puzzles

Postby ttt » Fri Jul 30, 2010 5:47 pm

Hi my Big Brother :D,
I’m back by your Thread and from now I’ll consider to spend my free time for this.
Look at tarek's thread and your last list then try on below first:

Code: Select all
100000005000000039005030800009050080700002000010400000000080050020007000400100600 colBF2 326
000001003000000090006090800008000009700002600010400500003080050020100000400007000 colefg colg182


Calling to Steve K, ronk, Allan Barker, RW, abi, StrmCkr... and anyone: HOW YOU CAN ATTACK above puzzles then downgrade them to hard puzzles – not hardest :D

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Re: Solving Hardest Puzzles

Postby champagne » Fri Jul 30, 2010 9:00 pm

ttt wrote:Hi my Big Brother :D,
I’m back by your Thread and from now I’ll consider to spend my free time for this.
Look at tarek's thread and your last list then try on below first:

Code: Select all
100000005000000039005030800009050080700002000010400000000080050020007000400100600 colBF2 326
000001003000000090006090800008000009700002600010400500003080050020100000400007000 colefg colg182


Calling to Steve K, ronk, Allan Barker, RW, abi, StrmCkr... and anyone: HOW YOU CAN ATTACK above puzzles then downgrade them to hard puzzles – not hardest :D

ttt

Hi ttt

These 2 have none of the pattens described here (contrary to Platinum Blonde as you could see)

I'll give you to morrow some ideas about the potential using Allan Barker model.

Next post, nearly ready should be dedicated to the SK loop

champagne

PS: I see still a lot to do using AUR's, your specialty. I will select puzzles where you shoul be in a position to find interestig things
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Re: Solving Hardest Puzzles

Postby champagne » Sat Jul 31, 2010 8:16 am

Hi "ttt",

As promised some data linked to your 2 puzzles.

colBF2 326

Code: Select all
||1     346789 234678 |26789 24679 4689  |247    2467  5     
||268   4678   24678  |25678 12467 14568 |1247   3     9     
||269   4679   5      |2679  3     1469  |8      12467 12467 
-----------------------------------------------------------
||236   346    9      |367   5     136   |12347  8     123467
||7     34568  3468   |3689  169   2     |13459  1469  1346   
||23568 1      2368   |4     679   3689  |23579  2679  2367   
-----------------------------------------------------------
||369   3679   1367   |2369  8     3469  |123479 5     12347 
||35689 2      1368   |3569  469   7     |1349   149   1348   
||4     35789  378    |1     29    359   |6      279   2378   

That puzzle has a potential base fo an EXOCET in r12c7, but the only possible target could be r47c9,
which is unusal and does not work.


the potential response with floors 1247 is very low

2:r1c4
N:r12c5 r47c9
nperm:78
the only positive point, linked to the previous remark is that r4c79 are potentially limited to 1247.

If I include AUR's, the potential inctreases substantially.

1:r7c9
2:r1c48r2c5
4:r1c8r2c6
7:r1c4r2c2r3c4
N:r12c5r47c9
nperm:36

This is a typical structure where it should be possible to find a SLG including AUR's, likely with a high rank.
Here is the reduced PM

Code: Select all
X     47+   247+  |27+   247+  4+    |247   247+  X     
2+    47+   247+  |27+   1247+ 14+   |1247  X     X     
2+    47+   X     |27+   X     14+   |X     1247+ 1247+

2+    4+    X     |7+    X     1+    |1247+ X     1247+
X     4+    4+    |X     1+    X     |14+   14+   14+   
2+    X     2+    |X     7+    X     |27+   27+   27+   

X     7+    17+   |2+    X     4+    |1247+ X     1247+
X     X     1+    |X     4+    X     |14+   14+   14+   
X     7+    7+    |X     2+    X     |X     27+   27+ 


Another possibility appears including AUR's, with floors 147

1:r2c6r45c7r78c9
4:r3c2r4c9
7:r2c4r3c8r6c7r9c2
N:r2c5
nperm:51 floors1457



Code: Select all
X     47+   47+   |7+    47+   4+    |47+   47+   X     
X     47+   47+   |57+   147+  145+  |147+  X     X     
X     47+   X     |7+    X     14+   |X     147+  147+ 

X     4+    X     |7+    X     1+    |147+  X     147+ 
X     45+   4+    |X     1+    X     |145+  14+   14+   
5+    X     X     |X     7+    X     |57+   7+    7+   

X     7+    17+   |X     X     4+    |147+  X     147+ 
5+    X     1+    |5+    4+    X     |14+   14+   14+   
X     57+   7+    |X     X     5+    |X     7+    7+   


Not as interesting as the first one, (the potential target is not there), but to be considered as well.


colefg colg182
has a very limited potential

Code: Select all
||2589  45789 24579 |25678  24567  1     |247   2467  3     
||12358 34578 12457 |235678 234567 34568 |1247  9     124567
||1235  3457  6     |2357   9      345   |8     1247  12457 
----------------------------------------------------------
||2356  3456  8     |3567   13567  356   |12347 12347 9     
||7     3459  459   |89     135    2     |6     1348  148   
||2369  1     29    |4      367    89    |5     2378  278   
----------------------------------------------------------
||169   679   3     |269    8      469   |12479 5     12467 
||5689  2     579   |1      3456   34569 |3479  34678 4678   
||4     5689  159   |23569  2356   7     |1239  12368 1268 

same potential base and a classical potential target r4c8 r7c9.

The potential for floors 1247 without AURs is poor

1:r9c9
2:r6c1
4:r5c2
N:r12c3r4c8r7c9
nperm:131

but includes the target

Again, if I includes AUR's, the potential increases with no change in cells limited to 1247.

1:r9c9
2:r1c8r2c9r6c1
4:r1c8r2c3r5c2
7:r1c8r3c2
N:r12c3r4c8r7c9
nperm:50 floors1247

It should be again possible to find a SLG of a relatively high rank using AUR's.
here the reduced PM

Code: Select all
2+    47+   247+  |27+   247+  X     |247   247+  X     
12+   47+   1247+ |27+   247+  4+    |1247  X     1247+
12+   47+   X     |27+   X     4+    |X     1247  1247+

2+    4+    X     |7+    17+   X     |1247+ 1247+ X     
X     4+    4+    |X     1+    X     |X     14+   14+   
2+    X     2+    |X     7+    X     |X     27+   27+   

1+    7+    X     |2+    X     4+    |1247+ X     1247+
X     X     7+    |X     4+    4+    |47+   47+   47+   
X     X     1+    |2+    2+    X     |12+   12+   12+   


good luck

champagne
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Re: Solving Hardest Puzzles

Postby ttt » Thu Nov 04, 2010 5:06 pm

Hi All,
As reference: deductions for eleven's puzzle after ronk’s deductions. It’s too complex to present as diagrams so look like T&E, but if use (249)r56c4 as “Floor Pattern” then you can see it more simpler :D

Code: Select all
..9...4...7.3...2.8...6...71..8....6....1..7.....56...3....5..1.4.....9...2...7..


Using Xsudo V.99m:
eleven's puzzle: Raw Rank = 10 (linksets - sets)
30 Sets = {1R1 249R3 2479R7 6R8 24679C1 1C2 6C7 249C9 25N1 2N3 56789N4 1B7 6B3 7B2}
40 Links = {6r2 249r5 2479r6 1r8 1r9 12479c4 7c5 2c6 168n1 7n5 13n6 7n7 1n8 6n9 1b1 2b1489 4b19 5b1 6b78 7b7 9b347}
4 AURs = (92)R65C41, (94)R65C41, (92)R65C94, (94)R65C94
AUR points {aur 2r5c1 4r5c1 2r5c9 4r5c9 9r6c4 }
10 Eliminations --> r9c48<>4, r56c2<>2, r13c4<>2, r5c2<>9, r6c4<>9, r7c5<>9, r8c6<>2

Image

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Re: Solving Hardest Puzzles

Postby StrmCkr » Fri Nov 05, 2010 7:38 am

000001003000000090006090800008000009700002600010400500003080050020100000400007000 colefg colg182

i was quasi attempting a solution path but i was using an issopmorph
Code: Select all
 *-----------*
 |5..|1..|..3|
 |.2.|.4.|...|
 |..8|7..|9..|
 |---+---+---|
 |...|..4|...|
 |.1.|2..|.4.|
 |...|.6.|..8|
 |---+---+---|
 |..3|...|8..|
 |.6.|..7|.2.|
 |9..|...|..5|
 *-----------*


not sure if it helps:

i found a nested sk-loop in the grid in its usual spot problem is first proving that R2C8 = 6 or linking it back to the sk-loop n e on see a way?? {ive been trying}

this is the truth/set with R2C8 = 6

Hidd [23,224] 42 Candidates,
15 Truths = {28N1 1379N2 28N3 28N7 379N8 28N9}
19 Links = {1r28 4r8 7r2 1c18 4c2 7c28 39b1 15b3 458b7 379b9}
18 Eliminations --> r2c13<>7, r4c28<>7, r6c28<>7, r67c2<>4, r46c8<>1, r7c9<>79, r9c7<>37,
r1c3<>9, r3c1<>3, r8c5<>1, r8c4<>4,

Code: Select all
.---------------------.----------------------.-----------------------.
| 5      479    4679  | 1      289     2689  | 24      678     3     |
| 1367   2      1679  | 35689  4       35689 | 1567    15678   167   |
| 1346   34     8     | 7      235     2356  | 9       156     24    |
:---------------------+----------------------+-----------------------:
| 23678  35789  25679 | 3589   135789  4     | 123567  135679  12679 |
| 3678   1      5679  | 2      35789   3589  | 3567    4       679   |
| 2347   34579  24579 | 359    6       1359  | 12357   13579   8     |
:---------------------+----------------------+-----------------------:
| 1247   457    3     | 4569   1259    12569 | 8       1679    14679 |
| 148    6      145   | 34589  13589   7     | 134     2       149   |
| 9      478    1247  | 3468   1238    12368 | 13467   1367    5     |
'---------------------'----------------------'-----------------------'
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Re: Solving Hardest Puzzles

Postby ronk » Fri Nov 05, 2010 1:11 pm

StrmCkr wrote:000001003000000090006090800008000009700002600010400500003080050020100000400007000 colefg colg182

i was quasi attempting a solution path but i was using an issopmorph
Code: Select all
 *-----------*
 |5..|1..|..3|
 |.2.|.4.|...|
 |..8|7..|9..|
 |---+---+---|
 |...|..4|...|
 |.1.|2..|.4.|
 |...|.6.|..8|
 |---+---+---|
 |..3|...|8..|
 |.6.|..7|.2.|
 |9..|...|..5|
 *-----------*

I like the idea of morphing a puzzle to maximize symmetry, but why change clue values too? It makes comparison to prior work, whether or not posted, unnecessarily difficult.
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Re: Solving Hardest Puzzles

Postby StrmCkr » Fri Nov 05, 2010 5:18 pm

I like the idea of morphing a puzzle to maximize symmetry, but why change clue values too? It makes comparison to prior work, whether or not posted, unnecessarily difficult.


i changed clue values to make it look similar to Strmckr's 11.4 and i was using ideas from my work on my own puzzle to solve it as they are pretty close with some slight differences

(actually it was so i could test if i could simply copy paste the sk-loop linksets from my own puzzle onto the same grid if the clues where identical but that didn't go so good using allans software... end up having to manually build it any way )

i should have changed it back to the original code before i posted it..... i'll edit the puzzle back to normal but leave it morphed...


edit: here is the puzzled changed back (i changed the middle band slightly for a slightly better symmetrical view)
with R2C8 =3, the sk-loop is in the regular spot

Hidd [22,230] 44 Candidates,
16 Truths = {28N1 1379N2 28N3 28N7 1379N8 28N9}
21 Links = {1r1 5r2 6r28 9r8 5c28 6c18 9c2 24b1 567b3 179b7 245b9}
23 Eliminations, 1 Assignment --> r145c8<>5, r1c56<>1, r2c13<>5, r45c2<>5, r47c2<>9, r19c7<>5, r45c8<>6,
r7c9<>45, r1c3<>4, r3c1<>2, r3c9<>6, r8c6<>6, r8c4<>9, r9c7<>2,
r1c8=1

Code: Select all
 *-----------*
 |7..|6..|..2|
 |.8.|..9|...|
 |..1|5..|4..|
 |---+---+---|
 |...|..3|..1|
 |...|.9.|...|
 |.6.|8..|.9.|
 |---+---+---|
 |..2|...|1..|
 |.3.|.5.|.8.|
 |4..|...|..7|
 *-----------*
Some do, some teach, the rest look it up.
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