The New Sudoku Players' Forum

[champagne]

Here the second UA4

Code: Select all

98765.......4..........3...87..2.9.6.95.6..726.2...85.25.....9..68....277.9...5.8
98765.......4..........3...87..6.9.2.95.2..766.2...85.25.....9..68....277.9...5.8 # original


and another possible definition of the property

If an UA of the solution grid is in the given, then you can switch to the twin(s) puzzle(s)

[coloin]

[code]...IMO These twin close to the original have a better chance to give good results

Maybe .. im not sure what is the best way to extend the vivinity search..
blunderbust aproach is what I am doing !!

[champagne]

chunk 18 m closed (solution grids rank 18M1 to 19M)
not bad, but 11.6 remains difficult to pass with skfr

Code: Select all

67..41...9...3.........8......45..13...1.38.9....8954..3..94.5....3.51.4.4.81.93.;11.3/11.3/10.4
.......8...2........4..76...8.31..651..5.67.8....7813.6.8.35.71...7.18.6.71....5.;11.3/11.3/2.6
..4....8............2..76...8.31..651..5.67.8....7813.6.8.35.71...7.18.6.71....5.;11.3/11.3/2.6
67...1...9...3.........8......45..134..1.38.9....8954..3..94.5....3.54.1.4.81.93.;11.4/11.4/10.4
..4......37.4..2........149...64..211..9.86.44...1298.....84..6.4.1.9..2...26.4..;11.4/11.4/2.6
.72..5.1.5.........9....54....53..94...4.98.19...1835.....54.89.893.14.5......1..;11.4/11.4/2.6
......9784.68..3..............31..57...9.58.3....7819...7.59.81..87.3..9...18.73.;11.5/11.5/2.6
4.68.7......2.1....2....8.9...7...25..79.21.8.....579.....29.51..15.8..7...17.98.;11.5/11.5/3.4
...9.7...397......84....7....679..12..91.26.5....5697.....15......2.91..91.67..2.;11.6/10.3/2.6
8.4..2.6..........2..659......56..797..2.15.6....9721.....16.9....9.57.1...72.65.;11.6/11.4/2.6
2.4..7.3.......78..1..3.......78..13...1.35.6....6587.....51.68...6.83.7..837..5.;11.6/11.6/2.6

[champagne]

2 more chunk closed

chunk 19 similar to previous ones

Code: Select all

....9.2.......1....347.2.....921..561..6.57.9....7912.....56.9.6..9.75.....12.67.;11.3/11.3/2.6
.4...8....9...13....7.........87..65...5.61.3....1378.36..85....1.3.75.6..516..3.;11.3/11.3/2.6
.....6...29...1.....7........531..877..6.53.1....7865..7..53.1....1.75.8.5.86.73.;11.4/11.4/10.4
97.........8........4.5....7.956..21...2.19.71...9756.....72.....76.51.2..591.67.;11.4/11.4/2.6
...87.....4.....6.29.....8...513..78..37.86.5....6531.....87.56...5.38.1...61.7..;11.5/11.5/2.6
84.........2........7.51......79..65..61.27.9..9.6512.....29...91.5.76.2...61.95.;11.5/11.5/8.3
.....3....94........2....8.1..65..787..3.16.5....8731.....16.5....5.81.7.5173.86.;11.5/11.5/9.2
....86.....6....7.29.........531..87...6.53.1....7865..7..53.1....1.75.8.5.86.73.;11.5/11.5/9.4
9.2...3....4...5.....13.......87..56.8.5.61.3.6..1378.....68.37...3.16.5...75..1.;11.6/11.6/2.6
974.........57......2.....7...78..13.8.1.35.6....5687.6.8.37..13..6.5..8...81....;11.6/2.0/2.0

and a poor in very high ratings

Code: Select all

3.8.........6.7.........5.....97..657..5.61.2..6.1279.2.1.69.57...1.52.9...72..1.;11.3/11.3/2.6
85.....2.......8...7.281......64..9846.9.81.2....12.......94.869..1.62.4...82.9..;11.3/11.3/2.6
85.....2.......8...7.281......64..9846.9.81.2....12.......96.849..1.42.6...82.9..;11.3/11.3/2.6
5.7.21...8.............9......46..124..1.29.8....9864...2.84.6....2.61.4..491.82.;11.4/11.4/10.4

The first step (target 33 millions solution grids processed) could be over in 2 months
I started implementation of a tailor made vicinity search to work on the best seeds

[champagne]

chunk 21 closed, only 5 skfr>=11.3, but a new 11.7
now five 11.7 in expanded puzzles,

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8.....2.1.3....9....79.2......12..65.6.7.91.2....5679.....95.1....2.16.9...67.52.;11.4/11.4/10.3
59...3........7.....8.2.......64..3246.3.27.8....7846...4.86.2....2.48.3...73.64.;11.4/11.4/11.1
.38..19......9....9......1....21..65.2.5.67.9..6.7912.....52.91...9.7..6...16.27.;11.4/11.4/2.6
..8.........671...3......67...79..56...1.27.9....6512.5.7.26.9....9.7...9.251.67.;11.6/11.0/2.6
.415...........5...9.7........31..56..36.57.8....7813.8...63......8.76.567.15.38.;11.7/11.3/7.1


[champagne]

chunks 22 and 24 closed one more 11.7

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......2...16...3.95.4.3....7..45..32...7.94.54...2379...2.95......2.4..3.4.37..2.;11.3/11.3/2.6
.12...8............5..8..6..2364..877.....6.4......32..7..24..6...7.62.82..83.74.;11.3/2.0/2.0
.1...5..93.4..........7.....2.65..97.6.9.72.1....2156.....96.759....21......1.92.;11.4/11.4/2.6
4.62..9........312.2..........71..232..3.57.9....2915.....52.919..1.3..7...97..3.;11.5/11.5/2.6

Code: Select all

2.6.....9.....3.......9...1...31..981.39.84.5....4513.8...39.1..9.5.1..3...48.95.;11.3/10.9/10.4
......8.5.....3....42.5.3..7..31..56...6.57.8....7813..35.86......5.1..3..173.58.;11.3/11.3/2.6
.4.1.2...2...9......8......7..65..12.2.9.75.6..6.2197...2.76..9.6.2.91.7...51....;11.3/11.3/2.6
..8..7.....2.....39.4...5...8.31..56...6.57.8.5..7813.8.5.63..1...8.1..5...75....;11.6/1.5/1.5
..8.......72.....39.4...5...8.31..56...6.57.8.5..7813.8.5.63.71...8.1..5...75....;11.6/10.4/7.2
.2.8.....4.6.3..........1.3...31..72.3.7.58.1.7..8253...7.23..5...1.82.7...57.3..;11.6/11.6/7.1
..8.....1314.........51.......12..79.2.7.95.6....5621.9.2.61..76..9.5..2...27....;11.6/2.0/2.0
.34....6.2...56...6.8...9..7..21..561..6.57.9....7912...5.62.9....7.1......59....;11.7/11.7/3.4


The ratio number of start/ solution grid continues to go down slowly, now 1.3 for an average expected of 0.5

[champagne]

chunks 23 and 25 closed, no 11.7, next to come i in chunk 26

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3.8..............5....7..1..2.65..97.6.9.72.1....2156.9...16.5....7.29.6..659.17.;11.3/11.3/2.6
.34...9.....6.9...9........1..97..657..5.61.2....1279.....65.21..12.7..9...19.57.;11.3/11.3/3.4
3.......2..7..2...8.....9..7.921..651..5.67.9..6...12.....21.9.2..9.56.1...76.25.;11.3/11.3/3.4
24..........7......9......5...31..56..36.57.8..6.7813.....86..186.1.75.3...53.68.;11.4/11.4/8.9
24...3........1.....1....58...13..65...7.81.3....6578.3...86.7....3.75.66..51.83.;11.5/11.5/10.2

Code: Select all

9..52.....48.....5.......6....97..211..6.59.7....1265.....57..6.7.1.95.2...26.17.;11.3/10.3/8.3
9..52.....487............6....97..211..6.59.7....1265.....57..6.7.1.92.5...26.17.;11.3/10.4/7.1
9..52.....487............6....97..211..6.59.7....1265.....57..6.7.2.91.5...16.27.;11.3/10.4/7.1
..4..9....7.....2...8...6...2.97..657..5.61.2....1279.6.2.95.....51.72.6.17......;11.3/10.9/2.6
9..52.....487..2.........6....97..211..6.59.77...1265.....57....7.1.95.....26.17.;11.3/11.1/3.4
......38.6...2.....91.......8.64..324..3.27.8..3.7846...2.86.74...2.4..3.4.73....;11.3/11.3/2.6
..6.4.......8.....35.........946..12...1.29.812..9864.....84.26..26.98.1...21..9.;11.3/11.3/2.6
.38..1..........7.....5.....6.21..97...5.62.1.2..7956...7.65.1....1.79.6..692.75.;11.3/11.3/7.6
.7.1......5..64..........4.1..64..98...9.81.2....1246...8.26..4...8.16.9..649.82.;11.4/11.4/2.6


[champagne]

chunks 26/27 closed with a new 11.7
Approaching the chunk 33 planed to be the last scan in this phase.

Now preparing a vicinity search around the best seeds seen here.
I'll open new threads to comment on this new task. One or 2 threads for the process, one for the results.
This thread will continue to receive results of more chunks in due time

Chunks 33 should hit one solution grid of the "loki" family.

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..87......146.5.........5....921..56.2.5.67.9.6..7912.9....2......9.76.5..71..29.;11.3/11.3/3.4
....6.....4.....8..92....6....65..13...8.75.6....3187..31.76..8...5.37.1.7.18.63.;11.6/11.6/9.2
.4.........2.....35...38...7..65..31...3.18.71...8756.....73..6...8.61.5...51.37.;11.7/11.7/3.4

Code: Select all

.1........9..4...2..6..8...7..32..64..36.48.7....8723.....73.26...4.2....3.86.47.;11.3/11.3/2.6
.5........91.........4.8......23..46...8.72.3....6487..36.42..7..73.64.2...78.36.;11.3/11.3/2.6
.91.......5..........4.8......23..46...8.72.3....6487..36.42..7..76.34.2...78.63.;11.3/11.3/2.6
8..............587.428..61.1..78..65.6.1.37.8....5613.....38.5....5.7......61.87.;11.3/11.3/2.6
..7....4..1..4.....45.......6.12..98...4.61.2.2..8946.8...62..4...8.46.9...91.8..;11.4/2.0/2.0
..7.4.....1.....4..45.......2.46..89...1.24.6.6..9812.8...26..4...9.48.2...81..9.;11.4/2.0/2.0
.76...1.....3.......2.........45..13...1.38.91...8954..9..34.51.419.5..8...81.49.;11.5/11.5/2.6


[champagne]

chunk 29 should be closed to-morrow
chunks 30;31 closed

Not very rich, but 2 11.7, likely same solution grid, in the chunk 30

Code: Select all

....5....9.2.6...5......176...87..311..5.68.7.8..1356.6...37......1.56.3...68.7..;11.3/11.3/2.6
.....4..21.3.9.4.........9..5.92..766..7.59.4.9..4625...6.59..7...4.26.....67.5..;11.3/11.3/3.4
1...7.....563...........2.3...84..21...7.34.8..8.2173.....84..28..1.73.4...23.18.;11.3/11.3/7.1
4.8.............91.5...7......21..56.2.5.67.9....7912.....62.1...69.12.5...75.96.;11.4/11.4/2.6
........87.9.......2........3.68..41...1.28.3.1..4326...4.18.3....3.61.43.142.68.;11.5/10.5/10.2
4.67...2................987...35..7.3..8.75......2983.....73.98.7.9.52.3.3.28.7..;11.7/11.7/2.6
4.67...2.7..............987...35..7....8.75....7.2983.....73.98.7.9.52.3.3.28.7..;11.7/11.7/2.6


Code: Select all

.......9..12........45..8...3.69..156..1.39.8....8536.....56.89...9.81.3.8.31..5.;11.3/10.8/2.6
.......9..12..9.....4...8...3.69..156..1.39.8....8536.....56.89...9.81.3.8.31..5.;11.3/10.8/2.6
.4......923................12.65..975..9.72.17...2156.....79.1..7.1.59.6...26.75.;11.3/11.3/2.6
4.18.....2.......36.....9..5.4....981.39.8.......4513..4..83.51.5.4.1..9.1.59..4.;11.4/10.3/2.6
4.18.9...2.......36.....9..5.4....981.39.8.......4513..4..83.51...4.1..9.1.59..4.;11.4/11.1/2.6
4........9...5............6...31..651..6.57.8....7813...5.83.718.75.16....176.58.;11.4/11.4/2.6
4..5...........7..9...73...7..65..31.6.3.18.7....8756.3...16.7...17.5...6..83.15.;11.4/11.4/3.4
8.6......4.............1......79..56.6.1.27.97...6512.6...27.9..7.9.62.59..51.67.;11.4/11.4/9.0


We are close to a switch to the second phase, the vicinity search.
I'll comment in the next post some thing seen in my tests

[champagne]

It seems that I missed one report.
chunks up to 35M are now closed, and due to some delay in the vicinity search start, I also hav an ongoing scan of the chunk 36 (solution grids 36M1 to 37M)

This is a little more that what I intended to do in the direct scan.

Best results for the missing closed chunks

chunk 29

Code: Select all

9.......2.6.....3....3.5......48..73..45.72.8....3254.....54.877..2.3...45.87.32.;11.3/11.1/7.3
9.......2.6.....3....3.5......48..73..45.72.8..8.3254.....54.87...2.3...45.87.32.;11.3/11.3/7.3
.8...5..3....7..4..6......9..7....253..2.97.4.4..5739.....24.57.7.5.39.....79.43.;11.4/11.4/2.6
.75..4...8.......4...9.8......69..41...4.28.9..4.8126.....46.121..8.94.6...21.9..;11.5/11.5/2.6


chunk 32

Code: Select all

..1....8.9..4....6.5.....4.7..32..64...6.48.7..4.8723.....36.78...7.24.3...84.6..;11.3/11.3/2.6
....3.5....6........14........97....7.93.24...23.4579.....93.573..5.42.9.9.72.3..;11.3/2.0/2.0
....3.5....62.......1.........97....7.93.24...23.4579.....93.573..5.42.9.9.72.3..;11.3/2.0/2.0
4.8............197..........2.56..79...2.15.6.6..9721.9...16.5...69.57.1...72.96.;11.5/11.5/2.6
4.8............791..........2.56..79...2.15.6.6..9721.9...16.5...69.51.7...72.96.;11.5/11.5/2.6


chunk 33

Code: Select all

69.8.3.7......2.......5......7.3..84.....43.7....7852.....87.32..34.57.878.32.4..;11.3/10.4/2.6
......879..........237........59..615..6.89.7....7158..9..17..66..9.57.8...86.19.;11.3/11.3/2.6
......978.........1.3..8..6...27..94...8.96.7....4628.9...87.6....6.48.98..92.74.;11.3/11.3/2.6
9...8....2...3.....5.....3..6.31..877..6.53.1....7865.8...57..3...1.35.8...86.71.;11.3/11.3/2.6
.237..4........78.7........6..91..479..8.76.1....6489.....71.6....6.9....6148.97.;11.3/11.3/3.4
.237..4........78.7........6..97..419..8.16.7....6489.....17.6....6.9....6148.97.;11.3/11.3/3.4
24......38..7.6............5..31..8778.6.53.1....7865...8.57.3....1.3.....586.71.;11.4/11.1/3.4
......7..4..5.....9...76...7..65..31.6.3.18.7....8756.6...13.7...17.5...3..86.15.;11.4/11.4/3.4
91..........62.....5..........46..78..47.83.2....3264.....84.238..3.6..73..27.86.;11.5/10.2/2.6
...271.....2......4.89...2..6.79..12...1.26.5.2..6597.2...1..5....5..2.1...62.79.;11.5/11.5/2.6


chunk 34

Code: Select all

2........97.8.................57..63...3.61.836..8175.....65.311.37.86.5.5.13.8..;11.3/10.9/2.6
...1.......2...8....6.9....1.354..89...8.9.......1345..91.85.3..3.9.15.8.5.43.91.;11.3/11.3/2.6
8..7.2.........7..47.....1........9756.9.72.1.....156.....96.75.9.2.51.66..17.9..;11.3/2.0/2.0
.5......1..........7.814......46..89..91.24.6.6..9812.....86.1.6..2.19.8...94.26.;11.4/11.4/2.6
..6...34...19......72...89....54..895..8.91.3....1345.....95.1....3.1......48.93.;11.6/10.9/2.6


chunk 35

Code: Select all

...6.7...4.......12......6....13..56...7.81.3....6578..5..81.3..1.3.65.83..57.61.;11.3/11.3/7.2
..1.....2..8..........5..9....54..235.42.37.9....7945..3..95.74.7.3.42.....72.93.;11.4/11.4/2.6
..1.....2..8..........5..9....54..235.42.37.9....7945..7..95.34.3.7.42.....32.97.;11.4/11.4/2.6
.5..........6.2....7......1...89..46.642.18.9..9.6421.....86.9.6..4.91.8...12.46.;11.5/11.5/7.1
..6..1....5......2..7...8.....46..89.891.2....64...12.9...24.6.4..9.62..6..81.94.;11.6/10.3/2.6
..62.1....5......2..7...8.....46..89.891.2....64...12.9...26.4.6..9.42.....81.96.;11.6/11.6/2.6
.75.4...............1.......8.46..23.2.7.84.6.64.3278.....86.3...63.48.2...27.64.;11.7/11.4/2.6


chunk 36 (last one should be closed in 2/3days

[champagne]

the last chunk (36) is now closed with 2 new 11.7, likely in the same solution grid

Code: Select all

9..713...4.......7.........1..65..78.8.3.16.5....8731.....75.6...58.67.1...13.85.;11.3/11.3/2.6
.....9...3.5.....6.......4....64..21...9.86.4.6..1298...2.84.6....1.62.88.629.41.;11.3/11.3/6.6
.68....3..1.32....3........8..45..23..57..8.4......75..23.45......8.73.278.23..4.;11.3/2.0/2.0
4.......8..9.......2..87....6.81..73...7.62.1.1..3286.....63.8....1.86.76..27.31.;11.6/11.6/9.7
.15.4......7................2.46..89...1.24.6.64.9812.....86.9...69.48.29..21.64.;11.7/11.4/10.3
.15.4......7................2.46..89.8.1.24.6.64.9812.....86.9...69.48.2...21.64.;11.7/11.4/2.6

I wanted to cover 33 million solution grids, so the job is done
the next phase will be to work in the vicinity of these results.

I started tests on the results of the 21 first million solution grids.
I'll report on this in other threads.
My first test has been in the vicinity of puzzles rating >=11.2.
I got one solution grid with puzzles rating skfr 11.8. This will be the start for a deeper vicinity search.
Next is the vicinity of puzzles rating 11.0 11.1 but due to the number of such puzzles, the vicinity is expected to be covered next week.

[ghfick]

I am exploring the chunks looking for interesting paths after the TH. In chunk 35,

..1.....2..8..........5..9....54..235.42.37.9....7945..3..95.74.7.3.42.....72.93.;11.4/11.4/2.6

After the TH, YZF_Sudoku can find only impossible pattern forcing chains to advance the puzzle like:

Impossible Pattern(168{r4c267,r5c258,r7c147,r8c589,r3c29,r6c19,r9c6}) Forcing Chain: Each true guardian of Impossible Pattern will all lead To: r3c2<>6
2r3c2
4r3c2
2r6c1 - 2r6c2 = 2r3c2

A really tough one?

[marek stefanik]

There are a couple tricks to this one.
After TH 168# => –168r9c9:

Code: Select all

,---------------,-----------------,----------------,
| 346   59    1 | 4689  368  7    | 3568  468  2   |
| 2346  59    8 | 1469  136 b16–2 | 1356  146  7   |
| 2346  246   7 | 1468  5    1268 | 1368  9   b16–8|
:---------------+-----------------+----------------:
| 7     168   9 | 5     4   #168  |#168   2    3   |
| 5     168   4 | 2    #168  3    | 7    #168  9   |
| 1268  1268  3 |#168   7    9    | 4     5   #168 |
:---------------+-----------------+----------------:
|a18    3     2 |#168   9    5    |#168   7    4   |
| 9     7     5 | 3    #168  4    | 2    #168 a18–6|
| 148   148   6 | 7     2  a#18   | 9     3   #5   |
'---------------'-----------------'----------------'

Let a be the digit in r8c9.

Suppose there exists a solution where a is different from the digit in r9c6.
From this solution, remove all digits outside # and set ar9c9.
That gives us a 3-colouring of TH, which is a contradiction.
Therefore, in all solutions, a appears in r9c6 and then also in r7c1. –6r8c9

Consider c456789. Each of them contains one of 168 in each band.
Therefore, the permutations of 168 in c456 have the same parity. The same is true for c789.

Notice that c58 also have the same parity, as all their respective 168s are different:
The top digits cannot be both 1s or both 8s, because they would have to be in the same row.
They also cannot both be 6s because of r8.
The middle digits are in the same row and cannot be the same, which also applies to the bottom digits.

Therefore, c456789 all have the same parity.

Let b be the digit in r3c9.
Since c69 have the same parity and their bottom digits are the same, their top digits are the same also.
Therefore, we get br2c6, –2r2c6, –8r3c9.

Code: Select all

,-------------,----------------,----------------,
| 346  59   1 | 4689  368  7   | 3568  468  2   |
| 2    59   8 | 1469  136 b1–6 | 1356  146  7   |
| 346  46   7 | 1468  5    2   | 1368  9   b1–6 |
:-------------+----------------+----------------:
| 7    168  9 | 5     4    168 | 168   2    3   |
| 5    168  4 | 2     168  3   | 7     168  9   |
|b1–68 2    3 |a18–6  7    9   | 4     5    168 |
:-------------+----------------+----------------:
|a18   3    2 | 168   9    5   | 168   7    4   |
| 9    7    5 | 3     168  4   | 2     168 a18  |
| 148  148  6 | 7     2   a18  | 9     3    5   |
'-------------'----------------'----------------'

In r6, a must take r6c4 (–6r6c4) and b (which is different from a because of c9) must then take r6c1 (–8r6c1).
Now, br3c9 and br6c1 together see all candidates of 6b1. –6b, stte