JExocet Pattern Definition

Advanced methods and approaches for solving Sudoku puzzles

Re: JExocet Pattern Defintion

Postby denis_berthier » Wed May 29, 2013 10:48 am

champagne wrote:
denis_berthier wrote:[b]It appears that 3 out of the 10 secondary JExocets allow no elimination.
Counting JExocets without checking whether they are useful is therefore not a good idea.

Even if you don't use the abi loop, it would be good to code completely the exocet rules.
In the case of double exocets, forgetting to apply the "double" rule leads to a completely wrong picture.


I stated clearly what I've coded. I'm not speaking of double Exocets but of basic JExocets.
I certainly misunderstood the meaning of the "04a double exocet" file but my examples show nonetheless that detecting a JExocet isn't enough to prove it allows eliminations.

In some cases, when a pair of specially related JExocets is present, more eliminations can be obtained if another rule (double JExocet) is applied. However, JExocets are already very complex patterns and double ones are still more complex.
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Re: JExocet Pattern Defintion

Postby champagne » Wed May 29, 2013 10:58 am

denis_berthier wrote:In some cases, when a pair of specially related JExocets is present, more eliminations can be obtained if another rule (double JExocet) is applied. However, JExocets are already very complex patterns and double ones are still more complex.


I think that for a human player detecting a double exocet when you found the first one is very simple.

On the other way, but I don't know how this work in your lay-out, when you have an exocet, you have more than just direct eliminations.

Just to stay simple, if at any moment you find a,b valid in the base in a chain, then the target is a,b, with a lot of consequences. (and reverse)

Coding the exocet without such effects is a poor use of the pattern.
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Re: JExocet Pattern Defintion

Postby denis_berthier » Wed May 29, 2013 11:14 am

champagne wrote:when you have an exocet, you have more than just direct eliminations.
Just to stay simple, if at any moment you find a,b valid in the base in a chain, then the target is a,b, with a lot of consequences. (and reverse)
Coding the exocet without such effects is a poor use of the pattern.


Mixing up everything is the best way of creating confusion.
Many rules have occasional consequences.

If special JExocet cases have systematic consequences, you can try to define a more specialised rule including these special conditions.

In SudoRules, if the application of a rule creates the conditions for another rule to be applied, I don't have to write it; it's automatically taken into account.
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Re: JExocet Pattern Defintion

Postby David P Bird » Wed May 29, 2013 11:32 am

Denis, This exchange goes back to the heart of the issue regarding patterns on the original thread. Your approach is centred on them as providing eliminations, which makes combinations of two patterns look very complicated. However if they are also considered as a source of inferences then it's not so complicated at all. This happens all the time at lower levels when say we construct a chain through a finned fish and an ALS.

The JExocets that don't provide eliminations still provide inferences about the distributions of the digits in the JE bands that can be in conjunction with other inference patterns to produce eliminations. The fin cells for the partial fish also provide eliminations if and when the base digits can be reduced by other methods. To trash JEs that don't provide eliminations is therefore throwing information away. This is regardless of the eliminations that ABI loops may provide if their use is accepted.

From what you write, your computer solver must be repeatedly rediscovering simple patterns whereas a more intelligent system would remember them.
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Re: JExocet Pattern Defintion

Postby champagne » Wed May 29, 2013 11:58 am

denis_berthier wrote:In SudoRules, if the application of a rule creates the conditions for another rule to be applied, I don't have to write it; it's automatically taken into account.



That's fine, the only rule for an exocet is

if 'a' is in the base, it is in the target and reverse.
if 'a' is not in the base, then it is not in the target and reverse

All the rest is indirect or combined effects.
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Re: JExocet Pattern Defintion

Postby denis_berthier » Wed May 29, 2013 12:36 pm

David P Bird wrote:Denis, This exchange goes back to the heart of the issue regarding patterns on the original thread. Your approach is centred on them as providing eliminations, which makes combinations of two patterns look very complicated.

A combination of two sub-patterns is always a combination of two sub-patterns, whichever way you use them


David P Bird wrote:From what you write, your computer solver must be repeatedly rediscovering simple patterns whereas a more intelligent system would remember them.

Wrong, my solver keeps track of all the sub-patterns, if they are used in full rules
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Re: JExocet Pattern Defintion

Postby denis_berthier » Wed May 29, 2013 12:38 pm

champagne wrote:That's fine, the only rule for an exocet is
if 'a' is in the base, it is in the target and reverse.
if 'a' is not in the base, then it is not in the target and reverse
All the rest is indirect or combined effects.


That's typical of your total lack of rigour.
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Re: JExocet Pattern Defintion

Postby champagne » Wed May 29, 2013 12:53 pm

denis_berthier wrote:
champagne wrote:That's fine, the only rule for an exocet is
if 'a' is in the base, it is in the target and reverse.
if 'a' is not in the base, then it is not in the target and reverse
All the rest is indirect or combined effects.


That's typical of your total lack of rigour.


This is not an acceptable answer
you should tell what is wrong or what is missing
I am ready to learn more about exocets :D
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Re: JExocet Pattern Defintion

Postby denis_berthier » Wed May 29, 2013 2:05 pm

In the first 100 puzzles of the "03 E Exocet seen" list, I've found 12 basic J-Exocets that have no eliminations.


Hidden Text: Show
Code: Select all
98.7.....6.....7....7.5....5....4.3...89..5......2..1..3.....4...98..6......1...2;44;GP;H7
J4-Exocet-in-columns:
     base digits = n3, n4, n1, n2
     base cells = r3c1, r3c2
     S columns = c3, c4, c7
     target cells = r2c4, r1c7



....56.8..5.7....3..8......2.....9...4.5....7....92.6.3.4.....15..1..4...1.....7.;61;elev;31
whip[1]: r6n7{c3 .} ==> r4c2 <> 7
whip[1]: r6n7{c3 .} ==> r4c3 <> 7
J4-Exocet-in-columns:
     base digits = n8, n9, n2, n6
     base cells = r9c1, r9c3
     S columns = c2, c4, c9
     target cells = r7c4, r8c9



1....67...5.7....3..8.....4.4.5..3......2..9........45.7.9...3.6...1......2..8...;69;elev;28
hidden-single-in-a-row ==> r3c1 = 7
J4-Exocet-in-rows:
     base digits = n6, n8, n1, n2
     base cells = r5c7, r6c7
     S rows = r4, r2, r7
     target cells = r2c8, r7c9



...1....9.......85..9.5..6...5.3...6.7...2...1..4.......3.8..9..2...73..4........;82;col;H3
J4-Exocet-in-rows:
     base digits = n4, n7, n1, n2
     base cells = r1c7, r2c7
     S rows = r3, r4, r7
     target cells = r4c8, r7c9



1....6....571......9..7..1...8...........89.29..5...6.....42..3.3....4..7..6...9.;84;elev;61
J4-Exocet-in-columns:
     base digits = n4, n8, n2, n3
     base cells = r1c2, r1c3
     S columns = c1, c4, c8
     target cells = r3c4, r2c8



1......8..5......6..93..4...7......18......5...4.2.6.....26...7...93......2..43..;129;elev;113
J4-Exocet-in-rows:
     base digits = n5, n8, n1, n7
     base cells = r7c6, r8c6
     S rows = r9, r3, r6
     target cells = r3c5, r6c4




9876.....65....7...........5...4..3..2......1..68..5....59..8......3..2......1..4;153;GP;H21
J4-Exocet-in-columns:
     base digits = n2, n4, n1, n3
     base cells = r3c1, r3c2
     S columns = c3, c4, c7
     target cells = r2c4, r1c7



1....6....571.......9...51..4....3.......8..29..7...6......24..5..6...9.....3...8;155;elev;129
J4-Exocet-in-columns:
     base digits = n3, n8, n2, n4
     base cells = r1c2, r1c3
     S columns = c1, c4, c8
     target cells = r3c4, r2c8



98.7.....76....5....5.6.....4.....3...98..6.......2..1..79..8......1...4.....3.2.;180;GP;H27
hidden-pairs-in-a-block: b8{r8c6 r9c5}{n7 n8} ==> r9c5 <> 5, r9c5 <> 4, r8c6 <> 6, r8c6 <> 5
J4-Exocet-in-columns:
     base digits = n3, n4, n1, n2
     base cells = r3c1, r3c2
     S columns = c3, c4, c7
     target cells = r2c4, r1c7



1...5..8..5...9.31..9...5.....6....4.67.4....9....58....2..........7..2.8....31..;187;elev;109
whip[1]: r5n8{c6 .} ==> r4c5 <> 8, r4c6 <> 8
J4-Exocet-in-columns:
     base digits = n4, n7, n2, n6
     base cells = r3c8, r3c9
     S columns = c7, c1, c6
     target cells = r2c1, r1c6



.2....7..4...8...6..9....1...1...9...7.6...5.5....8..36..8....5.....3.2.....45...;196;elev;81
hidden-single-in-a-block ==> r8c5 = 6
J4-Exocet-in-rows:
     base digits = n7, n9, n1, n2
     base cells = r8c4, r9c4
     S rows = r7, r2, r6
     target cells = r2c6, r6c5



.2...67..4......3...9.....5....3...4.7...28..5......9.7....1....1.62......68..1..;200;elev;84
hidden-single-in-a-column ==> r2c3 = 7
J4-Exocet-in-columns:
     base digits = n3, n9, n4, n5
     base cells = r7c4, r7c5
     S columns = c6, c2, c7
     target cells = r9c2, r8c7
Last edited by denis_berthier on Wed May 29, 2013 2:08 pm, edited 2 times in total.
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Re: JExocet Pattern Defintion

Postby champagne » Wed May 29, 2013 2:06 pm

Hi David,

Here a lot of 132 puzzles where my solver found both exocet and skloop (3 digits exocet)
This is in the green zone, which means that some basic moves can destroy them. In the search, basic moves are limited to triplet and swordfish.

I had a quick look and found such case using the solving process.




Hidden Text: Show
98.7.......6.5.........69..4...3..2..1......4..76..8..3.......1.2.....3...89..7..
98.7.......6.5........6.9..4....3.2..1......4..76..8..3.......1.2.....3...89..7..
98.7.......6.5.4.......3...8..9......7...8.3...2.4.6...5...12....1.2...6.......49
98.7.....6.....5....5....74.7..3...2..48..7.......1.9...85..6......2..31.....9...
98.7.....6.....5....5....74.7..3...2..48..7.......9.1...85..6......2..39.....1...
98.7.....6.....5....5.4..7..7..3...2..94..6.......1.8...65..4......8..1......2..3
98.7.....6.....5....7....64.9..3..2..1...5.....84..7....46..8......1...3.....2.5.
98.7.....6.....7....7....54.3..2..1...84..6.......1..9..58..4......9..2......3..1
98.7.....6.....7....7....54.3..6..2...54..8.......2..1..95..4......1..6......3..2
98.7.....6.....7....7....54.6..3..2...94..5.......1..8..56..4......2..13.....8...
98.7.....6.....7....7.5..4..3...2.....48..5......1..92..84..6......3..2......9..1
98.7.....6.....7....7.5..4..3...2.....48..5......9..12..84..6......3..2......1..9
98.7.....6.....7....7.5..4..3...2..1..45..8......1..6...84..9......6...2.....1.3.
98.7.....6.....7....7.5..4..3...2..9..58..4......1..2...86..5......3...2.....9.1.
98.7.....6.....7....7.5..4..3..2...6..48..5.......1.2...84..9......3...2.....6.1.
98.7.....6.....7....7.5..4..7...3..2..95..8......6..1...89..4......1...3.....2.6.
98.7.....6.....7....7.5..4.3...8..2...46..9.......2..1..64..5......2..3......1..8
98.7.....6.....7....7.5..4.7....3.2...85..4......9...1..64..8......1...3.....2.9.
98.7.....6.....7....7.5..8.4...3...2..89..6.......2.1..3..1...4..95..8.......4.2.
98.7.....6.....7....7.54....6..3..2...95..4.......1..8..59..6......2...3.....8.1.
98.7.....6.....75...7.4.....3...5..2..69..4......2..1...84..9......5...3.....1.2.
98.7.....6.....8....5....74.7..3...2..68..5.......1.9...84..6......2..1......9..3
98.7.....6.....8....5.4..7.3...2...1..63..9.......8.3...86..5......3..4......1..2
98.7.....6.....9....5....743...2...1..69..5.......1.8...46..7......3..1......8..2
98.7.....6.....9....5.4..7.7...8......69..5.......3.21..95..6......2...8.....1.3.
98.7.....6.....9....7.5.....4...3.2...98..6......1...3..89..7......2..4......4..1
98.7.....6...5......4..86..4....98....3.2..7....1....5.4...39....92....1....1..5.
98.7.....6...5.7....7..4.....84..9......3..6......2..1..49..8......2..1......6..3
98.7.....6...8.7....7..5....4...3.2...69..5......2...3..85..9......41..........14
98.7.....6...9.8....7..5...4......32..89..6......13....7...2..1..68..9.........4.
98.7.....65....7....7.4....3......2...89..6......21..5..68..9......5..1......3..2
98.7.....65....7....7.4....3....2.1...59..4......1...8..65..9......8..2......3..1
98.7.....65....7....7.4....3....2.1...69..4......1...5..86..9......5..2......3..1
98.7.....65....7....7.4....3....2.1...69..5......1...8..94..6......3...1.....8.2.
98.7.....65....7....7.4....3....2.1...84..9......1...5..68..4......5...2.....1.3.
98.7.....65....7....7.4....3....2.1...89..4......5...2..64..9......2..3......1..5
98.7.....65....7....7.4....3....2.1...98..4......1...5..64..8......51.2.........3
98.7.....65....7....7.4....3....2.5...84..9......1...2..98..4......2..3......5..1
98.7.....65....7....7.4....3....5.2...84..6......2...1..69..4......1...5.....2.3.
98.7.....65....7....7.4....3....8.2...95..4......2...1..69..5......3...2.....1.8.
98.7.....65....7....7.4....3...2..1...54..6.......1..8..69..5......8..2......3..1
98.7.....65....7....7.4....3...2..1...69..4.......1..5..94..8......3...1.....5.2.
98.7.....65....7....7.4....4....3.6...98..5......2...3..54..9......1.........6.21
98.7.....65..4......7..65..7....38.....2...1.....9...2.7...56....3.2...4...1...9.
98.7.....65..4......7..65..7....38.....2...1.....9...2.7...86....3.2...4...1...9.
98.7.....7..........6.5.4..3...4.7....48...6......2.1..3..9.5.....1...2......8..6
98.7.....7.....6....6.54....3..2..1...48..5.......1..9..85..4......9..2......3..1
98.7.....7.....8....6.5.....4...3.2...76..5......1...3..85..6......2..4......4..1
98.7.....7.....9....6....5.4...3..2...89..6.......2..1..98..7......1..4......4..3
98.7.....7...6......5..94..3..8...5..6..7......2..5..4..9..1.4.....3.9.2......6.1
98.7.....7...9.6....6..5....4..3..2...79..5.......2..3..85..9......4..1......1..4
98.7.....76....5....4.5....3....8.2...69..7......2...1..76..9......3...2.....1.8.
98.7.....76....5....4.5....3...2..1...95..7.......8..2..64..9......3..8......2..1
98.7.....76....5....4.5....3...8..2...65..9.......2..1..76..4......3...2.....1.8.
98.7.....76....5....5......4...3..2..1...2..3..68..9....79..6......14..2.......1.
98.7.....76....5....5......4...3..2..5...1..3..65..9....79..6......42..1.......4.
98.7.....76....5....5....4..3..2......74..6.......1.29..86..7......9..1......2..3
98.7.....76....5....5....4..3..2......74..6.......9.21..86..7......1..9......2..3
98.7.....76....5....5....4..3..2...1..74..6.......1.9...85..4......3..1......9..2
98.7.....76....5....5....4.3...2..1...95..4.......1..6..79..8......6..2......3..1
98.7.....76....5....5....4.3...6..2...95..4.......2..1..79..8......1..6......3..2
98.7.....76....5....5.4.....3.....2...65..4......12..9..86..7......2..3......9..1
98.7.....76....5....5.4.....3...2.1...74..6......1...9..86..4......3...1.....9.2.
98.7.....76....5....5.4.....3..2..1...75..4.......1..9..86..7......9..2......3..1
98.7.....76....5....5.4....3....2.1...89..7......1...6..74..9......6..2......1..3
98.7.....76....5....5.4....3....2.1...98..4......1...6..79..8......3...1.....6.2.
98.7.....76....5....5.4....3....2.6...84..9......1...2..79..4......2..3......6..1
98.7.....76....5....5.4....3....2.6...95..8......1...2..78..4......3..28.....6..1
98.7.....76....5....5.4....3....8.2...65..4......2...1..76..9......1...8.....2.3.
98.7.....76....5....5.4....3....8.2...65..7......1...8..94..6......2..1......3..2
98.7.....76....5....5.4....5...3..2...76..9.......8..1..65..7......1...8.....2.3.
98.7.....76....8....5.4......98..7......3..2......1..6..85..9......6..3......2..1
98.7.....76....8....5.4.....3..9..2...65..4.......2..1..86..7......1..9......3..2
98.7.....76....9....5.......4..3..2...89..7.......1..3..78..6......24.1.........4
98.7.....76....9....5......4...3..2..5...2..1..69..7....95..6......4...3.....1.4.
98.7.....76....9....5.4......94..6......3..2......1..8..69..7......2..1......8..3
98.7.....76....9....5.4......96..4......3..2......1..8..79..6......2..1......8..3
98.7.....76....9....5.4....3....6.2...85..4......2...1..94..7......61..2.......3.
98.7.....76..5......4..97..4....79.....3...2.....1...5.7...46.....2...1.....3..5.
98.7..6......96.......58.7.7...6.5...4......3..2....1.6....57...3.....42..1......
98.7..6....5.4..3......9...7..8.6....6.........4.5..2...3...2.5....2.3.1.......4.
98.7..6....5.6..4......3...7..8......3...92....2.1...4..1.5.4.....6....1.......95
98.7..6....5.6..4......9...7....3....9.8.......6.5...43......25..1.2.4.........17
98.7..6....5.6..4......9...7....3....9.8.......6.5...43......25..1.2.4.........18
98.7..6....7..........95.7.4.......3.3..2.1....95...6.1.......4.4...32....89...5.
98.7..6....7....5.....6...44....3.7..2.1.......6.5.9..3..2......1...4.....8.7.5..
98.7..6....7....5.....9..4.3..2......4...1.....9.5.8..2....4..6.1.3.......8.6.5..
98.7..6....7.54..........5.8.....3...3......2..69...4.1...2.8....86...9......5..1
98.7..6....756.........9...4......3..3..2...4..6..89..3......1..1......2..9..67..
98.7..6..5...4......3..9.2.85.4.......9..6..2....7.9....1..32......8...1.......36
98.7..6..5...9......7..6...4....3.2...5.8.7.....2....3.5...1.4...9.5.8.....4....1
98.7..6..54..6......69......7...3.2...8.5.9.....1....3..4.9.8.....2....1.....1.7.
98.7..6..54..9......3..8.9.3....6.5...62....1....4.2...3...5.6....4....7....2.1..
98.7..6..7...6......65.4...5..3...2..6......9..7.4.8....8.7.5.....2.9..3.......1.
98.7..6..7.5........4......8..5..7...6..3..2......1..4..76..5......2...1.....4.3.
98.7..6..7.5........4......8..5..7...6..3..4......2..1..76..5......4...2.....1.3.
98.7..6..7.5........4......8..9..7...6..3..2......1..4..76..9......2...1.....4.3.
98.7..6..75.........4.8..7.4...3..9...3.....2...1.25...4..9..8....5.6..1......2..
98.7..6..75.........4.8..7.4...3..9...3.....2...5.21...4..9..8....1.6..5......2..
98.7..6..75.........4.8..7.8...4..9....3....5.....62...9..1..4...15....2.....2..3
98.7..6..75.........4.8..7.8...4..9....5....3.....62...9..1..4...13....2.....2..5
98.7..6..75.........4.9..7.4...5..8...56..3.2.....1....9..7..5....1..2.......6..3
98.7..6..75.........6.4.....3...2.9...75..4......1...2..86..5......2...3.....9.1.
98.7..6..75.....8...6.......4..3...2..86...7......21....58...6.....143..........1
98.7..6..75.....8...6......4...3.2...1...2..3..59...7...86...5.....4.3.......1..4
98.7..6..75.....8...6......4...3.2...1...2..3..89...7...56...9.....1.3.......4..1
98.7..6..75.....8...6......43..2.1....59...6......1..2..78...5.....1...4.....43..
98.7..6..75.....8...6......6...4.3....89...7......2..4.3..2.1....56...9......1..2
98.7..6..75.....9...6......4...3......85...7......21.3.2..4...1..96...8......14..
98.7..6..75..6......6..4....3.9...2...8.4.5.......2..9..5.7.8.....2...1......1..3
98.7..6..75..6......6..4...3....2.1...9.4.7.....1....2.9...8..3..5.7.4.....2...8.
98.7..6..75..6......6..8...4....3.2...9.8.7.....2....3.9...1..4..5.7.8.....4...1.
98.7..6..75..8......6......4..3...2...8.9.7.......1..3..7.5.8.....4.2..1.......4.
98.7..6..75..9......6......4..3...2...7..2..3..5.8.9....9.7.8.....1....4.....4.1.
98.7..6..76.........5.4....5....3.2...64..7......8...1..76..4......2...8.....1.3.
98.7..6..76..5......4......3....2.....6.7.8.....6...53.1.2....5..9.814.......7.1.
98.7..6..76..5......5......4....3.2..36.8.7.....1....3..9.7.5.....2...4......4..1
98.7..6..76..5......5......4.7.6.8...3.....4....2.4..1..6.8.9.....1....3.....3.2.
98.7..6..76..5......5......4.7.8.5...3...4.2....1....4.7...3.1...8.7.9.....2....3
98.7..6..76..5......5......4.9.6.5...3...4.2....1....4..6.8.7.....2....3.....3.1.
98.7..6..76..5......5......4.9.6.8...3...4.2....1....4..6.8.5.....2....3.....3.1.
98.7..6..76..8......5......4..3...2..1.2....3..9.6.8....7.5.9.....1....4.....2.1.
98.76....54.........3..59..7....65.....2...8.....1...24...3...8.7...46.....1...3.
98.76....54.........7..58..8....93....32...6.....1...4.7...89.....4...1....1....2
98.76....54.........7..58..8....93....34...6.....2...1.7...89.....2....4...1...2.
98.76....7..54......5..87..3......2..4......9..6.8.1...3.....4..2...1..3..78..6..
98.76....7.6..54.........7.43....2...1...2..8..2....5...1..35.....89...........69
98.76....75....9....6......4....3.2..279..8......2...1..98..7......4...3.....1.4.
987......65.9..4....4......3...2..1...85..9.......1..7..64..5......7..2......3..1
987......65.9..4....4......3...2..1...86..9.......1..7..64..5......7..2......3..1
987......65.9..4....4......3...7..2...85..9.......2..1..64..5......1..7......3..2
9876.....65....8.........4..3..2..1...57..3.......3..6..64..7......9...2.....1.3.
champagne
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Posts: 5742
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Re: JExocet Pattern Defintion

Postby champagne » Wed May 29, 2013 2:14 pm

in the same area, sk loop + exocet 4 digits 344 puzzles

Hidden Text: Show
9..8..7...8..6......6....9.7...5..4..9.3..6.......2..13....1..2..97..8......4..5.
9..8..7...8..6..5...4..3..28...7.....6.9.......3..2..41...4...5..5....3......52..
9..8..7...8..6..5...7.....44.....9...3...8.2...16....7.5.3...6.....5.........2..1
9..8..7...8..9..6.........58..6...5..4...3..6..2.1....7..5...9..1..2......3..4...
98.........79..6.........7.8..6..9....5.4..3......2..1.5.7..8....6..3.2.....1...4
98.........79..6......5....7..6..8....4.3..2......1..3.9.8..7....6.2..1......3..5
98.........79..6......5....8..6..4....6.3..2......1..3.9.4..8....4.2..1......3..5
98.........79..6......7....8..6..7....6..5.4.....3...27..1..8....1..4.3.....2...5
98.......7..8..6....6.5.....7...4.3...95..8......2...1.2...1..4..86..9......3..1.
98.7.......6.5.........69..4......3..2...7..1..76..8..1.......2.3.....4...98..7..
98.7.......6.5.........69..4...7..3..3...2..1..96..7..3......2..1......4..79..5..
98.7.......6.5........6.9..4......3..3...2..1..56..8..3......2..1......4..95..6..
98.7.......6.5.4.......3...7....9....3.8...6...5.4.2....2.....6...2.15......6..4.
98.7.......6.5.4.......3...7....9.4..3.8....2..4.1.6...1.6..2....2....5.....2...4
98.7.......6.5.4.......3...7....9.4..3.8....2..5.1.6...1.6..2....2....5.....2...4
98.7.......6.5.4.......3...7..8...5..3...7.4...4.6...2..5.2..6....9...........2.1
98.7.......6.5.4.......3...8....9....3.8...7...5.2.6....1.....6...1.25......6..4.
98.7.......6.5.4.......3...8..9......7...8.3...2.4.6..1....52....5.....6....2...4
98.7.......6.5.4.......9.3.7....3....9.8.......2.4.5...5...12....4.....6....2..4.
98.7.......6.5.4.......9.3.7..3......9...8.....5.6.2...5.4..1....4....2.....2...6
98.7.......6.5.7.........6.5....4.....86...9.....3.2.1..79...8.....1...3.....24..
98.7.......6.5.7.........6.5....4.....96...8.....3.2.1..78...9.....1...3.....24..
98.7.......6.5.7.........6.5....43....98...5.....2...13....14....86...7.....4...2
98.7.......6.5.7.........6.6...4.3...2...1..4..96...8...85...7.....3...1.....42..
98.7.......6.5.7.........6.8....4..3.6..2.1....59...8...96...5.....1...2.....34..
98.7.......6.5.9...........4...9.6.....3...2......1..3.9..6.4....5..3..1..42...7.
98.7.......6.5.9.......6...4...3..2..1......4..79..6..2.......1.3.....4...95..7..
98.7.......6.9.5.......8.9.7...6..8..4...9..3..2...1..5...8..6..1....2....3.....4
98.7.......6.9.7.....5.6...4...3..8..2......1..3..76..2.......4.1.....2...7..93..
98.7.......6.9.7.....6.5...4...8..3..2......1..8..79..3.......4.1.....2...7..98..
98.7.......6.9.8.......8...8...5.6....54...3......2..1.5..6.9....71....4.....3.2.
98.7.......7.6.........57..4...9..3..2......1..95..8..3......2..1...8..4..89..5..
98.7.......7.6........5.7..4....5.3..2......1..86..5..1......4..3.....2...59..6..
98.7.......7.6........5.7..4....7.3..2......1..96..8..3....5.4..1......2..68..5..
98.7.......7.6.9...........8...9.7....5..4.3....2....1.5..7.8....6..1..4.....3.2.
98.7.......7.6.9.......5...4...7..3..2...6..1..69..5..3.......2.1.....4...86..7..
98.7.......7.9.6...........7...6.8....65...4...3..2..1.6..8.9.......4..2.....1.5.
98.7.......7.9.6...........8...6.9....5..4.3....2....1.7..8.5....61....2.....3..4
98.7.....6..........5.9.6...9..5.8.....4...3......2..7.6..8.5....1..4.2....3....4
98.7.....6.....5....5....7..6..4..3...85..7......2...1.5..1...4..69..8.......3.2.
98.7.....6.....5....5....76.6..4......89..6.......3.21..96..7......1..3......2..4
98.7.....6.....5....5.6..7..6...4.3...89..7......2...1..75..8......3..2......1..4
98.7.....6.....7....7....5.5...4...3..96..5......2..1..7..3...2..69..8.......1.4.
98.7.....6.....7....7....5.7...4...3..58..9.......2.1..3...4.2...95..8......1...4
98.7.....6.....7....7....854...3...2..65..9.......2.1...96..5......2..43.....1...
98.7.....6.....7....7....854...3...2..68..9.......2.1...56..8......41.2.........3
98.7.....6.....7....7....854...3..2...65..8.......2..1..96..5......41..2.......3.
98.7.....6.....7....7....854...3..2...65..9.......2..1..96..5......41..2.......3.
98.7.....6.....7....7.5.....7..4..3...89..6.......2..1..68..9......31.2.........4
98.7.....6.....7....7.5....5...4..3...95..6.......2..1.7...3..2..69..8......1..4.
98.7.....6.....7....7.5..6.7....4.3...98..6......2...1..65..8......3..4......1..2
98.7.....6.....7....7.5..8..7..4...3..89..6.......2.1...68..5......13.2.........4
98.7.....6.....7....7.5..8..7..4..3...86..5.......2..1..98..6......1..2......3..4
98.7.....6.....7....7.5..9.7...4...3..95..6.......2.1...69..8......31..4.......2.
98.7.....6.....7....7.6..5..5..4...3..96..5.......2.1...85..9......13..4.......2.
98.7.....6.....7....7.8..5..5..4...3..69..5.......2.1...85..6......13..4.......2.
98.7.....6.....7....7.8..5..5..4...3..96..5.......2.1...85..9......13..4.......2.
98.7.....6.....7....7.9..5..5..4...3..68..5.......2.1...95..6......13..4.......2.
98.7.....6.....75...7.5....4....3..2..98..5......2..1...65..8......1...3.....2.4.
98.7.....6.....8.........5.7...4..3...85..6.......2..1.7...4.2..3..1...4..68..5..
98.7.....6.....8....5....7..4..3......79..5.......2.31..85..7......4...2.....3.1.
98.7.....6.....8....5....7..9..4...3..75..9.......2.1..6...3.....98..5......1..24
98.7.....6.....8....5....7.5...4..3...98..7.......2..1..79..5......3..2......1..4
98.7.....6.....8....5.6..7..7..4...3..98..6.......2.1...65..9......31..4.......2.
98.7.....6.....8....7....5..6..4...3..85..6......2..1...56..7......3..2......1..4
98.7.....6.....8....7....5.4...3..2...68..7.......2..1..89..6......1..3......4..2
98.7.....6.....8....7.5.....4...3.2...68..7......2...1..86..9......12..3.......4.
98.7.....6.....8....7.5.....4..3..2...68..9.......1..3..89..6......4...1.....2.3.
98.7.....6.....8....7.5.....4..3..2...68..9.......1..3..89..7......4...1.....2.3.
98.7.....6.....8....7.5.....5.....4...68..7......32..1..89..6......4...2.....1.3.
98.7.....6.....8....7.5.....5...4.3...98..6......2...1..86..7......13.4.........2
98.7.....6.....8....7.5.....5..4..3...95..7.......2..1..89..5......3...2.....1.4.
98.7.....6.....8....7.5.....9...4.3...89..5......2..1..7...1..4..95..7......3..2.
98.7.....6.....8....7.8..9.7...9..8...5..4..3...2..1...7..6..5....1....4.....32..
98.7.....6.....85...5.....7.6..4..3...98..7.......2..1..76..9......1...2.....3.4.
98.7.....6.....87.....6...9.9..8...6..54...3......21...7..5...8...1...4......32..
98.7.....6.....87...7.5.....9...4..3..69...5.....2.1....86...9.....13..2......4..
98.7.....6.....9.........5.7...4..3...89..5.......2..4.7...1.4..2..3...1..95..8..
98.7.....6.....9....5....7..4..3......69..8.......2.31..86..7......4...3....1..2.
98.7.....6.....9....5....7..4..3...2..79..5.......2.1...95..7......1...3.....4.2.
98.7.....6.....9....5....7..5..4......79..8.......3.21..86..7......2...4....1..3.
98.7.....6.....9....5....7..6..4..3...78..5.......2..1.5..1..4...89..7.......3..2
98.7.....6.....9....5....7.4...3...2..69..7......1..3...96..8......2..4......3..1
98.7.....6.....9....5....7.4...3..2...89..7......2...1..98..6......1..4......2..3
98.7.....6.....9....5....7.5...4..3...69..7.......2..1..76..5......3..2......1..4
98.7.....6.....9....5....7.5...4..3...95..6......2...1..76..5......3..4......1..2
98.7.....6.....9....5.8..6.5...6..4...4..3..2...2..1...5..4..8....1..3.......2..7
98.7.....6.....9....7....5..4..3...2..95..6.......2.1...69..5......1...3.....4.2.
98.7.....6.....9....7.5.....4...3.2...98..6......2...1..89..7......3..4......1..2
98.7.....6.....9....7.5.....4...3.2...98..7......1...3..89..5......3..1......2.4.
98.7.....6.....9....7.5.....5.....4...85..6......32..1..69..7......14.2.........3
98.7.....6.....95...5.....7.9..4......65...8......32.1..78...6.....2...4.....13..
98.7.....6.....98...5.....7.5..4......96..8.......3.21..69..7......1...3.....2.4.
98.7.....6.....98...5.....77...4.3....86...9......2..1..68...7.....3.2.......1..4
98.7.....6...5......4..83..5......2..7.96......3..48....8....12...8..4.......1..3
98.7.....6...5......4..83..5...6.....7.5...8...8..4..2..2..1.3.....9.2........1.4
98.7.....6...5......4..83..7...6.....5.9...3...8..2..4..2..4.8....3..2........4.1
98.7.....6...5......4..86...6...34.....5...2.....1...7.4...53....32....5....6..1.
98.7.....6...5......4..86...9...58....32...5.....6...1.6...39.....5....7....1...2
98.7.....6...5......4..89..4....96....6.3..2....2...1..4...68....7.2...5...3....1
98.7.....6...5......4..93..5...8..2..7.6.......2..31....9....41...9..2.......4..3
98.7.....6...5......4..96..4....68.....3...52....1.....4...89....7.2..1....1....3
98.7.....6...5......5..68..5....89....74...3.....2...1.5...97.....3...4.....1...2
98.7.....6...5.8....5....7..4...3..2..85..7......2..3...68..5......12..........14
98.7.....6...5.8....5....7..4...3.2...98..5......1...3..85..9......3..4......2..1
98.7.....6...5.8....5....7..5..4...3..86..9.......2.1...68..5......13..4.......2.
98.7.....6...5.8....5....7..5..4...3..89..6.......2.1...98..5......13..4.......2.
98.7.....6...5.8....5....7..6......4..78..9......32.1...89..5......4..2......1..3
98.7.....6...5.9....5....7.5...4...3..98..6.......2.1...89..5......3..2......1..4
98.7.....6...8.7....7..5....6..4..3...96..8.......2..1..85..6......13..2.......4.
98.7.....6...8.9....7..5...7....4.3...68..7......2...1..96..5......1..4......3.2.
98.7.....6...9.5....4..6.3.2...8.....7.2.......6..1.4...13..4......6..5......51.3
98.7.....6...9.7....7..5....6...4.3...5.8.9.....2....1..8.5.6.....1....2.....3..4
98.7.....6...9.7....7..5....6..4..3...98..6.......2..1..85..9......13..2........4
98.7.....6...9.7....7..5....7...4.3...5.8.9.....2....1..8.5.6.....1....4.....3..2
98.7.....6...9.7....7..5....9...4.3...5.8.6.....2....1..8.5.9.....1....4.....3..2
98.7.....6...9.8....5....7..4..3...2..98..6.......2.3...86..7......1..2......4..1
98.7.....6...9.8....7..5....4...3.2...98..5......2...3..85..7......12..5.......14
98.7.....7.....6......5....6...4..3...85..7.......2..1.6..1...2.3...4.1...78..5..
98.7.....7.....6....6....5..4..3...2..86..9.......1.3...79..8......2...3.....4.1.
98.7.....7.....6....6.5.....4...3.2...76..5......1...3..85..7......3..54.....2..1
98.7.....7.....6....6.5.....4...3.2...79..5......1...3..95..7......3...4.....2.1.
98.7.....7.....6....6.5.....4...3.2...79..8......2...1..98..7......1..3......2..4
98.7.....7.....6....6.5.....4...3.2...89..7......2...1..76..8......1...3.....2.4.
98.7.....7.....6....6.5.....6..4..3...79..8.......2..1..98..7......1..82.....3.4.
98.7.....7.....6....6.5.....7...4.3...96..8......2...1.5...1.4...85..9......3...2
98.7.....7.....6....6.5....6....4.3...89..7......2...1..78..9......1..42.....3...
98.7.....7.....6....6.5..8..7..4...3..86..9.......2.1...79..5......1..4......3..2
98.7.....7.....6....6.5..9..4..3...2..95..8.......2.1...89..7......1..2......3..4
98.7.....7.....6....6.9..8.8...7..5...5..43.....2....1.6..8..9....1....2.....34..
98.7.....7.....8.........6.5...4..3...86..7.......2..1.5...4.2..3..1...4..98..5..
98.7.....7.....8....6....5..4..3...2..86..9.......1.3...79..6......2...3.....4.1.
98.7.....7.....8....6....5..4..3..2...79..6.......2..1..96..7......4...2.....1.3.
98.7.....7.....8....6.5.....4.....3...75..6......32..1..86..7......13..2.......4.
98.7.....7.....8....6.5.....4...3.2...86..7......2...1..98..6......1...4.....2.3.
98.7.....7.....8....6.5.....6...4.3...56..7......2...1..85..6......3...2.....1.4.
98.7.....7.....8....6.5.....9...4.3...85..6......2...1.3..1...2..98..7.......2.4.
98.7.....7.....8....6.5....6....4.3...78..9......3...2..95..7......1...4.....2.1.
98.7.....7.....86...6.....5.4..3...2..98..5.......1.3...79..6......4...1.....3.2.
98.7.....7.....9....6....5..4..3...2..76..8.......1.3...89..7......24..3.......1.
98.7.....7.....9....6....5..4..3...2..78..6.......1.3...89..7......2..1......4..3
98.7.....7.....9....6....5..6..4...3.2...3.1...96..8....85..7......1.........2.34
98.7.....7.....9....6....5.4...3...2..89..6.......1.3...76..8......4..13.....2...
98.7.....7.....9....6....5.5...4...3..96..7.......2.1...79..6......3...2.....1.4.
98.7.....7.....9....6.5.....4..3..2...86..7.......1..3..98..6......2...4.....3.1.
98.7.....7.....9....6.5.....7..4..3...86..5.......2..1.1...3.2...79..8......2...4
98.7.....7.....9....6.5..8..7...4.3...98..6......2...1..85..7......1..4......3..2
98.7.....7.....98...6.....58...4.3....79...5......2..1..98...6.....1.4.......3..2
98.7.....7...6......5..89..5....94...6.3...2...4.1..3..5...48.....1....2....3...6
98.7.....7...6......5..94..3...7..4..6.8.......9..2..5..2..5.1.....3.2.9......5..
98.7.....7...6......5..97..5....89.....4...3.....2..1..9...75....61....4....3..2.
98.7.....7...6......6..87..6....79.....5...4.....3..2..9...68....12....5....4..3.
98.7.....7...6......6..97..5....89.....4...3.....2..1..9...58....5.3...4...1...2.
98.7.....7...6.8....6....5.5....4..3..86..9......2..1...79..6......1...4.....3.2.
98.7.....7...6.9....6....5.4....3.2...89..6......1...3..96..8......3..4......2..1
98.7.....7...8......6..57..6....85.....4...3.....2..1..9...76....51....4....3..2.
98.7.....7...8......6..97..5....79.....4...3.....2..1..9...86....5.1..4....3....2
98.7.....7...9......6..89..8....75....5.4..3....2....1.5...67.....3...4.....1..2.
98.7.....76....5...........5...4..3...8..2..1..78..9...5..3...2..95..6......1..4.
98.7.....76....5....4....6...53..6......8...9.....2.1...36..4......1..2......9..8
98.7.....76....5....4....6...53..6......9...8.....2.1...36..4......1..2......8..9
98.7.....76....5....4....6...53..6......9..8......2..1..36..4......1...2.....8.9.
98.7.....76....5....4....6...54..7......8..3......2..9..16..4......3..2......9..8
98.7.....76....5....4....6...56..4......3..28.....2.....14..6......8..9......9..3
98.7.....76....5....4....6...56..4......3..29.....2.....14..6......9..8......8..3
98.7.....76....5....5.......4..3..2...79..6.......1..3..96..7......2...1.....3.64
98.7.....76....5....5......4...8..3...85..7......32..1..78..9......4...3.....1.2.
98.7.....76....5....5......5...4..3...65..7.......2..1.4...3.1...78..6......1..2.
98.7.....76....5....5......5...4..3...78..9.......2..1..85..7......3..2......1..4
98.7.....76....5....5......5...4..3...79..6.......2..1..65..7......1..4......3..2
98.7.....76....5....5......5...4..3...79..6.......2..1..95..7......3..2......1..4
98.7.....76....5....5......5...4..3...79..8.......2..1..95..7......3..2......1..4
98.7.....76....5....5....6...45..6......8..3......2..9..14..7......3..2......9..8
98.7.....76....5....5.6....6....4.3...76..9......2...1..95..7......1..2......3.4.
98.7.....76....5....5.6....6....4.3...78..9......2...1..89..7......3..2......1..4
98.7.....76....5....5.6....8...4..3...78..9.......2..1..89..7......1...4.....3.2.
98.7.....76....5....5.6..9.6...9..5....4....3.....21...5..8..6....1.34..........2
98.7.....76....8...........5...4..3...89..7......2...1.5..1...4..9..3.2...75..9..
98.7.....76....8....5........95..7......4..3......2..1..78..9......3..24.....1.7.
98.7.....76....8....5........98..5......4..3......2..1..89..7......7..2.....31..4
98.7.....76....8....5......4...3..2...68..9.......1..3..86..7.......3..4.....2.1.
98.7.....76....8....5......5...4..3...98..7.......2..1..85..9......1..4......3..2
98.7.....76....8....5......5...4..3...98..7.......2..1..86..9......1..4......3..2
98.7.....76....8....5......5...4..3...98..7.......2.1...85..9......1..4......3..2
98.7.....76....8....5......6...4..3...86..5.......2..1.5...1.2...68..7......3...4
98.7.....76....8....5......6...4..3...98..7.......2.1...86..9......1..2......3..4
98.7.....76....8....5......8...4..3...69..7.......2.1...78..9......3..4......1..2
98.7.....76....8....5......8...4..3...78..6.......2..1..96..7......3..24.....1...
98.7.....76....8....5......8...4..3...78..9.......2..1..95..7......1..4......3..2
98.7.....76....8....5......8...4..3...78..9.......2..1..96..7......3..4......1..2
98.7.....76....8....5......8...4..3...79..5.......2.1...98..7......3...2.....1.4.
98.7.....76....8....5.9..6.8...7..9....4....3.....21...7..5..8....1..3.......4..2
98.7.....76....9...........5...4..3...96..5.......2.1..5..2...3..69..7.......1.4.
98.7.....76....9....5.......4..3..2...86..7.......1..3..79..8......1..3......2..4
98.7.....76....9....5.......4..3..2...95..8.......2.19..89..7......4...2.....1.3.
98.7.....76....9....5.......5..4..3...89..7.......2..1..78..5......3..2......1..4
98.7.....76....9....5.......5..4..3...89..7.......2..1..78..6......3..2......1..4
98.7.....76....9....5.......5..4..3...89..7.......2..1..95..8......1..4......3..2
98.7.....76....9....5.......5..4..3...98..5......2...1..75..8......1..24.....3...
98.7.....76....9....5......4...3..2...96..7.......2..1..89..6......41..2.....6.3.
98.7.....76..5......4..97..4....79.....3...5.....2...1.7...64....8.1..2....2....3
98.7.....76..5......5..67..6....78.....4...32....1.....7...85.....3....4....2..1.
98.7..6......9.........6...5..4...3..4..8.9....2....1.1......5..6...94....38....2
98.7..6......95............6...5.8...4.6...3...2.....15....79...3.8...2...1.....4
98.7..6......95.4.........98.76.....6.3...7...2........7.2..8....2.4...1.....1.5.
98.7..6......96.......58...8....95...4.....3...2.....16...8.9...3.....2...1.....4
98.7..6......96.......58.7.8....97...4.........3....216...7.5...1.....4...2.....3
98.7..6......96.......85...7...6.8...4.....3...2.....16....89...3.....2...1.....4
98.7..6......98.......6....5..4...3..7..8.9....2..9..13.......5.4...78....1....2.
98.7..6......98.......65.8.4......32.6..5.9....1......2......4..7...68....3.....1
98.7..6....5.4..3......2...7....9....2.8..1....6.1...33......5...4.6.3.....1....4
98.7..6....5.4..3......9..27....2....9.8.......3.1..4.5....4.1...4...3......5...6
98.7..6....5.6..4......3...7....8....3.9..5....6.2...4.4.....1...2.5.4.........52
98.7..6....5.6..4......3...7....9..6.3.8.......2.1..5.4......2...1...5......2.1.4
98.7..6....5.6..4......3...7..3......3...92....6.1...45....8.1...1.5.4..........5
98.7..6....5.6..4......3...7..9......3...8.....2.5...66......54..4.2.1..........2
98.7..6....5.6..4......35..7..9......3...8.....2.1...42.......1..1.2.4.....1...2.
98.7..6....5.6..4......9...7....3....9.8.......6.4...53......21..4.1.5..........4
98.7..6....5.9..4......3..24...8..1..58.......1.9.......4.1..8....2..7.3.....6...
98.7..6....5.9..4......3..934..5.....5.....3...21.......3.4..1....9....7.....68..
98.7..6....5.9..4......4..98.....3..2.63......3..6...7.7.6..8......4..1......1..5
98.7..6....5.9..4......4..98..3.....2.6...3...3...6.7..6.8..7......1..9......5..1
98.7..6....7....5.....6...94....3.6..2.1.......9.5.8..1....4....3.2.......6.7.9..
98.7..6....7....5.....9....4..3...2..3...1.....6.8.5..3....4....1.2.......5.6.8..
98.7..6....7....5.....9....43.2.......9.6.8.......1...1..4...2..4...3.....6.5.9..
98.7..6....7.5........9..7.4....7..3.2....1....95...6.1.....2...3....4....86...5.
98.7..6....7.6.........5.7.4...9...3.2....1....86...5.3.....2...1......4..65...9.
98.7..6....7.95.......6....4......3..7..8.9....2.....13.......4.6...95....18...2.
98.7..6....7.95.......86...4......3..9..7.8....2.....13.......2.7...89....1....4.
98.7..6..5..........7.8..9.6...7..8....4.3..2......1...5..9..7...6..1..3...2..4..
98.7..6..5..........7.9..5.4...5..7....3....2.....21...9..8..4...4..62.....1....3
98.7..6..5...4......3..9.2.74..5.1....6..1..2...8.......9..32.....6...9........31
98.7..6..5...6......6....7..6...4.3...9.7.8.....2....1.5.1...4...8.9.5.....3....2
98.7..6..5...6..4...3..9..53....2..9.2.....1...8.......9...8..2...6..4......1..7.
98.7..6..5...8......6..5.8.4....6.9....3..2......2...1.9...4.6...4.1.7.....2....3
98.7..6..5...8..4...7..4...3....6..7..64...8.....2.....2......3..59..8.......2.51
98.7..6..5...9......4..8.3.79.5.......2..3.4.....6......8...4.1.....23.8.......2.
98.7..6..5...9......6....7.7....4..3..89..5......2..1...58..9......1..2......3..4
98.7..6..5...9......7..6....4...3.2...9.6.7.....1....3..8.7.9.....3....1.....2.4.
98.7..6..5...9..4......3..21.5.......9..4..1...4.....8..9.1..8....2..7.......6..3
98.7..6..5..4.......6.9..3.47.5..3....2.1...6.....8.....9.3.2.......2.9.........1
98.7..6..5..4.......6.9..3.7....53...4.8.......9.2...6..2.1.9.......9.21.........
98.7..6..54.........7.9..5.7...4..8....6....3.....2..1.9..8..7....1....2.....31..
98.7..6..7......8...5......8..9..7...6..4..3......2..1..86..9......1..2......3..4
98.7..6..7......8...5.....46...3.7...2...6..1..94.......78...4.....1...6.....23..
98.7..6..7......8...6.....5.4..3...2..96...7......21....79...6.....4.2.......1..3
98.7..6..7......9...6.....5.4..3...2..98...7......23....89...5.....1...3.....41..
98.7..6..7...8......5..6....4.3...2...6.9.8.......2..3..7.6.9.....1....4.....3.1.
98.7..6..7...9......56.....4....3.2..1......4..8.6.9..3.......2.2.1...3...7.5.8..
98.7..6..7...96........8...8......5..6...78....43....25......4..9..7.3....2.....1
98.7..6..7.5........6.8....8..6..7......4..3......2..1..78..5......3..2......1..4
98.7..6..7.5.8......6......6..8..9......4..3......2..1..89..7......3..2......1..4
98.7..6..75.........4.8..5.6....32...4..7..9...72....14...5..7....3....2.....61..
98.7..6..75.........4.8..7.4...7..8....3..2.......2..1.7..5..4....6..3.......1..2
98.7..6..75.........4.8..7.5...7..4....3....2.....13...7..5..8....2..1.......6..3
98.7..6..75.........4.8..755...7..9....3..2.......6..1.7..9..8....2..1.......3..2
98.7..6..75.........4.8..9.8...7..5....3..2.......2..1.7..9..8....6....2...1..3..
98.7..6..75.........4.9..7.4...5..9....3..2.......2..1.9..4..5....1..3.......6..2
98.7..6..75.........6.5..9.5...8..7....4..3.......2..1.7..9..6....1....4.....3..2
98.7..6..75.........6.5..9.8...9..5....4..3.......2..1.9..8..6....1..........34.2
98.7..6..75.........6.8..5.8...9..6....4....3.....21...6..5..8....1..2.......3..4
98.7..6..75.........6.8..9.8...6..7....4..3.......2..1.7..9..6....1....4.....32..
98.7..6..75.....8...6........86...5...7.4.3.......2..1..58...7.....3.2.......1..4
98.7..6..75.....8...6.......4..3...2..78...9......13....89...6......4..1.....32..
98.7..6..75.....8...6.......4..3...2..86...9......21....79...6.....4.2.......1..3
98.7..6..75.....8...6.......4..3...2..96...7......21....59...6.....41..3......2..
98.7..6..75.....8...6.......6..4.3....85...9......21....76...5.....2.4.......1..3
98.7..6..75.....8...6.......7..4...3..98...6......24....89...7.....1.2.......3..1
98.7..6..75.....8...6.......7..4...3..98...7......2..1..79...5.....1.4.......3..2
98.7..6..75.....8...6.......9..4.3....58...7......2..1..79...5.....1...2.....34..
98.7..6..75.....8...6.......9..4.3....79...6......2..1..98...7.....1.2.......3..4
98.7..6..75.....8...6......4...3...2..56...7......21....75...6.....4.2.......1..3
98.7..6..75.....8...6......4...3...2..56...7.....2.1....78...6.....4...3.....12..
98.7..6..75.....8...6......4...3.2....75...6......2..1..56...7.....4.........13.2
98.7..6..75.....8...6......4...3.2....75...6......2..1..86...7.....4.........13.2
98.7..6..75.....8...6......4...3.2...378...5......2..3..56...7.....2.1.......1..4
98.7..6..75.....8...6......5...4.3....98...7......2..1..86...9.....1.2.......3..4
98.7..6..75.....8...6......6...4...3..89...6......32....78...9......21.4.....1...
98.7..6..75.....8...6......6...4.3....89...6......2..1..76...9......3........14.2
98.7..6..75.....8...6......8...4...3..98...7......21....76...9.....3.4.......1..2
98.7..6..75.....8...6......8...4...3..98...7......21....86...9.....3...2.....14..
98.7..6..75.....8...6......8...4.3.2..76...9......3...2...3...1..98...7......14..
98.7..6..75.....9...6.......4..3...2..59...7......23....75...6.....2...1.....14..
98.7..6..75.....9...6.......4..3...2..96...7......21....58...6.....243..........1
98.7..6..75.....9...6.......6..4...3..89...7......21....78...6.....3.2.......1..4
98.7..6..75.....9...6.......6..4.3....59...6......2..1..95...7.....3...4.....12..
98.7..6..75.....9...6.......6..4.3....59...6......3..2..76...5......2..1.....14..
98.7..6..75.....9...6.......6..4.3....59...6......3..2..96...5......2..1.....14..
98.7..6..75.....9...6.......6..4.3....95...7.....2...1..76...5.....3...4.....12..
98.7..6..75.....9...6......4...3...2..56...7......21....75...6.....4.2.......1..3
98.7..6..75.....9...6......4...3...2..56...7.....2.1....79...6.....4...3.....12..
98.7..6..75.....9...6......4...3...2..86...7......21....78...6.....4.2.......1..3
98.7..6..75.....9...6......4...3.2....79...8......1..3..98...7.....12.........1.4
98.7..6..75.....9...6......5...4...3..75...6......21....59...7.....3...2.....14..
98.7..6..75.....9...6......5...4...3..95...7......32..2...1...4..76...5......41..
98.7..6..75.....9...6......5...4...3..95...7......32..2...1...4..89...5......41..
98.7..6..75..6.........8.9.5....6.8....4..3......2...1.9...5.6....3....2....1.4..
98.7..6..75..6.........9.8.8....7.6....4....3....2.1...7...6.9....1..4......3...2
98.7..6..75..6......6......4.9.8.5...3...4......5...42.6...2..1..8.5.7.....1...3.
98.7..6..75..6..8...6......6....4..3..89...6.....3.2....78...9.....21..4......1..
98.7..6..75..6..9...6......6..4.3.2...7.8.9..........1..9.7.8.....2...3......1..4
98.7..6..75..8......6........86..7......4..3......2..1..79..8......3..4......1..2
98.7..6..75..8......6......4..3...2...8.7.5.......1..3..7.5.8.....2....1.....3.4.
98.7..6..75..8......6......4..3...2...8.9.7.......1..3..7.5.8.....4.2..1.......3.
98.7..6..75..8..4...6......4..3...2...5.9.8.......2..3..7.5.9.....1....2.....4.1.
98.7..6..75..9......6.......4...3.2...7.8.9.....1....3..9.6.8.....3....4.....2.1.
98.7..6..76.........5......8...4..3...96..8.......2..13...2...4..69..7.......1.2.
98.7..6..76.........5.8..9.8...5..7....4.3..2......1...5..7..8....2..3.......4..1
98.7..6..76.........5.9..8.8...5..9....4..3.......2..1.9..6..5....5.1..4.....32..
98.7..6..76.........5.9..8.8...7..6....4....3.....21...9..8..7....3....2.....14..
98.7..6..76..8......5.......5.4...3...8.7.9.....2....1..7.9.5.....1....2.....3.4.
98.7..6..76..8......5.......5.4...3...8.9.7.......2..1..7.5.8.....1...4......3..2
98.7..6..76..8......5.......9...4.3...86..9......2...1.7..3..4...65..8.......1..2
98.7..6..76..8......5......4....3.2...6.9.8.....1....3..8.5.9.....3....4.....2.1.
98.7..6..76..8......5......4..3.2.1...8.9.7..........2..9.7.5.....2....4.....1..3
98.7..6..76..8......5......5....4.3...8.5.9.......2..1..6.9.5.....1...4......3..2
98.7..6..76..9......5.......4...3.2...7.8.9.....1....3..9.6.8.....3....4.....2.1.
98.7..6..76..9......5......4....3.2...8.6.9.....1....3..6.7.8.....3...1......2..4
98.76......5...76.........9.5.4..3....8.5...7.....2.1...6.8...5...3...4......12..
98.76....7..........5..89..4....97.....3...2.....1...3.9...78....4.3...6...2...1.
98.76....7..........5..89..5....48....4....3....23...1.9...57.....3...2.....1...6
98.76....7.....5....5....6..4...3.2...79..8......2...1..86..7......1...2.....4.3.
98.76....7.....8....5....6..9..4...3..79..5.......2.1...85..6......3..4......1..2
98.76....7.....8....5....6.5...4..3...95..6.......2..1..79..5......3...4.....1.2.
98.76....7....85.....54....8...7.6...9.....3...2.....15..6..7...3.....2...9....1.
98.76....75.........4..98..8....79.....3...2.....1...6.9...87.....23..1.........3
98.76....75....6....6......6..4...3...7.9.8.......2..1..9.8.7.....3....2.....1.4.
98.76....75....8....6.......4.....3...85..7......32..1..78..5......1...2.....3.4.
98.76....75....8....6......5....4.3...76..5......2...1..58..6......1..4......3..2
98.76....75....8....6......8....4.3...58..7......2...1..76..5......1...4.....3.2.
98.76....75....9....6......6..4...3...9.7.5.......2..1..8.9.6.....1...2......3..4
98.76....75...89....6........9.8.5.....4...3......2..1..5.9.8.....3...2......1..4
98.76....76....5....4........53..2......4..8......1..9..35..6......8..1......9..4
98.76....76....5....4........53..2......4..9......1..8..35..6......9..1......8..4
98.76....76....5....4........53..7......8..2......4..9..31..6......9...8.....2.4.
98.76....76....5....4........7.5.4.....8...9......3..2..5.4.1.....9....3.....2.8.
98.76....76....5....4........7.5.4.....9...8......3..2..5.4.1.....8....3.....2.9.
98.76....76....5....5........45..6......3..8......9..2..14..7......8..9......2..3
98.76....76....5....5........45..6......3..9......8..2..14..7......9..8......2..3
98.76....76....9....5........78..6......4..3......2..1..69..7......1..4......3..2
98.76.5..4....8.....5........8..97.....3...2.....1...4..7..68.....2...1.....4...3
98.76.5..5....8.....7.......6.4...3...9..57......2...1..5..96.....1...4.....3...2
987......6..8..7...5.......8...4..3..7.9..8.......2..1.9.7..5......1..4......3..2
9876.....6...9.8...5........9..7.6.....4...3......2..1.6..8.9.....1...4......3..2
champagne
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Re: JExocet Pattern Defintion

Postby champagne » Wed May 29, 2013 3:02 pm

David P Bird wrote:
you wrote:On my side, the "abi loop" is clearly a pattern and searched as such, may be because I made the analysis you mention later

Don't give up hope, there's still a chance that you may convert me!



Just to comment on that point:

As very often when I am working on patterns, I stay on the practical side. In that case, I did not try to design the "most general case". I just look for a pattern very similar to "fata morgana"

- 2 UR threats with no active digit in cross line 0
- one digit per block in that same cross line
- one digit in the target cross lines outside the exocet band
- one digit per band in the row/column containing the UR threat, not in the cross lines of the targets
- bi-value in each block (with a possibility of a group in the row column of the threat, but I I don't know if this came)

This seems very limited, but it works.

I do not intend to look for more before I see an example of another fruitful pattern.
champagne
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Re: JExocet Pattern Defintion

Postby daj95376 » Wed May 29, 2013 5:35 pm

denis_berthier wrote:J-Exocets in SudoRules

I have coded basic Jk-Exocets (k = 2, 3, 4, 5) in SudoRules.
By basic, I mean that, for each base digit, the instances of this digit in the S lines are covered by 2 orthogonal lines (no blocks are considered).

My rules are not yet fully tested, but I've tried them on the first puzzles in the "04a double exocet.txt" file in Champagne 2012-10-20. I chose the highest level ones because the results should be insensitive to the presence of other rules (here SSTS).
I find the same base digits and cells and the same target cells as in this list. As the eliminations are not listed, I can't check them.
...
It appears that 3 out of the 10 secondary JExocets allow no elimination.
Counting JExocets without checking whether they are useful is therefore not a good idea.

Denis,

Congratulations on being able to detect basic Jk-Exocet. I think this is an important first step. However, as already mentioned, more eliminations can often be derived by examining the JExocet with respect to surrounding conditions. Here's an example from your listing where I've folded your results into my solver's output: (ignore my solver's use of QExocet in the labels.)

Code: Select all
Puzzle #2: .23.....94.....1...9..3..4.2..81...4.....78..9...4...23...9...1.6..........5.....

 second J4-Exocet marked with respect to a secondary equivalence
 +-----------------------------------------------------------------------------------------+
 |  15678    2        3        |  1467    Q567-8    14568    |  567      5678    R9        |
 |  4       B578     B5678     |  2679     25678    25689    |  1        235678   35678    |
 |  15678    9        15678    |  1267    Q3        12568    |  567-2   #4       R5678     |
 |-----------------------------+-----------------------------+-----------------------------|
 |  2        357      567      |  8        1        3569     |  35679    35679    4        |
 |  156      1345     1456     |  2369     256      7        |  8        13569    356      |
 |  9        13578    15678    |  36       4        356      |  3567     13567    2        |
 |-----------------------------+-----------------------------+-----------------------------|
 |  3        4578     24578    |  2467     9        2468     |  24567    25678    1        |
 |  1578     6        1245789  |  12347    278      12348    |  234579   235789   3578     |
 |  178      1478     124789   |  5        2678     123468   |  234679   236789   3678     |
 +-----------------------------------------------------------------------------------------+
 # 201 eliminations remain

 ### -5678- QExocet   Base = r1c78   Target = r3c1,r2c5==r3c3

J4-Exocet-in-columns:
     base digits = n6, n7, n5, n8
     base cells = r1c7, r1c8
     S columns = c9, c1, c5
     target cells = r3c1, r2c5
      ==> r3c1 <> 1, r2c5 <> 2

 ### -5678- QExocet   Base = r2c23   Target = r1c5==r3c7,r3c9   no direct elims

J4-Exocet-in-columns:
     base digits = n7, n8, n5, n6
     base cells = r2c2, r2c3
     S columns = c1, c5, c9
     target cells = r1c5, r3c9
      ==> NO ELIMINATION

 *** double QExocet

When considering just the second JExocet, there aren't any "direct" eliminations. However, when r3c8=4 is factored in, then there is a secondary equivalence for r1c5==r3c7 that leads to r1c5<>8 and r3c7<>2. As also already mentioned, the presence of a "double" JExocet in the same chute often allows for additional eliminations to occur -- even if neither JExocet contains any direct eliminations. I'll skip this consideration for now.

So, finding a basic JExocet without any direct eliminations is just the jumping-off point for applying additional constraints. Constraints that often haven't been properly identified/formalized. Thus, an opportunity for this thread as extended JExocet-based patterns are partitioned into various groups.
daj95376
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Re: JExocet Pattern Defintion

Postby denis_berthier » Wed May 29, 2013 6:11 pm

daj95376 wrote:Congratulations on being able to detect basic Jk-Exocet patterns.

Thanks, but this was a mere exercise.
My main purposes were:
- to check the logical complexity of the simplest non-ambiguous case, when all the necessary details are written,
- to estimate the mean number of eliminations.

BTW, I can say that the core of the pattern isn't the base and target cells but the constraints in the S columns, as David suggested.


daj95376 wrote:as already mentioned, more eliminations can often be derived by examining the JExocet with respect to surrounding conditions.

I understood, but this supposes additional work and therefore still higher complexity. This is much beyond my purposes. I don't plan to invest much time in JExocet extensions.


daj95376 wrote:So, finding a basic JExocet without any direct eliminations is just the jumping-off point for applying additional constraints. Constraints that often haven't been properly identified/formalized. Thus, an opportunity for this thread as extended patterns are partitioned into various groups.

It took 3 years before JExocets were (almost) clearly defined. I wish these extensions will be easier.
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Re: JExocet Pattern Defintion

Postby daj95376 » Wed May 29, 2013 6:49 pm

denis_berthier wrote:BTW, I can say that the core of the pattern isn't the base and target cells but the constraints in the S columns, as David suggested.

Here's my current perspective on quasi-basic JExocets:

*) Select base and target cells to test.

*) Select a value from the base cells and force all peers false that see all occurrences of this value in the base cells.

*) Search recursively for Hidden Singles in the resulting grid. Skip further testing if either target cell is forced true for this value.

*) Otherwise, continue and ...

*) Set a target cell false for the value and see if an X-Wing and/or additional Hidden Singles lead to the other target cell being true.

*) If the other target cell is forced true for this value, then repeat this logic for the other values in the base cells.

*) When all values in the base cells force at least one target cell to be true using the above logic, then a JExocet exists in my perspective.

I see the above being possible for a good manual solver. I believe this was one of David's objectives for the JExocet.

[Edit: corrected qualifier in statement with X-Wing.]
Last edited by daj95376 on Wed May 29, 2013 9:24 pm, edited 1 time in total.
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