The New Sudoku Players' Forum

by **champagne** » Thu Jan 15, 2009 5:06 am

ronk wrote:
champagne wrote:I proposed "bi bi" because it can be used indiferently in English and in French.

Most search engines discard two-letter words. For that reason alone, "bi bi" is an unwise choice.

ok ronk

Unhappily in english BB sounds "bi bi "

but in french it sounds " be be"

I see that this is not yet clear in writing

May be a specialist in language can help me to explain it it the appropriate way

anyway; I am waiting for a counter proposal from English Native Speakers

champagne.

by **champagne** » Thu Jan 15, 2009 8:36 pm

ronk wrote:
champagne wrote:I proposed "bi bi" because it can be used indiferently in English and in French.

Most search engines discard two-letter words. For that reason alone, "bi bi" is an unwise choice.

What would be your proposal :?:

by **champagne** » Thu Jan 15, 2009 8:38 pm

Hi,

this is a small data base for "bi bi" pattern analysis.
It contains about 80% of the puzzles published two days ago by tarek in the new "hardest sudoku" thread.
All of them have some "bi bi" pattern.
3BB indicate a "bi bi" pattern in the form 123 123
BB is a pattern 1234 1234
bb indicates a partial pattern bb(2) means that only 2 super candidates share the property.
SK indicate that the puzzle has the SK loop.

The first number after "id" of the puzzle is the run time in seconds without considering BB patterns.
When this number was small, I did not consider other data, except for "Fata Morgana". The cut off is about 10 seconds.
The second number is the run time including BB pattern processng. This reflects the present status of the program.
* indicates that some "double XWing" eliminations of super candidates have been found in that puzzle.

First group is 3BB puzzles ranked as in original list
Second group is BB puzzles same ranking
Thirs group is a small list of other situations as example SK + BB

champagne

.......39.8......5..9.6.8....5.9...67....2......4.......3.8..5..2.7..6..4.....1.. colx062,coloin 2.8 3BB r12c7 r4c8 r7c9
.....4.....2.3.....5.7....9..4..2.8..985....63.........8....79....8...6...5.1...8 tarx0035,tarek 28.1 1.5 *3BB r9c78 r7c4 r8c2
........2..1...7...3..5..9......6.4...3.4.8...4.5.9....9..6..3...2...1..7....3... tarx0006;Trompe_l'oeil 33.4 1.5 *3BB r5c46 r4c2 r6c8
..9.......6...3...1...7...54...52..7.....6.4..3.9.....2......1.....2.57...48....2 tarx0064,tarek 5.1 *3BB r9c78 r7c5 r8c1
.......89.....1.35..3.5......5.6...8.7...2...1..4.......6.9..5..2.7..6..4........ colx180,coloin 22.7 23.5 *BB r12c7 r4c8 r7c9
.....5..3..9....4..81.4.......7.......4..2..68...14.3.......2...4...6..79...5..1. tarx0108,tarek 49.5 1.9 *3BB r1c23 r2c5 r3c8
........3..1..9.6..5..8.4.....9...8...867.....1....2....6..7.2..3.8..5..4.......8 tarx0119,tarek 63.5 1.7 *3BB r6c45 r4c3 r5c8
........6..2....4..1...798....79.....8..5......3..8.1...6....2..9...51..4.......8 tarx0010,tarek *53.9 2.0 3BB r6c45 r4c2 r5c7
.....5.....3.7...8.9.8...4...5.....2.8.6..4..7...3......2...69...4...1...1.9....4 tarx0062,tarek 8.3 *3BB r78c9 r3c7 r5c8
........7..9.5.2..1....6.8....5..6...9.....3...64.2....8.6.......4.2.9..7......61 tarx0004,tarek, 5.3 *3BB r5c46 r4c3 r6c7
........7..1..9.8..3.6..5.9.9..25.......6....3..9...4...7....91.2.5..3..8........ tarx0003,tarek 6.1 *3BB r6c56 r4c7 r5c2
.....1.....7.2.....9.6.8..5..1..7....6.9....42.9.........8...59.8....4....6.3...8 tarx0079,tarek 4.7 *3BB r9c78 r7c2 r8c4
........6..9...4...1..7..8....7.1.3.1.8.3.5...3...2....8..2..1...6...9..4..3..... tarx0114,tarek 4.3 *3BB r5c46 r4c2 r6c8
..1.......5...6..16.7...........1..3...4.5.8..9..2..5...5..3..7....8..4..3.5..2.. tarx0014,tarek 5.8 *3BB r13c2 r4c3 r7c1
........7.2.4...6.1.....5...9...2.4....8..6..6..9.......5..3....3..8..2.7....4..1 TungstonRod,coloin 9.7 3BB r56c6 r2c5 r8c4
........2..8..91..5......4....9.7.....7.3.8.....8.1.3..4..6...5..97..3..2........ tarx0052,tarek 2.5 *3BB r46c5 r2c4 r8c6
........91......35..9.3.8....3.5...67....2......4.......6.8..9..2.7..6..4.....1.. weekender1,coloin 56.8 3.6 3BB r12c7 r4c8 r7c9
........3..1..56...9..4..7......9.5.7.......8.5.4.2....8..2..9...35..1..6........ tarx0001;Fata_Morgana 7.1 1.2 *3BB r5c46 r4c2 r6c8
........5..8..79...6..1..4....1.2.7.4...7...3.7.6......3..2..6...5...8..9.......7 tarx0002,tarek 32.4 2.3 *3BB r5c46 r4c2 r6c8
........9..6.1.7.24......3......12...6..2..5...28.7....3......4..8.7.6..9..1..... tarx0130,tarek 8.0 3BB r5c46 r4c3 r6c7
........2..8.1.9..5....3.4....1.93...6..3..8...37......4......53.1.7.8..2........ tarx0140,tarek 8.3 3BB r5c46 r4c3 r6c7
..6.......3...7..11.7.............9.3....6..5.5.8..2....3..5..6...2...4..4..9.8.. tarx0137,tarek 42.3 1.3 3BB r13c2 r5c3 r7c1
.......1......4.32.2..3.5.......7....4..2...5..89..4....78..6...3..1..5.9........ coly004,coloin 4.4 *3BB r12c7 r5c8 r8c9
.....7..8.3..2..9...84..3....6.......8.5..6..5.4..........9.8.2.1.....7.8..3..4.. tarx0121,tarek 42.3 1.3 *3BB r46c2 r3c1 r9c3
........9..1...6...5..7..4....4.7.8...3.8...5.8...2....78.2..5..39...1..6........ tarx0011,tarek 7.2 *3BB r5c46 r4c2 r6c8
.......93.8......5..3.6.8....5.9...67....2......4.......9.8..5..2.7..6..4.....1.. colx1665,coloin 4.3 3BB r12c7 r4c8 r7c9
........2..7...1...3..9..4......9.6.6...3.4.5.4...8....6..4..5...2...7..1..8..... tarx0145,tarek 5.5 *3BB r5c46 r4c2 r6c8
........6..5.3.7..2....8.1....9..8...5..8..4...87.3....1.3.......7.9.5..6.......2 tarx0013,tarek 23.8 1.9 *3BB r5c46 r4c3 r6c7
........8..3.9.4..6....7.1....5.97...3.....2...74........7....6..4.5.3..81....... tarx0007,tarek 6.4 *3BB r5c46 r4c3 r6c7
.2.4..7.........32.......94.9.2...7...6..5...8...1....5.1..8....3.9....7......6.. colx467,coloin 2.1 3BB r23c7 r4c9 r8c8
.....6.....1.2...3.3.8...7...6.....5.5.3..7..2....1.......9..4...5...98..9.4....7 tarx0008,tarek 53.2 3.2 3BB r78c9 r3c7 r5c8
........6..4.7.9.28......3......72...4..2..1...25.9....3......8..9.5.7..6......9. tarx0103,tarek 4.7 3BB r5c46 r4c3 r6c7
........7..4.2.6..8.....31......29...4..9..3...95.6....1......8..6.5.2..7......6. tarx0139,tarek 3.0 3BB r5c46 r4c3 r6c7
1.......2....1..3...5..34....2..1..4....8.7..6..9.......1..5.4.8.....5..9...6.... coly001,coloin 3.3 3BB r12c7 r4c8 r7c9
..8.......5...8..11.9.4........3......5..9..4.4.6...7.......6..5....4.29.2..7..3. tarx0061,tarek 28.6 2.9 3BB r13c2 r5c1 r8c3
........7..2...6...8..1..9....9.1.3.3...8...4.9...5....3..9..4...7...2..6..5..... tarx0146,tarek 5.0 *3BB r5c46 r4c2 r6c8

....9..5..1.....3...23..7....45...7.8.....2.......64...9..1.....8..6......54....7 coly013,coloin 1.4 BB r12c7 r4c9 r8c3 BB r56c8 r3c9 r9c7
...1....87.......9..6.9.5....8.6...5.....23...7.4..6....3.8..5..2...1....4....... coly012,coloin 3.7 BB r12c7 r4c8 r7c9 BB r56c9 r3c8 r7c7
........7..2..96..8...6...3....92.....46..5...1..54.....5.4.9...3.....7.1.......8 tarx0009,tarek 15.1 13.8 *BB r46c4 r2c5 r7c6
.....6..5.1.....2...9.3.4......7......48.9...8..4.39....7.8.3...5.....1.2.......6 tarx0012,tarek 3.2 BB r4c46 r5c7 r6c3
.......1...6....23.2..3.4..8....5....3..1...4..96........9..7...1..2..4.5....8... coly002,coloin 7.1 BB r12c7 r5c8 r8c9
........5..6..87..3......9....1.7.4...7...8...4...6....9..8...3..16..4..5...2.... tarx0067,tarek 2.5 BB r46c5 r2c4 r8c6
...2....87.......9..3.9.5....8.3...51.....3.....4..6....6.8..5..7...1...2....4... coly007,coloin 4.3 BB r12c7 r4c8 r7c9 BB r56c9 r3c8 r7c7
.1......8.7...4..9..3.9.5....8.3...5.2....3.....4..6....6.8..5.2....1......7..... coly010,coloin, 2.6 BB r2c17 r4c8 r7c9 BB r56c9 r3c8 r7r7
...1....8.7......9..3.9.5....8.3...57....23.....4..6....6.8..5.4....1...2........ coly006,coloin, 3.7 BB r2c17 r4c8 r7c9 BB r56c9 r3c8 r7r7
...1....87.......9..3.9.5....9.3...5.....23.....4..6....6.8..5.47...1...2........ coly008,coloin, 3.4 BB r2c17 r4c8 r7c9 BB r56c9 r3c8 r7r7
.....5..4.9.....2...6.7.3.....7..8....86.....13..8......3.1.6...2......54......9. tarx0068,tarek 16.0 18.*BB r6c46 r4c3 r5c7
........6..5..8.9..3.4..7....491........8..4.5....42....1..9.5..6....4.37........ tarx0005,tarek, 6.4 *BB r6c45 r4c8 r5c3
.....1.39........5..3.5.6....8.9...67....28..1..4.......9.8..5..2.......4..7..... colx001,coloin 28.6 BB r12c7 r4c8 r7c9
1.......5.2.4...6...3...7...9...4........9.8.8.26.........5.1...6.9...2...7.....3 colx134,coloin 32.0 BB r6c56 r4c8 r5c2
.......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7..... Golden_Nugget,tarek 56.7 30 *BB r12c7 r4c8 r7c9
........6..5..18...9...8.7....8.2.....3.1.2..4..5.3....6.....9...83..1..7.......4 tarx0075,tarek 22.5 18.3 *BB r46c5 r2c4 r8c6
3.......2.8..7..1...69......5.7.4...........8...51..7...9...3...1..4..8.2.......6 Pearly6000-1801,tarek, 33.0 21.6 *BB r5c46 r4c8 r6c2
7....4..8.1......9..6.9.5....8.6...5.....23.....4..6....3.8..5.2....1......7..... coly009,coloin 1.5 BB r12c7 r4c8 r7c9 BB r56c9 r3c8 r7c7
1.......7.2.4...6...3...5...9..4........62.4....9..8....5.....3.6.2...8.7....1... 67.2 77.9 SilverPlate,coloin BB r6c56 r4c8 r5c2
9....4....3..6..7...5...8...2.1.6.......7...3...2...1...8...9...7..1..6.4.......5 tarek071,tarek 29.6 29.6 *BB r5c46 r4c8 r6c2
1.......7.2.4...6...3...5...9..82.......9..8....6..4....5...1...6.8...2.7....3... BronzeMedalian,coloin 16.5 16 *BB r6c56 r4c8 r5c2

.....1..7....6..2.8..9..3...954....3..3...4..4......8......7..6.1..2....5..3..9.. tarx0018,tarek 2.5 *bb(2) r6c23 r4c7 r5c4
..4.....9.1...3.7.6.....2.......8....5..3..8....1.5.....2.....4.7.3...1.9...7.6.. tarx0037,tarek 7.0 SK *BB r46c5 r2c4 r8c6
1.........2.4...6...3...5.1.4..86.......49.8....2.....5.7...3...6.9...4.........7 CloudyBay,coloin 5.1 SK *BB r6c56 r4c8 r5c2
1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....5..34...7.....1.6.......7 dukdiamond1,coloin 3.2 SK *bb(2)r5c1289 r3c6 r7c4

by **ttt** » Thu Jan 15, 2009 9:28 pm

Hi champagne,
I don’t know why Platinum Blonde (hardest puzzle by q1 & q2) that has floor (679)r12c7, is not on your list…
I’m difficult to find “bi bi” by my eyes

, but that puzzle is solved the same way as Fata Morgana, Trompe L'oeil…

ttt

by **champagne** » Thu Jan 15, 2009 9:44 pm

ttt wrote:Hi champagne,
I don’t know why Platinum Blonde (hardest puzzle by q1 & q2) that has floor (679)r12c7, is not on your list…
I’m difficult to find “bi bi” by my eyes , but that puzzle is solved the same way as Fata Morgana, Trompe L'oeil…

ttt

I checked in the print, the program did not find a "bi bi" in that case. which does not prevent to solve it in a similar way.

Can be also a bug in the program.

I'll see later. Good remark.

champagne

by **champagne** » Fri Jan 16, 2009 12:01 am

ttt wrote:Hi champagne,
I don’t know why Platinum Blonde (hardest puzzle by q1 & q2) that has floor (679)r12c7, is not on your list…
I’m difficult to find “bi bi” by my eyes , but that puzzle is solved the same way as Fata Morgana, Trompe L'oeil…

ttt

I checked more carefully the print for Platinium Blonde.
As I told you, no full "bi bi" pattern found.

Starting from r12c7, several elementary "bi bi" came. As usual, most of have no weak link effect and should be hidden regarding present processing. These ones are relevant;

6r12c7 => r4c8 r8c3
7r12c7 => r4c8 r8c4
9r12c7 => r4c8 r9c4

One cell is common to the three, the other not. It is not a full "bi bi".

champagne

by **ronk** » Fri Jan 16, 2009 1:58 am

champagne wrote:
ronk wrote:
champagne wrote:I proposed "bi bi" because it can be used indiferently in English and in French.

Most search engines discard two-letter words. For that reason alone, "bi bi" is an unwise choice.

What would be your proposal

I've sometimes had dogs for a full year before deciding on a name, so you're asking the wrong person.

by **ttt** » Fri Jan 16, 2009 2:52 am

champagne wrote:I checked more carefully the print for Platinium Blonde.
As I told you, no full "bi bi" pattern found.

Yes, I see …
That meant, hardest puzzles should be checked by players. Right? Now, hardest puzzle based on q1 & q2 is heavily downgraded in the ranking (ER9.2 after two moves)

ttt

by **ronk** » Fri Jan 16, 2009 4:28 am

re Platinum Blonde champagne wrote:Starting from r12c7, several elementary "bi bi" came. As usual, most of have no weak link effect and should be hidden regarding present processing. These ones are relevant;

6r12c7 => r4c8 r8c3
7r12c7 => r4c8 r8c4
9r12c7 => r4c8 r9c4

One cell is common to the three, the other not. It is not a full "bi bi".

Perhaps you can propagate implications with grouped candidates:

(xy)r12c7 => (x|y)r4c8 & (y|x)r7c89

where x,y is any two of 6,7,9

by **champagne** » Fri Jan 16, 2009 4:34 am

ronk wrote:
re Platinum Blonde champagne wrote:Starting from r12c7, several elementary "bi bi" came. As usual, most of have no weak link effect and should be hidden regarding present processing. These ones are relevant;

6r12c7 => r4c8 r8c3
7r12c7 => r4c8 r8c4
9r12c7 => r4c8 r9c4

One cell is common to the three, the other not. It is not a full "bi bi".

Perhaps you can propagate implications with grouped candidates:

(xy)r12c7 => (x|y)r4c8 & (y|x)r7c89 or
(xy)r12c7 => (x|y)r47c8 & (y|x)r7c9

I had a similar feeling, but there is still a lot to do on my side to implement in a proper way the basic situation.

May be you will push me to speed up the process. "ttt" has shown he can do as well as Fata Morgana in that situation.

thanks
champagne

by **champagne** » Fri Jan 16, 2009 4:54 am

ttt wrote:That meant, hardest puzzles should be checked by players. Right? Now, hardest puzzle based on q1 & q2 is heavily downgraded in the ranking (ER9.2 after two moves)

ttt

I posted a similar reaction to tarek last post in "hardest sudoku" new thread.

Let me tell it in another way:

You can make a preliminary selection based on outdated ranking process. . .

Provide you take care to adjust the process to the "best known practices".

The family of "hardest puzzles" is not that big, it should be possible to find a process to apply the filter, at least in the final list .

champagne

ps: can you remind me the link to your "best solution for Platinium Blonde".

by **ttt** » Fri Jan 16, 2009 2:18 pm

champagne wrote:ps: can you remind me the link to your "best solution for Platinium Blonde".

Code: Select all: Platinum Blonde .......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6... *-----------------------------------------------------------------------------* | 35678 34589 34(679) | 4(679) 5689 4578 |(679) 1 2 | | 15678 14589 4(679) | 124(679)125689 124578 |(679) 56789 3 | | 15(67)8 158(9) 2 | 3 158(69) 15(7)8 | 4 58(679) (679)8 | |-------------------------+-------------------------+-------------------------| | 23(7) 234(9) 1 | 8 23(6) 234 | 23(679) 234(679)5 | | 235 6 34(9) | 124 7 12345 | 8 2349 149 | | 23578 23458 34(7) | 124(6) 12356 9 | 12367 23467 1467 | |-------------------------+-------------------------+-------------------------| | 123(6) 123 8 | 5 123(9) 123(7) | 123(679)23(4679)1(4679) | | 9 123 3(6) | 12(7) 4 12378 | 5 23678 1678 | | 4 7 5 | 12(9) 12389 6 | 1239 2389 189 | *-----------------------------------------------------------------------------*

Move 1: => r479c7<>9

Code: Select all: (6)r3c89-(6=hp79)r12c7* || (6)r3c5-(6)r4c5 || || || (6)r4c7-(6=hp79)r12c7* || || || (6)r4c8-(7)r4c8 || || || (7)r4c7-(7=hp69)r12c7* || || || || -------------------------------- || || | | || (7)r4c1--(7)r6c3=AUR(67)r12c37 | || || | || (9)r12c7* | || || | || (6)r8c3 | || | | || -------------------------- | || | | || | | (6)r3c1----(6)r7c1 | | || | | (6)r7c7-(6=hp79)r12c7* | | || | | (hp46)r7c89-(7)r7c89 | | || | | (7)r7c7-(7=hp69)r12c7* | | || | | (7)r7c6-(7)r3c6 | | || | -----------------------(7)r3c1 | | || | | (7)r3c89-(7=hp69)r12c7* | | | | | ------------------------------------------------

Move 2: => r467c7<>7

Code: Select all: (6)r3c89-(6=hp79)r12c7* || (6)r3c1-(6)r7c1 || || || (6)r7c7-(6=hp79)r12c7* || || || (hp46)r7c89-(9)r7c89=(9)r7c5---(9)r9c4=AUR(69)r12c47 || | || || | (7)r12c7* || | || || | (6)r6c4 || ---------------------------- | || | -------------------- || | | (6)r3c5----(9)r3c5=(9)r3c2-(9)r4c2=(9)r4c8-(6)r4c8 | | || | -----------------------------------(6)r4c5 | | || | | (6)r4c7-(6=hp79)r12c7* | | | | | -------------------------------------------------------------

After two moves above, the puzzle is still ER9.2

ttt

by **Allan Barker** » Sat Jan 17, 2009 3:30 am

Hi Champagne and ttt,

I just posted a comparison of some of the logic seen in puzzles like Fata Morgana and Platinum Blond here . I try to see how different principles relate. FM and PB make a good comparison particularly in light of all of the new things here. Please let me know where I might add or change things to give a better picture. After you guys are finished, I'm not sure there will be any more monsters.

However, there is I think some new logic in PB, at least I haven't seen it before in a monster.

Allan

by **champagne** » Sat Jan 17, 2009 7:07 pm

ronk wrote:
champagne wrote:
ronk wrote:
champagne wrote:I proposed "bi bi" because it can be used indiferently in English and in French.

Most search engines discard two-letter words. For that reason alone, "bi bi" is an unwise choice.

What would be your proposal

I've sometimes had dogs for a full year before deciding on a name, so you're asking the wrong person.

what about Flying Fish for an elementary "bi bi" pattern
It is BTW a kind of "fish" and can be used is simpler conditions

EDIT As nobody reacted, I take flying fish for an elementary "bi bi" and EXOCET for the full "bi bi"

I don't known how it sounds in Englsh, but exocet is the French name for a flying fish and it has been taken 20 years ago as name for a flying torpedo.

by **ttt** » Mon Jan 19, 2009 4:56 am

Hi champagne,
I don’t know below deduction on your list for SP or not: r6c5<>3

Code: Select all: Silver Plate 1.......7.2.4...6...3...5...9..4........62.4....9..8....5.....3.6.2...8.7....1... *-----------------------------------------------------------------------------* | 1 4(5)8 4689 |(35)68 23589 35689 | 2349 2(3)9 7 | | 589 2 (7)89 | 4 (357)189(357)89 | 1(3)9 6 189 | | 4689 4(7)8 3 | 16(7)8 12789 6789 | 5 129 12489 | |-------------------------+-------------------------+-------------------------| | 23568 9 12678 | 1(357)8 4 3578 | 12367 12(357) 1256 | | 358 1(357)8 178 | 1(357)8 6 2 | 1379 4 159 | | 23456 14(357) 12467 | 9 [1](357)(357) | 8 12(357) 1256 | |-------------------------+-------------------------+-------------------------| | 2489 148 5 | 6(7)8 789 46789 | 124679 12(7)9 3 | |(3)49 6 149 | 2 (357)9 (3457)9 | 14(7)9 8 1459 | | 7 (3)48 2489 |(35)68 3589 1 | 2469 2(5)9 24569 | *-----------------------------------------------------------------------------*

Edit:
Elimination r6c5=3:
1- If r6c5=1 => r6c5<>3
2- If r6c5<>1 => Floor (357)r6c56 => two sub-steps (diagram 1: r6c238<>7) & (diagram 2: r6c1289<>5) => pair (57)r6c56 => r6c5<>3
Conclude: r6c5<>3

Present as diagram:

Code: Select all: Diargam 1: Floor (357)r6c56 => r6c238<>7 (3)r45c4-(3=hp57)r6c56 || (3)r1c4—---(3)r1c8 || | || || | (3)r6c8-(3=hp57)r6c56 || | || || | (3)r4c8-(5)r4c8 || | || || | (5)r6c8-(5=hp37)r6c56 || | || || | (5)r9c8-(5)r9c4 || | || || -------------------(5)r1c4 || || || (5)r45c4-(5=hp37)r6c56 || (3)r9c4----(3)r9c2 | || | (3)r6c2-(3=hp57)r6c56 | || | (3)r5c2-(5)r5c2 | || | (5)r6c2-(5=hp37)r6c56 | || | (5)r1c2-(5)r1c4 | || -------------------(5)r9c4 || (5)r45c4-(5=hp37)r6c56

Code: Select all: Diagram 2: Floor (357)r6c56 after above step (r6c238<>7)=> r6c1289<>5 (3)r45c4-(3=hp57)r6c56 || (3)r1c4-(3)r1c8 || || || (3)r6c8-(3=hp57)r6c56 || || || (3)r4c8-(7)r4c8=(7)r7c8------------------(7)r8c7=AUR(37)r68c56 || | || || | (5)r6c56 || | || || | (3)r8c1-(3)r9c2 || | || || -(7)r7c4=(7)r3c4-(7)r3c2=(7)r5c2-(3)r5c2 || || || (3)r6c2-(3=hp57)r6c56 (3)r9c4-(3)r9c2 || (3)r6c2-(3=hp57)r6c56 || (3)r5c2-(7)r5c2=(7)r3c2—-----------------(7)r2c3-AUR(37)r26c56 | || | (5)r6c56 | || | (3)r2c7-(3)r1c8 | || -(7)r3c4=(7)r7c4-(7)r7c8=(7)r4c8-(3)r4c8 || (3)r6c8-(3=hp57)r6c56

We can eliminate some candidates but quite complex and I havenot yet study more…

ttt

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