Maximum number of clues for a given SE rating

Everything about Sudoku that doesn't fit in one of the other sections

Re: Maximum number of clues for a given SE rating

Postby 999_Springs » Sat Dec 15, 2018 9:55 pm

qiuyanzhe wrote:Hi 999_Springs,
This is my second try of modifying your 10.6, surprisingly it is SE10.5.
10.5 | 42 | 7.96..8..6.398..57.8..7...98.2.57.9.9....6.78.6789.5..5.17.89...76..9.85.9856.7..

well done on finding this 10.5, i also found the same puzzle last night during my search

the best thing about this 10.5 is that it is a diamond, meaning that the first move in the puzzle is 10.5
Code: Select all
7.96..8..
6.398..57
.8..7...9
8.2.57.9.
9....6.78
.6789.5..
5.17.89..
.76..9.85
.9856.7..  10.5/42 diamond

i also found this 10.6 with 41 clues
Code: Select all
7.96..83.
6..98..57
.8..7...9
8.14.7.9.
9....6.78
.6789.5..
5..7.89..
.76..9.85
.9856.7..  10.6/41


i've been doing a systematic search in the area of the puzzles i found that broadly goes like this:

repeat {
move the 1,2,3,4's around the puzzle, check for new hardest puzzles
remove 1 or more 5,6,7,8,9 clues and check if the puzzle doesn't begin with a single, check for new hardest puzzles
} until no more puzzles found

here are all the 10.5's and 10.6's that i've found so far, with some highlights of the (lots of) 10.4's. ED (diamond rating) is rating of the first step. all of these puzzles have the same solution grid except for one
Code: Select all
7.96..83.6..98..57.8..7...98.14.7.9.9....6.78.6789.5..5..7.89...76..9.85.9856.7..  10.6/41
..96..8..6.398..57.8..7...98.1.57.9.9....6.78.6789.5..5..7.89....6..9.85.9856.74.  10.6/40 ED=10.5
..96..8..6.398..57.8..7...98.1.57.9.9....6.78.6789.5..5..7.89....6.49.85.9856.7..  10.6/40
..96..8..6.398..57.8..7...98...57.9.9..1.6.78.6789.5..5..7.89....6..9.85.9856.74.  10.6/40 original
7.96..8..6..98..57.8..7....8.14.7...9....6.78.6789.5..5..7.89...76..9.85.9856.7.2  10.6/39
7.96..83.6..98..57.8..7....8.14.7...9....6.78.6789.5..5..7.89...76..9.85.9856.7..  10.6/39
7.96..8..6..98..57.8..7......1457...9....6.7..6789.5..5..7.89...76..9.85.9.56.7.2  10.6/37

7.96..8..6.398..57.8..7...98.1.57.9.9....6.78.6789.5..5.27.89...76..9.85.9856.7..  10.5/42 diamond
7.96..8..6.398..57.8..7...98.1.57.9.9....6.78.6789.5..5..7.89...76..9.85.9856.74.  10.5/42 ED=10.4
7.96..8..6.398..57.8..7...98.1457.9.9....6.78.6789.5..5..7.89...76..9.85.9856.7..  10.5/42
7.96..8..6.398..57.8..7...98.1..7.9.9....6.78.6789.5..5.27.89...76..9.85.9856.7..  10.5/41
7.96..8..6.398..57.8..7...98.14.7.9.9....6.78.6789.5..5..7.89...76..9.85.9856.7..  10.5/41
7.96..8..6.398..57.8..7...98.1..7.9.9....6.78.6789.5..5..7.89...76..9.85.9856.74.  10.5/41
7.96..8..6..98..57.8..7...98.1..7.9.93...6.78.6789.5..5..7.89...76..9.85.9856.7.2  10.5/41
7.96..8..61.98..57.8..7....82..57...9....6.78.6789.5..5..7.89...76..9.85.9856.74.  10.5/40 ED=10.4
..96..8..6.398..57.8..7...98...57.9.9....6.78.6789.5.15..7.89....6.49.85.9856.7..  10.5/40 ED=10.3

..598....8..7.65.9..9.53.8678...569.95..678.1..689..575.8.7.96...75.9..849.6.8..5  10.4/43 ED=10.3
7.96..8..61.98..57.8..7...982..57.9.9....6.78.6789.5..5..7.89...76..9.85.9856.74.  10.4/42 diamond
7.96..8..6..98..57.8..7...9821.57.9.9....6.78.6789.5..5..7.89...76..9.85.9856.74.  10.4/42 diamond
7.96..8..6..98..57.8..7....821.57...9....6.78.6789.5..5..7.89...76..9.85.9856.74.  10.4/40 diamond
7.96..8..6.398..57.8..7....8...57...9....6.78.6789.5.15.27.89...76..9.85.9856.7..  10.4/40 diamond
7.96..8..6..98..57.8..7...98.14.7.9.9....6.78.6789.5..5..7.89...76..9.85.9856.7.2  10.4/40 skfr 10.5


also found this one from the earlier pattern search
Code: Select all
128975346
394618257
567...981
846....79
71.....23
23.7...64
972...435
483597612
651342798  3.4/62


qiuyanzhe wrote:
Hidden Text: Show
P.S.
999_Springs wrote:123948657
467315982
895...314
984...376
37.4...29
25.....43
642...735
538672491
719534268  6.0/63

Here you made a typo aha.. 3 in r4 should be at r4c6

thanks for finding that - fixed

now that this post is the top of a new page - which is so great, because now you don't have to browse through my 9-year-old posts when clicking last page... oh god 2009 was such a simpler time in my life i miss those days - i'll repost the puzzle list so that you don't have to look back through those old pages. i'll also keep a record of the puzzle list by editing this post rather than do new ones

updating 3.4 8.0 8.2 8.7 9.3 9.4 9.6 9.7 9.8 10.5 10.6

ER |clues
----+-------------
1.0 | 80 |
1.2 | 77 |
1.5 | 68 | 1.8469.535.61.39..4932.51.6715942638839651...264837591647528319381794265952316..7
1.7 | 63 | 568749132791283645423165.9.6143..52.235.14..69875264131764.2.5..596.12.4.42.5..61
2.0 | 69 | 437691825268537941159842763892..5.3.615..3.8.743..8.5.326789514574316298981254376
2.3 | 64 | 327415698159862347684...25194....17571.....2353...1.69893..4716475186932261937584
2.5 | 61 | ...49.185..41..937.91.73642...7..451.1..4.273.4.231869459617328182354796376928514
2.6 | 66 | 219356784843..76596574982..19874.5.64325619787658.9.4.976.854..3219748655846...97
2.8 | 60 | 85.79263.673814925..9356.8778.5.9.6.9.56.3.78..61785495.7.81.96.9..6785.468935712
3.0 | 63 | 1239486574856179239672..81487..2..9623...6.8165.....42316...275592371468748562139
3.2 | 63 | 18.2.79.5.59..1827.72589.1.7186245932649531789357182..89.1.57.2521.76.89.47892.51
3.4 | 62 | 128975346394618257567...981846....7971.....2323.7...64972...435483597612651342798
3.6 | 54 | ......387....7.659.798.3421..5.3.946.6....735.....5812257389164498516273316247598
3.8 | 59 | 415.67.8967.89.4.589.4.5.67.6974285.287.596.4.546.89727.19845.69.85.674.546.7..98
4.0 | 50 | .4.731.9.1........9.78.....4863579127529148363192685475.31824.9..1.......94673.5.
4.2 | 70 | 96173254884395672172581463919467385268752.3.4352..8.67419385276238.67..55762...83
4.4 | 66 | 3495812676283975145714629384537296817861..492912.4.753165..4..92379...46894.....5
4.5 | 67 | 13524678926...75344.735.21665..3.1277235614988.1.726535..623971372..4865916785342
4.6 | 65 | 31524678942...75636.735.24125..3.1768365714927.1.623585..623917.72.84635.637.5824
4.7 | 64 | 9768125..813594726.5.376189768923415..516789..91458.676.97.1.585.72896.118.6.597.
4.8 | 61 | 1..2..953...51.28..523..14.2.5.38761.61.72538...156492574823619329641875618795324
4.9 | 59 | 1..2..953...51.28..523..14.2.5.38761.617.2538...156492574823619628..1375319675824
5.0Quad | 55 | 123754689548916732679283154861342597735...421294.7.368..6.2.9...5.....4.....3....
5.0UL10 | 63 | .1582.73.37.41.52828.735.6.867241395193658247542973.8.75.3.281..381.7.52.21584.73
5.1 | 55 | 1492573..62783.54.8356.42.7564728.3.2835.....971463825756..2..3.98..6.52.12..56..
5.2 | 61 | .285.9437357.4.8.949.3785.2.73..4928..98..374842793651784.36.952..9857439354.7.86
5.3 | 48 | .61..452.298...6144.561298..42...738..6...49.98....16.62..7835185.1..276.1.2..849
5.4 | 49 | 632145978817.92..4.4..87.1....85....16.274......96....481529.6.753416..9296738.4.
5.6 | 70 | 12345678945678912378913256423.9.58.66.52.893.8973612453625174985.86943.29..82365.
5.7 | 65 | 16324578942...73565.736.12421..3.567736..24988.5.762133..621975671..3842952784631
5.8 | 64 | 483126795159..76822675893415268..91.7189.245.394...82.671298534942...178835...269
5.9 | 64 | 176238594845179362932...7184573...81281.5..366938...75728...643569483127314.2.859
6.0 | 63 | 123948657467315982895...314984..3.7637.4...2925.....43642...735538672491719534268
6.1 | 60 | 528...341931524786476381592.19...85..64...17..53...62.195438267382976415647...938
6.2 | 65 | 947521683128763549653984127296...374731642958584397216..5.794.2..24..79.4792..8..
6.5 | 61 | 1.87.3649634.19..7..74861.3316872495785941362.4.3657185716.89.446...7..18.31.4.76
6.6 | 69 | 63972415872...6439.4..3.26746..7.382.932.8746287643591376482915854197623912365874
6.7 | 64 | 12.689.7586.735..175.142...385274169942561738671398.5.438926517596417...217853...
6.8 | 64 | 6..1..38..3.5.8.1..183...9...1723846243816759876459123127934568369285471485671932
6.9 | 65 | ..2.4.658....6.42346.25.971.4.532769926487135...619284685124397319876542274395816
7.0 | 63 | .134.7825..48.263128.1.3947....243183429187568.1.36294429671583.382451.91..3894.2
7.1 | 65 | 642319578187...439359...261914283657276...8935389..142721495386493...715865.3.924
7.2 | 65 | .6..92.84..4.16.35....54.96126935478759428361843167952...243617632571849417689523
7.3 | 61 | 371542986682...345459...217914376528768...13.523...76.135984672247...893896...451
7.4 | 50 | 9785..6..5..6.7.98.6..98.5789..567...567...89..7.8956.7..8.59466.597.821.8926.375
7.5 | 53 | .5....217....5.8348..3..659..8...57127....946......382582941763746523198931786425
7.6 | 57 | .45.67.896.78.94.589.45.67.4..57.896.69..8547578946123.5479..6878.6.495.9.6.857.4
7.7 | 57 | 4.5.67.8967..894.589.4.567.568.94..77.45..8969..67854.15794..682498.675.38675.9.4
7.8 | 56 | 59.86.7..86...7.95.475.968271892.5.6934156278256.789..62.78..59.85.9..67.796.582.
7.9 | 55 | 95.76.8..86...9.75..78.596268..9.5.7.2567..89.795.862.7164532985.8927..629.18675.
8.0 | 55 | 76.85.9..59...6.78..87.961568..9..57.1567.89..795.81.685.917.6.9472635811.64857.9
8.1 | 50 | 6857.29..71.95..86.49.86.5789.6.5.7..56..78.9.3789.56.96.5..7.852..7869..78.69..5
8.2 | 53 | 6759823148..75.926.29..685778.5.9.6.95..67.38..68..5795.7.9.68..68.75.9..9.6.8745
8.3 | 58 | ....472969...8.45747.5.9831..4...789.9...8164....94523549876312638412975721935648
8.4 | 54 | 59.86.7..86...7.95.475.968.7189..5.6934156278256.789..62.78..59.85.9..67.796.582.
8.5 | 54 | 59.86.7..86...7.95.475.968.7189..5.6934156278256.7891.62.78..59.85.9..67.796.58..
8.6 | 48 | 9758..6..6..97.8.5.8..56.7989.5..467.567.891...7.6958.76..9..585.86.729...9.857.6
8.7 | 50 | 59176.8..8625..9.7..7.98.56673.89..5..56.7.89.89.5.67.7.68.5.9.9.8.7.56..549.67.8
8.8 | 54 | 59.86.7..86...7.95.475.968.7189..5.6934156278256.789..62.78..59.8529..67.796.58..
8.9 | 53 | 57.96.8..86...7.953.98.567.78.59..6.9.5..67.81.678..596132589472976..58.458.79..6
9.0 | 53 | 7956..8..813.95.76246.87.9567.8.9.5.92.56.78.358.7.6.95627..9.8.379.856..89.56..7
9.1 | 51 | 57.96.8..86...7.953.98.567.78.59..6.9.5..67.81.678..596..2589472976..58.458.79..6
9.2 | 52 | 95.76.8..86...9.75..78.596.68..9.5.7..567..89.795.862.7164532985.8927..6.9.18675.
9.3 | 49 | 7956..8..812395476..6.87.9567.8.9.5.9..56.78..58.7.6.956.7..9.8..79.856..89.56..7
9.4 | 49 | 6857..9..7..95.186..9.8625789.6.537..56..78.9..789.56.96.5..7.85...7869..78.694.5
9.5 | 50 | 7956..8..81..95.76.46.87.9567.8.9.5.92.56.78..58.7.6.956.73.9.8.379.856..89.56..7
9.6 | 50 | 675982.1.8..7.6529..9.5.78678...569.95..6783...689..575.8.7.96..675.9.48.9.6.8.75
9.7 | 49 | 57.96.8..86...7.95..98.567.78.59..6.9.5..67.8..678..59612.589.73976..58.458.79..6
9.8 | 50 | 95.76.8..86.1.9.75..78.596.68.29.5.7..567..89.795.86..74635..985.89.7..6.9.48675.
9.9 | 49 | 8759..6..6..87..59..9.65.7878...95.6932456781.5678..9.5.8..796..6.59.8.7.976.8..5
10.0| 49 | 8756..9..61..98.75.49.75.8678...956.92.5.67.8.5678...959..6.8.7.3785.69..689.7.5.
10.1| 51 | 95.76.8..86...9.75..78.596.68..9.5.7..567..89.795.86..7164532985.8927..6.9.18675.
10.2| 49 | 6857..9..71395..86249.86.5789.6.5.7..56..78.9..789.56.96.5..7.85...7869..78.69..5
10.3| 49 | 57.96.8..86...7.953.98.567.78.59..6.9.5..67.81.678..596..258947.976..58..58.79..6
10.4| 49 | 7956..8..81..95.76.46.87.9567.8.9.5.92.56.78..58.7.6.956.7..9.8.379.856..89.56..7
10.5| 42 | 7.96..8..6.398..57.8..7...98.2.57.9.9....6.78.6789.5..5.17.89...76..9.85.9856.7..
10.6| 41 | 7.96..83.6..98..57.8..7...98.14.7.9.9....6.78.6789.5..5..7.89...76..9.85.9856.7..
11.2| 37 | 6....2.5952..4..1...35..2..3..1945...1.658.3...5273..1..4..51...3..2..4575.4....8

i dream of someday getting a 38+ clue puzzle hard enough to enter champagne's hardest database that would beat mauricio's old puzzle for the highest number of clues in his database
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs
 
Posts: 457
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

Re: Maximum number of clues for a given SE rating

Postby 999_Springs » Mon Dec 17, 2018 7:52 pm

found 12 new puzzles, highlights include a nice pair of quads found from the pattern search
Code: Select all
128935647
367841925
954...381
87.....56
21.....79
64.....32
781...263
496372518
532618794  5.0/60 (Naked Quad)

123965847
489317526
576..8913
8.4....75
2......89
6......34
945...762
368572491
712694358  5.4/59 (Hidden Quad)

unfortunately these don't generalise to naked/hidden triples (3.6 or 4.0) because puzzles at this level are heavily reliant on xy(z)-wings and ur's to advance a stuck position, and these are rated lower than quads. if you ask me i think it is a stupid idea and makes absolutely no sense to have quads after ur's and xy(z)-wings, especially since "direct" pairs and triples were given such low ratings (also an xy(z)-wing can very rarely eliminate one of the eight candidates that make up a UR and thus destroy it)

also found this lovely
Code: Select all
4.9315.82
.12948.53
385...491
548....67
9.14...28
23..8..14
894...276
153672849
.2.894135  5.1/57 (UL10 with hidden triplet)

which was found by finding a 63-clue UR with hidden triplet and extending the UL by 6 cells to fill the rest of the puzzle out. this is quite nice since practically all the 5.1's in the patterns game are UL10 with naked pair rather than hidden triplet (again it makes no sense for SE to rate a UR/UL with naked n-subset the same as a hidden n+1-subset and i read somewhere that nick said this was a bug to be fixed, but he never did, so whatever)

all the new puzzles found since last update
Code: Select all
1298657343459718268672..19597612..5823..5..1751.....62492.1.5836513..279783592641  2.5/64
1289354673768412959542..81384912..5623.....8161.....24581.9.6724625..139793612548  2.8/63
25671834978.69.125..9.25678375286914698.7.253.2.5397869...578625.286.497867942531  4.6/67
25671843978.59.126..9.2657857.6829.3392.7.685.689352.79...578628.526.794627849351  4.7/65
128935647367841925954...38187.....5621.....7964.....32781...263496372518532618794  5.0/60
4.9315.82.12948.53385...491548....679.14...2823..8..14894...276153672849.2.894135  5.1/57
123965847489317526576..89138.4....752......896......34945...762368572491712694358  5.4/59
87569....6..5.79.8..9..85677819...569...5678..5678...956487..9.398..567.127369845  7.4/52
59.76.84.86.5..9.7..7.98.5667..89..5..56.7.89.89.5.67.736845.9.918273564.5.916738  7.5/54
67598.1.48..75.9.6..9..685778.5.9.6295..67.18..68..5795.7.9.681.68.75293.9.6.8745  9.1/53
87569....6125.79.834921856778.9...569...5678..5678...956.87..9..98..567...7.698.5  9.3/51
59.86.7..86...7.95..75.968.7.89..5.6912356478.56.789..6..78..59.85.9..67.796.584.  9.4/50

i also found 1to9only's 5.8/64 and eioru's 6.1/60 like a zillion times each

the puzzles from the top end were found by adding things to dobrichev's puzzles. this also produced a nice 5.0/63 different to the current one from which i could remove cells to get the 4.6 and 4.7, which i'm surprised were never found with so few clues remaining. i think the UR/UL area is pretty much exhausted at this point
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs
 
Posts: 457
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

Re: Maximum number of clues for a given SE rating

Postby eleven » Mon Dec 17, 2018 11:22 pm

Thanks for the puzzles. Something for after X-mas days ...

I just looked at the first one. I see a 10-cell UR, but don't know, how to use it effectively.
Code: Select all
 *---------------------------------------------------*
 |  4   #67   9    |  3    1     5     | #67   8  2  |
 | #67   1    2    |  9    4     8     | #67   5  3  |
 |  3    8    5    |  27   26    67    |  4    9  1  |
 |-----------------+-------------------+-------------|
 |  5    4    8    |  12   23    139   |  39   6  7  |
 |  9   #67   1    |  4    356  #67+3  |  35   2  8  |
 |  2    3   #67   |  57   8    #67+9  |  59   1  4  |
 |-----------------+-------------------+-------------|
 |  8    9    4    |  15   35    13    |  2    7  6  |
 |  1    5    3    |  6    7     2     |  8    4  9  |
 | #67   2   #67   |  8    9     4     |  1    3  5  |
 *---------------------------------------------------*

Maybe 3r5c6 -> 56r5c57 & 9r6c6 -> 6r6c3 => -6r5c2,r6c6

Instead i solved it this way:
Code: Select all
 *---------------------------------------------------*
 |  4    67   9    |  3    1     5     |  67   8  2  |
 |  67   1    2    |  9    4     8     |  67   5  3  |
 |  3    8    5    |  27  a26    67    |  4    9  1  |
 |-----------------+-------------------+-------------|
 |  5    4    8    |  12  a23    139   |  39   6  7  |
 |  9   b67   1    |  4    35-6 b367   |  35   2  8  |
 |  2    3    67   |  57   8     679   |  59   1  4  |
 |-----------------+-------------------+-------------|
 |  8    9    4    |  15   35    13    |  2    7  6  |
 |  1    5    3    |  6    7     2     |  8    4  9  |
 |  67   2    67   |  8    9     4     |  1    3  5  |
 *---------------------------------------------------*
(6=3)r34c5 - (3=6)r5c26 => -6r5c5
eleven
 
Posts: 1946
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Re: Maximum number of clues for a given SE rating

Postby qiuyanzhe » Mon Dec 17, 2018 11:58 pm

999_Springs wrote:7.5 | 53 | .5....217....5.8348..3..659..8...57127....946......382582941763746523198931786425
I noticed that there were only 52 givens in the previous 7.5 puzzle(said to have 53), luckily we've got a 54-clue one these days :lol: .
qiuyanzhe
 
Posts: 71
Joined: 21 August 2017
Location: China

Re: Maximum number of clues for a given SE rating

Postby qiuyanzhe » Tue Dec 18, 2018 3:19 pm

Hi 999_Springs,
999_Springs wrote:6.6 | 69 | 63972415872...6439.4..3.26746..7.382.932.8746287643591376482915854197623912365874
6.7 | 64 | 12.689.7586.735..175.142...385274169942561738671398.5.438926517596417...217853...

The current 6.7 puzzle requires a Bidirectional Y-cycle (5 cells).
I tried on Forcing X-Chain (7-8 nodes), and got
Code: Select all
6.7 | 65 | 2346.7.8969..23.47.7..4.23632..6.4784.67.8392789234615..7382964842196753963475821

It relies on the same thing as the 6.6 puzzle, and all 5-node X-chains are broke by extending some blank cells to three.
qiuyanzhe
 
Posts: 71
Joined: 21 August 2017
Location: China

Re: Maximum number of clues for a given SE rating

Postby 999_Springs » Tue Dec 18, 2018 10:08 pm

i'm trying out a new systematic approach that goes like this:

seeds = [dobrichev's 9.5+ puzzles with 1,2,3,4 shoved into a block/row/column]
repeat {
for each puzzle, add a clue in each possible location
solve all singles
rate it (first with skfr)
discard all puzzles with less than a certain rating }

gives amazing results for the available ratings (as long as they're not singles). found 10 new puzzles

the first pass of the loop reproduced the 5.0UL10 7.5 9.1 9.3 9.4 from the previous post, as well as this one that i missed
Code: Select all
95.76.8..86.4.9.75..78.596.684.9.5371256734893795486..7.6.54.985.89.7..6.9..8675.  8.4/55

the second pass found all these in just a few minutes (plus the 7.4 from the previous post)
Code: Select all
57.96.8.286.127.95.298.567.78259..6.9.52.67.8.3678.2596..358927397612584258479..6  3.8/61
79586.43.8.39.56.71.6.735986741892539123567843587..1695396.78...8753.9.6.61.98375  5.0UL10/64
875692...6..51792812934856778.923.569.2.5678335678.2.956.87..92298.3567.4.72698.5  6.5/63
7639548125847..93612938645789...567..56.78..9..769.58.9.5.6.7.86.85.7.9..7.8.9.65  7.5/55
59476381286.5..937..7.984566734891254.56.7389.8935.6747.68.529.9.8.7.56..5.9.6748  7.6/61
6857..9..73295..86419.86.578946.5.7.356..78.91278935649615..7.8543.7869.278.69..5  7.7/59
59.86.71.86...7.95..75.968.7389..5269..3564784562789316..78..59.85.9..67.796.584.  8.9/55
59.86.74.86.4.7.95..75.968.7389..5169..35627825617893462.78..59.8529..67.796.582.  8.3/58 tie

haven't run it through a third pass yet. this method looks very promising for filling out gaps in most of the range

i wrote:i think the UR/UL area is pretty much exhausted at this point

wow i spoke too soon lol

found a new 5.0UL10/64 above that is reducible, by removing cells, to a UL8/66 and a UL6/68 (reducing it to a UR doesn't work, you just get a 5.6). 13 clues missing and it's not been found yet? incredible. a few more iterations of this and i'll find an 82-clue 4.6 :P
Code: Select all
34895.67.956..78.31278369542315894678641732955796..1386937.85..785.9.3.6412365789  4.6/68
34895.67.956..78.31278369542315894678641732955796..1386937.85..58529.3.6.12165789  4.7/66

eleven wrote:Thanks for the puzzles. Something for after X-mas days ...

I just looked at the first one. I see a 10-cell UR, but don't know, how to use it effectively.

cheers :) SE finds the ul10 with hidden triplet 5,6,7 r5c56r6c46; -3r5c5, and then an xy-wing r5c5 -> r5c2,r6c4; -7r6c3

qiuyanzhe wrote:The current 6.7 puzzle requires a Bidirectional Y-cycle (5 cells).
I tried on Forcing X-Chain (7-8 nodes), and got
Code: Select all
6.7 | 65 | 2346.7.8969..23.47.7..4.23632..6.4784.67.8392789234615..7382964842196753963475821

very nice! i hadn't looked in that direction, i thought 5-cell xy-loops were more common and found a lot more 64's, it's great to find that the other type of 6.7 has more clues in it
qiuyanzhe wrote:I noticed that there were only 52 givens in the previous 7.5 puzzle(said to have 53), luckily we've got a 54-clue one these days :lol: .

make it 55 :)
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs
 
Posts: 457
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

Re: Maximum number of clues for a given SE rating

Postby 999_Springs » Mon Dec 24, 2018 4:40 pm

did the same thing a third time and it found these ones
Code: Select all
5938647..8641273951275396847.89..5.69.2.56.78456.789..641783259385.9..672796.58.3  1.7/64
68572193472.95.186..9.86257891645372256..784943789256196.5..7.85...78693.78.694.5  3.2/64
59.86.71.86.1.7.95..75.968.7389..5269..35647845627893164.78..59.8549.167.796.584.  7.7/59 diamond
79586123482.9.5617..627.59867..89.5.9...5678..587.2.695.962784..875..92626..98.75  7.8/57
the 7.7 ties with the other one but i like this one better because 7.7 diamonds are hard to find, says every patterns game player. further runs produced no more puzzles

i restarted the same thing with different seeds (dobrichev's other puzzles that i didn't use) and got these
Code: Select all
9786..5.15..7186.9.6..5927889.5.6712.56.7.893..789.4567..96..85635187924.89..5.67  7.5/56
98.65.73.67...8.593.592768.89354612745617289312789354656...9.78738.6591.2.978.365  6.5/64

move the 2 in r3c5 to r1c3:
98265.73.67...8.593.59.768.89354612745617289312789354656...9.78738.6591.2.978.365  3.2/64 tie
i like the first 3.2/64 better because it has 3 x-wings at the start and this one only has 2

and a 3.8/60 that you can tweak it up a bit and get this
Code: Select all
981632547672584139345179628893.56.71.56..789.4.789..565647..98.7.9.68.15..89.576.  3.8/62

finally, Ruud's Benchmark Sudoku List contains a nice example of a naked-triplet-in-a-column, which is a rating that my generation methods haven't seen yet
EDIT: you can fill in r9c78 and keep the rating the same
Code: Select all
579.....8
148.297.3
263.789.4
61.895.37
857....91
93...78.5
795.4.382
421983576
386752149  3.6/60 (naked triplet)
and the best thing is if you switch the 57UL6 in blocks 1,4,7 and remove r7c3,r9c34 you get
Code: Select all
759.....8
148.297.3
263.789.4
61.895.37
875....91
93...78.5
59..4.382
421983576
38..52149  4.0/57 (hidden triplet)
which means i can finally get rid of that trashy tabloid newspaper puzzle that's been sitting in the 4.0 spot this entire time :D the quality of the metro has really gone downhill since then (except the £1.99 mcdonalds vouchers)

records so far: (updating quite a lot of these)

ER |clues
----+-------------
1.0 | 80 |
1.2 | 77 |
1.5 | 68 | 1.8469.535.61.39..4932.51.6715942638839651...264837591647528319381794265952316..7
1.7 | 64 | 5938647..8641273951275396847.89..5.69.2.56.78456.789..641783259385.9..672796.58.3
2.0 | 69 | 437691825268537941159842763892..5.3.615..3.8.743..8.5.326789514574316298981254376
2.3 | 64 | 327415698159862347684...25194....17571.....2353...1.69893..4716475186932261937584
2.5 | 64 | 1298657343459718268672..19597612..5823..5..1751.....62492.1.5836513..279783592641
2.6 | 66 | 219356784843..76596574982..19874.5.64325619787658.9.4.976.854..3219748655846...97
2.8 | 63 | 1289354673768412959542..81384912..5623.....8161.....24581.9.6724625..139793612548
3.0 | 63 | 1239486574856179239672..81487..2..9623...6.8165.....42316...275592371468748562139
3.2 | 64 | 68572193472.95.186..9.86257891645372256..784943789256196.5..7.85...78693.78.694.5
3.4 | 62 | 128975346394618257567...981846....7971.....2323.7...64972...435483597612651342798
3.6 | 60 | 579.....8148.297.3263.789.461.895.37857....9193...78.5795.4.382421983576386752149
3.8 | 62 | 981632547672584139345179628893.56.71.56..789.4.789..565647..98.7.9.68.15..89.576.
4.0 | 57 | 759.....8148.297.3263.789.461.895.37875....9193...78.559..4.38242198357638..52149
4.2 | 70 | 96173254884395672172581463919467385268752.3.4352..8.67419385276238.67..55762...83
4.4 | 66 | 3495812676283975145714629384537296817861..492912.4.753165..4..92379...46894.....5
4.5 | 67 | 13524678926...75344.735.21665..3.1277235614988.1.726535..623971372..4865916785342
4.6 | 68 | 34895.67.956..78.31278369542315894678641732955796..1386937.85..785.9.3.6412365789
4.7 | 66 | 34895.67.956..78.31278369542315894678641732955796..1386937.85..58529.3.6.12165789
4.8 | 61 | 1..2..953...51.28..523..14.2.5.38761.61.72538...156492574823619329641875618795324
4.9 | 59 | 1..2..953...51.28..523..14.2.5.38761.617.2538...156492574823619628..1375319675824
5.0Quad | 60 | 128935647367841925954...38187.....5621.....7964.....32781...263496372518532618794
5.0UL10 | 64 | 79586.43.8.39.56.71.6.735986741892539123567843587..1695396.78...8753.9.6.61.98375
5.1 | 57 | 4.9315.82.12948.53385...491548....679.14...2823..8..14894...276153672849.2.894135
5.2 | 61 | .285.9437357.4.8.949.3785.2.73..4928..98..374842793651784.36.952..9857439354.7.86
5.3 | 48 | .61..452.298...6144.561298..42...738..6...49.98....16.62..7835185.1..276.1.2..849
5.4 | 59 | 123965847489317526576..89138.4....752......896......34945...762368572491712694358
5.6 | 70 | 12345678945678912378913256423.9.58.66.52.893.8973612453625174985.86943.29..82365.
5.7 | 65 | 16324578942...73565.736.12421..3.567736..24988.5.762133..621975671..3842952784631
5.8 | 64 | 483126795159..76822675893415268..91.7189.245.394...82.671298534942...178835...269
5.9 | 64 | 176238594845179362932...7184573...81281.5..366938...75728...643569483127314.2.859
6.0 | 63 | 123948657467315982895...314984..3.7637.4...2925.....43642...735538672491719534268
6.1 | 60 | 528...341931524786476381592.19...85..64...17..53...62.195438267382976415647...938
6.2 | 65 | 947521683128763549653984127296...374731642958584397216..5.794.2..24..79.4792..8..
6.5 | 64 | 98.65.73.67...8.593.592768.89354612745617289312789354656...9.78738.6591.2.978.365
6.6 | 69 | 63972415872...6439.4..3.26746..7.382.932.8746287643591376482915854197623912365874
6.7 | 65 | 2346.7.8969..23.47.7..4.23632..6.4784.67.8392789234615..7382964842196753963475821
6.8 | 64 | 6..1..38..3.5.8.1..183...9...1723846243816759876459123127934568369285471485671932
6.9 | 65 | ..2.4.658....6.42346.25.971.4.532769926487135...619284685124397319876542274395816
7.0 | 63 | .134.7825..48.263128.1.3947....243183429187568.1.36294429671583.382451.91..3894.2
7.1 | 65 | 642319578187...439359...261914283657276...8935389..142721495386493...715865.3.924
7.2 | 65 | .6..92.84..4.16.35....54.96126935478759428361843167952...243617632571849417689523
7.3 | 61 | 371542986682...345459...217914376528768...13.523...76.135984672247...893896...451
7.4 | 52 | 87569....6..5.79.8..9..85677819...569...5678..5678...956487..9.398..567.127369845
7.5 | 56 | 9786..5.15..7186.9.6..5927889.5.6712.56.7.893..789.4567..96..85635187924.89..5.67
7.6 | 61 | 59476381286.5..937..7.984566734891254.56.7389.8935.6747.68.529.9.8.7.56..5.9.6748
7.7 | 59 | 59.86.71.86.1.7.95..75.968.7389..5269..35647845627893164.78..59.8549.167.796.584.
7.8 | 57 | 79586123482.9.5617..627.59867..89.5.9...5678..587.2.695.962784..875..92626..98.75
7.9 | 55 | 95.76.8..86...9.75..78.596268..9.5.7.2567..89.795.862.7164532985.8927..629.18675.
8.0 | 55 | 76.85.9..59...6.78..87.961568..9..57.1567.89..795.81.685.917.6.9472635811.64857.9
8.1 | 50 | 6857.29..71.95..86.49.86.5789.6.5.7..56..78.9.3789.56.96.5..7.852..7869..78.69..5
8.2 | 53 | 6759823148..75.926.29..685778.5.9.6.95..67.38..68..5795.7.9.68..68.75.9..9.6.8745
8.3 | 58 | ....472969...8.45747.5.9831..4...789.9...8164....94523549876312638412975721935648
8.4 | 55 | 95.76.8..86.4.9.75..78.596.684.9.5371256734893795486..7.6.54.985.89.7..6.9..8675.
8.5 | 54 | 59.86.7..86...7.95.475.968.7189..5.6934156278256.7891.62.78..59.85.9..67.796.58..
8.6 | 48 | 9758..6..6..97.8.5.8..56.7989.5..467.567.891...7.6958.76..9..585.86.729...9.857.6
8.7 | 50 | 59176.8..8625..9.7..7.98.56673.89..5..56.7.89.89.5.67.7.68.5.9.9.8.7.56..549.67.8
8.8 | 54 | 59.86.7..86...7.95.475.968.7189..5.6934156278256.789..62.78..59.8529..67.796.58..
8.9 | 55 | 59.86.71.86...7.95..75.968.7389..5269..3564784562789316..78..59.85.9..67.796.584.
9.0 | 53 | 7956..8..813.95.76246.87.9567.8.9.5.92.56.78.358.7.6.95627..9.8.379.856..89.56..7
9.1 | 53 | 67598.1.48..75.9.6..9..685778.5.9.6295..67.18..68..5795.7.9.681.68.75293.9.6.8745
9.2 | 52 | 95.76.8..86...9.75..78.596.68..9.5.7..567..89.795.862.7164532985.8927..6.9.18675.
9.3 | 51 | 87569....6125.79.834921856778.9...569...5678..5678...956.87..9..98..567...7.698.5
9.4 | 50 | 59.86.7..86...7.95..75.968.7.89..5.6912356478.56.789..6..78..59.85.9..67.796.584.
9.5 | 50 | 7956..8..81..95.76.46.87.9567.8.9.5.92.56.78..58.7.6.956.73.9.8.379.856..89.56..7
9.6 | 50 | 675982.1.8..7.6529..9.5.78678...569.95..6783...689..575.8.7.96..675.9.48.9.6.8.75
9.7 | 49 | 57.96.8..86...7.95..98.567.78.59..6.9.5..67.8..678..59612.589.73976..58.458.79..6
9.8 | 50 | 95.76.8..86.1.9.75..78.596.68.29.5.7..567..89.795.86..74635..985.89.7..6.9.48675.
9.9 | 49 | 8759..6..6..87..59..9.65.7878...95.6932456781.5678..9.5.8..796..6.59.8.7.976.8..5
10.0| 49 | 8756..9..61..98.75.49.75.8678...956.92.5.67.8.5678...959..6.8.7.3785.69..689.7.5.
10.1| 51 | 95.76.8..86...9.75..78.596.68..9.5.7..567..89.795.86..7164532985.8927..6.9.18675.
10.2| 49 | 6857..9..71395..86249.86.5789.6.5.7..56..78.9..789.56.96.5..7.85...7869..78.69..5
10.3| 49 | 57.96.8..86...7.953.98.567.78.59..6.9.5..67.81.678..596..258947.976..58..58.79..6
10.4| 49 | 7956..8..81..95.76.46.87.9567.8.9.5.92.56.78..58.7.6.956.7..9.8.379.856..89.56..7
10.5| 42 | 7.96..8..6.398..57.8..7...98.2.57.9.9....6.78.6789.5..5.17.89...76..9.85.9856.7..
10.6| 41 | 7.96..83.6..98..57.8..7...98.14.7.9.9....6.78.6789.5..5..7.89...76..9.85.9856.7..
11.2| 37 | 6....2.5952..4..1...35..2..3..1945...1.658.3...5273..1..4..51...3..2..4575.4....8

-------

right, so i think i'm pretty much done with this thread at this point. i've now covered all possible ratings up to 10.6 and found improvements for most of them, and have basically exhausted my avenues of generation and don't expect to find many more. later i might give the top end (10+) another fling if i feel like it. if anyone else wants to contribute further that's great but i'm going to give this thread a rest for now
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs
 
Posts: 457
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

Re: Maximum number of clues for a given SE rating

Postby qiuyanzhe » Thu Dec 27, 2018 1:43 am

Found a 4.6|69(prev 68)

It is interesting that I found this

Code: Select all
4.6 | 69 | 459872361826143975137569.8.671.945.89857.16..243658719764.1589.3924871565189.6..7
4.7 | 67 | 24915367836789..1515867.39.574.698.16815.79..932418567496.8175.7239451868157.6..9
5.0UL | 65 | 15.67.38938915..6767.89315.947.165.85167.89..823549671495.6781.2314857967689.1..5

Inspired by ..5..6879.69781..578.592.6...68539.78.7.695..59...7.86..897465.65...879.97.6.5..8, which has a super-long 12 middle part.
Hidden Text: Show
Code: Select all
To make it clearer:
oo.oo....
o....ooo.
..o..oo.o
oo...o.o.
.o.o...oo
..ooo.o..
oo...o..o
..ooo...o
..o.o.oo.

By moving the 1234s we get
Code: Select all
R 7.2 7.8 7.1 7.6 8.8 7.9 7.6 8.0 8.8
C 7.6 7.6 2.6 7.9 7.8 4.6 8.2 8.0 8.8
B 2.6 7.6 7.6 7.6 7.9 8.8 7.8 7.8 8.8

This is my third grid containing 2.6 or 2.8, this 4.6 is absolutely surprising.

P.S. I want to do a search for such thing(4-grid? 4-pattern? I forgot the name, it means only 4 digits remaining) with unique solutions. And such data are all by manual typing.. I wonder if there could be any program that would help.
qiuyanzhe
 
Posts: 71
Joined: 21 August 2017
Location: China

Re: Maximum number of clues for a given SE rating

Postby qiuyanzhe » Sat Dec 29, 2018 12:18 am

It's a bit off topic, but here are the 4-patterns that I have tried, they all have a '2.6', so maybe that's why these cannot reach 9.5+...?
1-3:
Hidden Text: Show
Code: Select all
..5..6789
.6789...5
89.57..6.
..695.8.7
9.8.67.5.
57...89.6
..968.57.
75...96.8
68.7.5.9.

R 7.2 7.6 2.8 7.6 8.0 7.9 7.6 7.8 9.0
C 7.6 7.6 2.6 7.9 7.8 2.6 9.0 7.6 8.0
B 2.6 7.6 7.6 7.6 7.8 8.0 7.8 7.8 7.8

----------------------

Code: Select all
..5..6789
.6789...5
89.57..6.
..675.9.8
7.8.69.5.
95...86.7
..968.57.
67...589.
58.9.7..6

R 7.2 7.6 2.6 7.6 8.8 7.9 7.6 8.0 8.8
C 7.6 7.6 2.6 7.9 7.8 2.6 8.4 7.7 8.8
B 2.6 7.6 7.6 7.6 7.9 8.8 7.8 7.8 8.8

----------------------

Code: Select all
..5..6879
.6978...5
78.59..6.
..685.9.7
8.7.695..
59...7.86
..897.65.
65...879.
97.6.5..8

R 7.2 7.8 7.1 7.6 8.8 7.9 7.6 8.0 8.8
C 7.6 7.6 2.6 7.9 7.8 4.6 8.2 8.0 8.8
B 2.6 7.6 7.6 7.6 7.9 8.8 7.8 7.8 8.8

----------------------

4-6:
Hidden Text: Show
Code: Select all
..5..6789
.6978...5
78.59..6.
..685.9.7
5.7.698..
89...7.56
..867.59.
97...56.8
65.9.8.7.

R 7.2 7.8 7.2 7.6 8.0 7.9 7.6 7.9 8.2
C 7.6 7.6 2.6 8.3 7.8 6.7 7.9 7.8 8.0
B 2.6 7.6 7.8 7.6 7.9 8.0 7.8 7.8 7.9

----------------------
Easy5
Code: Select all
....56789
.69.78..5
5789...6.
..56.789.
68..95.7.
79.8..5.6
.567..9.8
9..58.6.7
8.7.69.5.

R 9.1 6.7 7.1 8.9 7.6 7.9 9.0 8.8 7.6
C 8.9 8.9 8.8 6.7 8.3 9.0 7.6 2.6 7.6
B 9.1 7.6 2.6 8.9 7.9 7.6 8.8 9.0 7.8

----------------------
Easy6
Code: Select all
....56789
.69.78..5
5789...6.
..56.789.
68..95.7.
79.8..5.6
..658.9.7
8.7.69.5.
95.7..6.8

R 9.0 6.7 7.1 8.0 7.6 7.9 8.9 7.6 7.8
C 9.0 8.0 7.8 6.7 8.3 8.3 7.6 2.6 7.6
B 9.0 7.6 2.6 8.0 7.9 7.6 7.8 7.8 7.8

----------------------
qiuyanzhe
 
Posts: 71
Joined: 21 August 2017
Location: China

Re: Maximum number of clues for a given SE rating

Postby 999_Springs » Sat Dec 29, 2018 7:42 pm

qiuyanzhe wrote:Found a 4.6|69(prev 68)

It is interesting that I found this

Code: Select all
4.6 | 69 | 459872361826143975137569.8.671.945.89857.16..243658719764.1589.3924871565189.6..7

wow. of all the ratings i would have least expected THIS one to be improved AGAIN. nice one hahahah :)

P.S. I want to do a search for such thing(4-grid? 4-pattern? I forgot the name, it means only 4 digits remaining) with unique solutions. And such data are all by manual typing.. I wonder if there could be any program that would help.

this sort of approach was discussed here - the interesting stuff starts from page 3 onwards. the term you are looking for is a 4-template. i've only very briefly looked through that thread, but it looks like one way to generate 4-templates is you can start with a 4-rookery which means a collection of cells in an empty sudoku grid such that every row/column/block contain 4 of them, and try to find ways to fill it in with 1,2,3,4 to find all 4-templates that fill it. a 4-rookery can have 1 corresponding 4-template (great), or more than 1 (not so great), or very rarely 0 (yuck)

dobrichev's results for skfr difficulty rating of the 4-templates can be found here. his post is a little bit unclear but i think he does an exhaustive search meaning that he covers every possible puzzle that has 999991110 clue distribution, up to isomorphism, and there are about 2.4 million of them. i sent him a pm earlier asking if he still had the puzzles but he said no, and said he was thinking about how to generate the grids from scratch but never got back to me on that. i suggest you send him a pm if you want to investigate this further. also note that dobrichev's puzzles will always include your puzzles generated by taking a 4-rookery and putting 1,2,3,4 in a row/column/block, but your puzzles will not generate all of his, because his 3 extra clues don't have to be in the same row/column/block. so your puzzles will be a proper subset of his puzzles
here are the 4-patterns that I have tried, they all have a '2.6', so maybe that's why these cannot reach 9.5+...?

you're probably not getting any 9.5+'s because they're extremely rare. don't know how familiar you are with SE, but SE rating frequencies sort of drop off very rapidly at around 9.2/9.3. if you look at the skfr distribution for his 2.4 million puzzles you'll find that only 491 are rated skfr 9.5+ (or 654 if you include the 9.4's which are more likely to be rated 9.5 with SE), so if you only have 6*27=162 puzzles you will be very unlikely to find one

i'm trying to do the same method but not an exhaustive search as that is far too difficult, so i'm starting with the puzzles at the top of champagne's potential hardest list and removing all 1,2,3,4's, filling in 1 row/column/block and adding 1 more clue (the extra clue allows for loads more valid puzzles), rating them, and filling in singles. i will edit this post when i get results

edit: i've done the first 1500 puzzles from champagne's list (so i'm now halfway down the 11.4's). this generated 59480 puzzles, probably a lot of them isomorphic to each other. the highest skfr rating was 9.1; there were 5 puzzles with skfr 9.1. SE rated all of them 9.2 which is really weird

these are new best records:
Code: Select all
980750620750062890206098517697245138008970256502086749060537982829614375375829461  1.7/66
980761502700285096265934871020896057078500609659007280592078060807600905006059728  7.9/56
007650890689070500500809076090506087806907350075080609123765948754098060968000705  8.1/51
007580960690700805850069700716234598089157006500698017105970680060805179978016050  8.2/54

and some honourable mentions - interesting puzzles tied with the current records
Hidden Text: Show
Code: Select all
981705600752160089346298715524817936839600157617359800198570060465901078273486591  4.5/67
985736124600190785107805396060457918591283467478619532710308659009560871856971243  4.6/69
210056789057189060698700105065978001721005896980261570136807950579610008842593617  5.2/61
980700465651489723007056189705608294806090507090570806328945671569127348174863952  5.7/65
985706000600481759147095608050978006009602875768503090890054067500067980076809500  7.4/52
970864050865007409400590678157608094239475186648900705380749560504086907796050840  7.7/59
980710605500069078476528009700635891195287060368941752850096007609072580207850906  8.3/58

all of these are ties. the 5.7 is a BUG type 4 - the other one was a BUG type 2. the 4.5 and 7.7 only have 3 digits missing; the current ones have 4
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs
 
Posts: 457
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

Re: Maximum number of clues for a given SE rating

Postby 999_Springs » Mon Jan 14, 2019 2:27 am

mathemagics and 1to9only did some fantastic work in the hardest 6x6 thread. i wrote a short script to convert, where possible, the 6x6 puzzles to standard 9x9 puzzles (with the same complements) by cramming 7,8,9's into random places to try to create valid hard 9x9s with many clues. for instance
Code: Select all
....5.
4....3
...5.1
...34.
3.2.1.
.6..3. SE 8.4
becomes
Code: Select all
....8.957
9....7834
487953126
...8.9571
...37.489
879541263
7.8.9.312
.6..3.798
392718645 SE 8.4

18749/30927 of the PW1 6x6 puzzles can be converted into 9x9s, including all the SE 8.4's and the 8.2 and the 7.5
30210/45926 of the PW2 6x6 puzzles can be converted into 9x9s
i forgot to record the stats for the TW puzzles
these are all lower bounds, my code to do it has some glitch where a few % of puzzles make it stall for a really long time (some valid, some not) so i just skip those. there could be a little more

new bests: (the 5.7 was hand-modified to remove 2 cells from the pm grid)
Code: Select all
....8.9579....7834487953126...8.9571...37.4898795412637.8.9.312.6..3.798392718645  8.4/57
8.....19794...7825157892346.89...5717.4...968615978234.6.78.45959..64782478529613  8.3/60
..3..7689...89.237789236154..8.4.791.7.9..348941378526.97...8128..1..975512789463  8.2/57
81..92567...8.7192927156834.98.6.3717....1958531978246...71.689.8...9713179683425  7.8/60
8.9.1.357.567..819137859426......9787..98.2319831275645.82..79339..7.682672398145  7.7/60
.234.67894.7.89236689327145231..48979758..462846792351..29.8574..4.7.928798245613  5.7/66

a few ties:
Code: Select all
..8...93793..7.845457893126.89.3167461...738937496825179..8.413...3..798843719562  7.7/60
8....9167..6.7.893197836245..8...75997....386365987412.8....9747...94628649728531  7.5/56

and one more from continuing the method in the previous post, taking champagne's hardest and removing 1,2,3,4's (now reached the end of the 11.4's; highest skfr was 9.2)
Code: Select all
98.7.6.5265.28.79.217.95.68829547..64768..925531962874.486295.7792.5.68..65.78249  5.2/62
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs
 
Posts: 457
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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