## 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

That's a well compressed SE 8.4 indeed !

Some short krakens solve it, like this:
Code: Select all
`+------------------+-------------------+----------------+|  8    24    34   | #234    1     9   | 5    6    7    ||  456  245  #34+6 |  7     #234  #234 | 8    1    9    ||  1    9     7    |  8      5     6   | 2    3    4    |+------------------+-------------------+----------------+|  9    8     4-6  | #34+6   34    1   | 7    2    5    || a46   1     5    |  246    24    7   | 9    8    3    ||  3    7     2    |  9      8     5   | 6    4    1    |+------------------+-------------------+----------------+|  7    45    1    |  245    6     24  | 3    9    8    || a45   6     8    | #34+5   9     34  | 1    7    2    ||  2    3     9    |  1      7     8   | 4    5    6    |+------------------+-------------------+----------------+`

Deadly pattern 234 in the marked cells.
6r2c3 or 6r4c4 or 5r8c4 - (5=46)r85c1
=> -6r4c3
eleven

Posts: 3067
Joined: 10 February 2008

### Re: Maximum number of clues for a given SE rating

eleven wrote:Deadly pattern 234 in the marked cells.
6r2c3 or 6r4c4 or 5r8c4 - (5=46)r85c1
=> -6r4c3

Nice! Written as an Almost-ALS-XY-Wing:

(6)r4c4 = [(6=45)r58c1 - (5=342)r841c4 - (2=346)r2c563] => -6 r4c3; stte

SpAce

Posts: 2671
Joined: 22 May 2017

### Re: Maximum number of clues for a given SE rating

bunch of tiny improvements:
Code: Select all
`983567124672413..91452893..45.13.29.219..4..3.3.9.241.32..9..41.9134...2.64.2193.  7.4/5598.716...6.12947.84273581968..129.67.1647.98.79.86...1.48637.19169542873.7.9816..  7.5/5998176...26.7..98.13..18.769576948123194...6878..67149546.2179.82198.6.747.8.9.216  7.9/59 skfr 7.898.75.64.7569...284..6.85798345697125.9.7.836.67.8.495.458.796.69...5.87.78.96.54  8.0/56 skfr 7.998.7..6.575..6938.3.65.8.97679.5...82.598.73683..7695.1986..57.5238.7.69467.9582.  8.1/55 skfr 8.0893674521.128534...45129..395741.3.22.4935.1713.7.29454.13..25.5..2.1.3432.54.1.8  8.2/589...21.43.153492..234..69.114.938..2..945213.3526178945.12.43.942..93.15.931.542.  9.0/56 skfr 8.998.7..6.575..69.8..265.8.7926.9.75.8.95.867...78..5.9681269..57539.7.86.64785.9..  9.4/5198.75.6..1.78.6.956.5..9.787985.3.6.2..69758.356.8.9.757.9..8.646..78.598.9.657..  9.7/51 skfr 9.6`

bunch of ties, only some of which have been checked for non-isomorphism:
Code: Select all
`981465...427389516536127489..569.1.8..981..5...857396.892731645753946821..4258793  5.8/64123465..9456789132789213..42.835194.391.472..5.4.923.1842936.1.617528493935174.2.  7.2/65985761..2612394758347285196.39.786.5.765.9.8.85.62397..289365.756.8.7..979..5286.  7.6/61985716.2.612349785347258196.39.7586..5689...787.6325.9.2856397.59..276.876.98..5.  7.6/6198.7526..7.5.61.981.68.9.5787.9.6.2525..8796.6.92.578.318694572497528..6562173849  7.7/61 skfr 7.698.723.161.74689...6.159.78.96841..771893.64..3.67.189.71.86.9464..978.18.9.1476.  8.0/56953..2.14.1.49.253.245319..5673491824912...3.382.154.9.39154.2.14..2.39.27.9.3.41  8.0/5698.7246.1.67891...1425367896.1.4.97887496.1...9.17846...9.178.64.8659.17716.8..9.  8.5/569.2.34.1..3.9814.241..2639.8214.593...32198.4.943.8.2114.8932..3..152.49259647183  8.8/579857..61.261.89.7.34751628947395816219267...8658..19.75.41978.6819.6.7..7.68...91  8.9/59 skfr 8.75.91.867.7.659...818.6.75.9258319467391764285674285.9.9658..7..4..97685.8.745.9.6  8.9/5998.7..6.575..68.9.2.69.5.788.95.6..762..87.595.7.9.8.61728.956.39865.7..46527.98.  9.2/5298.7..6.575..69.8.1.68.5.978.75.6..961..97.585.9.8.7.62719.856.36815.97.49567.8..  9.2/529.17.3.24..342.9.124.19..3.4.23.7.1931.9.42...9.21..43..9.314.212..493..534672198  9.4/5198.7..6.12.69.1.8717..68.9.6.1.279.87.98.61..82..19.7636817...9417.9.86.59268.71.  9.5/52`

all of these (except the 5.8 tie which is a patterns game puzzle) were produced using the same method as before by removing all occurrences of 4 numbers in champagne's hardest list, except in 1 block/row/column, and messing around with them

also a present for tarek at his request, a non-jellyfish 5.2:
Code: Select all
`1..2..953...51.28..523..14.2.5.38761.617.2538...15642967..2381531.8.5672528671394  5.2/57 UL10 type 3 with naked triplet`

this 5.2 is a UL10 type 3 with naked triplet, and is a simple modification of my 4.8

EDIT: tarek posted a UL12 type 3 with naked pair (se 5.1) with 57 clues here, stating that this was a patterns game puzzle by champagne. since UL ratings don't increase beyond UL10, you can remove 2 clues from the UL and get a 5.1 with 59 clues. my previous 5.1/57 earlier in the thread was in fact a UL10 with hidden triplet, not with naked pair. you can also remove 2 clues from the UL10 to get a UL8 with naked pair that ties with the current 4.8/61
Code: Select all
`.62431...14.869..33..75216421.6.3.4...62.43.1.34517..6653178492471926538.2.345617  5.1/59 UL10 type 3 with naked pair`

as this is a new page, here is the full list updated from qiuyanzhe's list on the previous page to include all the puzzles at the top, plus the 3.0/65 from earlier that he missed:

ER |clues
----+-------------
1.0 | 80 |
1.2 | 77 |
1.5 | 68 | 1.8469.535.61.39..4932.51.6715942638839651...264837591647528319381794265952316..7
1.7 | 66 | 98.75.62.75..6289.2.6.98517697245138..897.2565.2.86749.6.537982829614375375829461
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 | 64 | 981346572654297138237.8.469.798.42.642.76.98..689.2347746.298.3.126.879489.47.62.
3.0 | 65 | 56872193479234.1..143....27985634271321..7.4.67421.3..8369724154591837622174..893
3.2 | 65 | ..5678..9.6.25978.78913425653.72689..768935.289241563795736142864.58297...8947.65
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 | 63 | .2894.35775....8949438571268.9.64275.6.27.948274589631.8.49.763...7.5489497638512
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 | 68 | .8.9.2467..9.6782326783419589..23674.247.6938736489251...298716918675342672341589
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
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
5.0Q| 60 | 128935647367841925954...38187.....5621.....7964.....32781...263496372518532618794
5.0U| 65 | 15.67.38938915..6767.89315.947.165.85167.89..823549671495.6781.2314857967689.1..5
5.1 | 59 | .62431...14.869..33..75216421.6.3.4...62.43.1.34517..6653178492471926538.2.345617
5.2 | 62 | 98.7.6.5265.28.79.217.95.68829547..64768..925531962874.486295.7792.5.68..65.78249
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 | 66 | .234.67894.7.89236689327145231..48979758..462846792351..29.8574..4.7.928798245613
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 | 66 | 42385179685937621467149283519.68.327362.1..89.8.2396.193612...824.9681.3.18.43962
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 | 55 | 983567124672413..91452893..45.13.29.219..4..3.3.9.241.32..9..41.9134...2.64.2193.
7.5 | 59 | 98.716...6.12947.84273581968..129.67.1647.98.79.86...1.48637.19169542873.7.9816..
7.6 | 61 | 59476381286.5..937..7.984566734891254.56.7389.8935.6747.68.529.9.8.7.56..5.9.6748
7.7 | 61 | .2893.4579...47823437852196....89674..47..98587946531258....749.9..74538743598261
7.8 | 61 | 8...19567.517.689296785213418....279.9..27681276981345....78913..91..728718293456
7.9 | 59 | 98176...26.7..98.13..18.769576948123194...6878..67149546.2179.82198.6.747.8.9.216
8.0 | 56 | 98.75.64.7569...284..6.85798345697125.9.7.836.67.8.495.458.796.69...5.87.78.96.54
8.1 | 55 | 98.7..6.575..6938.3.65.8.97679.5...82.598.73683..7695.1986..57.5238.7.69467.9582.
8.2 | 58 | 893674521.128534...45129..395741.3.22.4935.1713.7.29454.13..25.5..2.1.3432.54.1.8
8.3 | 61 | ...89.457.8..57923957234816..8.1967464.72.189719468532.7..8.291.9..4.768861972345
8.4 | 61 | 8...19567...7..81919785623498...1725.15..79833729856417.1.6.398.68.9.172239178456
8.5 | 56 | 47.563...5.6879.34983142576.6..374.52946513877354.8.6.35...674...73.465.64.7.5..3
8.6 | 54 | 952637814..341529.41.289.3..491.3.28.3..249.12.1.96.4339...14.212.9483....43.21.9
8.7 | 51 | 3....1542251.4..3..4.2531..41.5..2.3.2531.4....3.24.155841923671...35824.324..951
8.8 | 57 | .82.61.4.6.14...82.4728.16.475136928219857634863924..1.286..41.1.6.4289...4.182.6
8.9 | 59 | 7..9426539325164..5647382913.562...484.3..56262.85431.2.64.513.1.326..4545.1.3.26
9.0 | 56 | 9...21.43.153492..234..69.114.938..2..945213.3526178945.12.43.942..93.15.931.542.
9.1 | 54 | 9857.6..16741..98.123498576.6197...8..861.79..97.8216..168.9..78.92.761.7.2.618.9
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 | 51 | 98.7..6.575..69.8..265.8.7926.9.75.8.95.867...78..5.9681269..57539.7.86.64785.9..
9.5 | 52 | .5482.13.2.134...5.83.514.2.4..3521.3.5.12.4.1.248.5.351.2.43...2.1.3.54436578921
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 | 51 | 98.75.6..1.78.6.956.5..9.787985.3.6.2..69758.356.8.9.757.9..8.646..78.598.9.657..
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
999_Springs

Posts: 591
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

### Re: Maximum number of clues for a given SE rating

coloin wrote:Here is a few of the puzzles i made - with the method - and MD really took it furthur......

This is one of the many 4-templates which solve with 3 clues
Code: Select all
`..1..2.34.3..142..4.23...1...423.1..12..4...33....142..1.4..3.2.43.2...12..1.3.4.`

Combining with all the possible essentially different 5-templates gives many many non-minimal puzzles with 999991110 clue distribution [48 clues]

Picking out some of these with a high ER
And there might be 100,000 minimal puzzles from each non-minimal each with at least this ER.

Code: Select all
`                                                                                    q2                              SE      56..897..7.815.9.6..96.7.5889...65.76.78.5.92.5.79.68.98..7..653.596.87..765.8..9 #  3406 FNBP C48/M2.78.84          9.7          5....97..7.815.9....96.7.58.9....5.7..7..5.92.5.79.68.98..7..653.59..87..765.8..9 # 95278 FNBP C40/M2.18.728        10.4          5...........1.......96.7.58...........7..5.92.5.79.68..8.....653..9...7..76..8..9 # 95278 FNBP C26.m/M2.18.364      10.4                                                                                                                                            56..897..7.816.9.5..97.5.6897...85.68.65.7.92.5.69.87.68..7..593.795.68..958.6..7 #  3406 FNBP C48/M2.78.84          9.7          56..897.....16...5...7.5.6.97...85.68.65.7.92.5.69.87.68..7..593...5.6....5..6... # 96000 FNBP C37/M2.8.2460        10.1          5...897.....1..........5.6.97...85....6....92...6..87..8..7..593..........5..6... # 96000 FNBP C24.m/M2.3.37179     10.4 `

And these minimal puzzles exceed their rating with 48 clues.

Next i could do is look for 23-24 puzzles in the lists with xxxxx1110 clue counts.....

I am half expecting that this area of "puzzle space" is unexplored

C

i have been taking a look at coloin's idea to take dobrichev's existing 48 clue puzzles, swap out the 5-template with the 56789 numbers with another one, and systematically remove clues.

my method is as follows:
starting from one of the hardest 48-clue 999991110 puzzles, do all the singles and locked candidates, then:
repeat {
find all possible 5-templates for the 56789 numbers that haven't been removed yet
for each template:
remove 1-4 clues all of the same number (5+ clues gave almost no yield)
rate with skfr and check that the first cell does not solve trivially (ep must be >= 9)
} until no new puzzles found

i did this on all of dobrichev's 48-clue skfr 10+ and the few 9.6+ puzzles on the next page of that thread, together with all the 9.6+ puzzles posted so far in this thread too. the number of puzzles i got from each seed varied greatly; some seeds produced no puzzles at all; the one that produced the most puzzles was this one
57.96.8..86...7.953.98.567.78.59..6.9.5..67.81.678..596..258947.976..58..58.79..6
which gave 56 new puzzles on a first pass and several hundred on the next one.

after discarding duplicates, i got a few thousand puzzles (i didn't count them). the highest skfr ratings were:
skfr 10.6 x 3 (most clues: 41)
skfr 10.5 x 42 (most clues: 43)
skfr 10.4 x 258 (most clues: 47)

i manually rated the 10.5+ and some (not all) of the 10.4's with SE and got:
SE 10.7 x 0
SE 10.6 x 50 (most clues: 43)
SE 10.5 x 76 (most clues: 46) (there could be many more as i didn't try all the skfr 10.4's)

it's really annoying that all the skfr 10.6's stayed as SE 10.6 while most of the 10.5's and some 10.4's went to SE 10.6... i was really hoping to find an elusive SE 10.7 there somewhere but all i got was 50 SE 10.6's. what a disappointment

here are all the skfr 10.5+ and SE 10.5+
129 puzzles: Show
Code: Select all
`.956..8..61..89.5..48.57.9695.7.8.6.82.56.97..76.9.5.856.8..7.9.3.9.568..89.76..5  ; 46 skfr 10.4 SE 10.5 new best for SE 10.5.956..8...1..89.5..48.57.9.95.7.8.6.82.56.97..76.9.5.856.8..7.9.3.9.568..89.76..5  ; 44 skfr 10.4 SE 10.5.956..8..61..58.9..48.79.5695.7.6.8.82.59.67..76.8.5.956.9..7.8.3.8.5.6..8..67..5  ; 44 skfr 10.4 SE 10.5.956..8...1..58.9..48.79.5.95.7.6.8.82.59.67..76.8.5.956.9..7.8.3.8.5.6..8..67..5  ; 42 skfr 10.4 SE 10.557.96.8..69...8.573.87.569.76.59..8.8.9..75.61.5.8..799..2..748..78..9...8..79..5  ; 43 skfr 10.4 SE 10.5.7.96.8..98...5.673.67.859.69.87..5.7....69.81.8.9..768..25.649..96...8..6..89..5  ; 42 skfr 10.4 SE 10.5.7.96.8..98...5.763.68.759.69.78..5.8....69.71.7.9..687..25.649..96..7...6..79..5  ; 42 skfr 10.4 SE 10.557.96.8..86...5.793.97.865.95.67..8.6.8..95.71.758..967..25..48..58..7...8...7..5  ; 43 skfr 10.5 SE 10.4 new best for skfr 10.5.7.96.8..69...8.573.87.596.76.59..8.8.9..75.61...8..799..25.748..78...9..8..79..5  ; 42 skfr 10.4 SE 10.557.96.8..69...8.573.8..569.96.58....8.7..95.61.5....897..25.948.598......8..97..5  ; 41 skfr 10.4 SE 10.557.96.8..69...8.573.87.569.96.85..7...5..79.61.7.9..857..2..549..95..7...5..79..8  ; 42 skfr 10.4 SE 10.557.96.8..69...8.753.8..796.96.87..5.8.5..97.61.7....987..28..49..97...8..8..95..7  ; 41 skfr 10.4 SE 10.557.96....69...8.753.85.796.96.87..5.8.5..97.61.7.5..987..28.549.597......8..95..7  ; 43 skfr 10.4 SE 10.6 new best for SE 10.657.96.8...9...8.573.87.569.76.59..8.8.9..75.61.5....799..2..748..7...96..8..79..5  ; 41 skfr 10.4 SE 10.557.96.8...9...8.573.87.569.76.59..8.8.9..75.61.5....799..2..74...7...96..8..79..5  ; 40 skfr 10.5 SE 10.557.96.8..86...5.973.9..865.69.58..7.7.8..95.61.5....899..2..748..78..9...8..97..5  ; 41 skfr 10.4 SE 10.557.96.8..96...8.573.87.569.69.58....8.7..95.61.5.7..897..2..948..98......8..97..5  ; 41 skfr 10.5 SE 10.557.96.8..96...8.573.8..569.69.58....8.7..95.61.5....897..2..948..98......8..97..5  ; 39 skfr 10.4 SE 10.557.96.8..68...5.973.97.865.96.85....8.7..95.61.567..897..28..45..85......5...7..8  ; 41 skfr 10.5 SE 10.457.96.8..69...8.573.87.569.96.85......5..79.61.7.9..857..2..549..95......5..79..8  ; 40 skfr 10.4 SE 10.557.96.8..69...8.573.87.569.96.85..7...5..79.61.7.9..85...2..549..95..7...5...9..8  ; 40 skfr 10.4 SE 10.657.96.8..68...5.793.98.765.86.57....9.5..87.61.7.9..857..2...48..87......5..89..7  ; 40 skfr 10.5 SE 10.557.96.8.......8.573.87.569..6.57..8.8.7...5.61.5....797..2..94...9...76..8..97..5  ; 37 skfr 10.5 SE 10.5.7.96.8..96...8.573.87.596.79.65..8......97.61.6.7..956..2..549..95..6...5..96..8  ; 40 skfr 10.5 SE 10.5.7.96.8..96...8.573..7.596.79.65..8......97.61.6.7..956..28.549..95..6...5..96..8  ; 40 skfr 10.5 SE 10.589.57....5....87.9.17..958.9...37.5.7.8.95.6..5.8..9.768.95..72..978.6.5.75..6.9.  ; 41 skfr 10.4 SE 10.589.57....5....87.9.17..958.9...37.587.8..5.6..5.8....768.95..72..978.6.5.75..689.  ; 41 skfr 10.4 SE 10.589.57....5....89.7.17..958.7...35.989.5..7.6....9..7.565.89..72..875.6.9.79..685.  ; 41 skfr 10.5 SE 10.68.657....5....67.8.17..8.5667..35.8.9...87.6..8.6....776.85..92..976.8.5.58..967.  ; 41 skfr 10.5 SE 10.67..6..8..6.358..79.8..7...6....6879.9.71.5.68.6879.5..8..9.76.5.95..6.87.7685.94.  ; 43 skfr 10.4 SE 10.67.96..8..6.389..57.8..7..698...5697.9..1.7.86.6798.5..5....96.8..6..8.95.9856.74.  ; 43 skfr 10.4 SE 10.5..96..8..6.389..57.8..7..698...5697.9..1.7.86.6798.5..5....96.8..6..8.95.9856.74.  ; 42 skfr 10.4 SE 10.5.5.6..8..6.378..59.8..5...75...78.9.9..1.6.85.6859.7..8..9.75...96..5.78..586.94.  ; 40 skfr 10.4 SE 10.6.5.6..8..6.378..59.8..5...75...98.7.9..1.6.85.6857.9..8..9.75....6..5.98.9586.74.  ; 40 skfr 10.5 SE 10.6.5.6..8..6.378..59.8.....675...7698.9.61.8.75.7859.6..8..9..7.6.65..7.98.9.86.54.  ; 42 skfr 10.5 SE 10.6.5.6..8..6.378..59.8.....769...7856.5..1.6.98.6859.7..8..9..6.7.96..7.85..586.94.  ; 41 skfr 10.5 SE 10.6.5.6..8..8.375..69.6..8..7.9...76.8.6.81.5.97.7589.6..5..9.87.6.96..7.58.8.56.94.  ; 42 skfr 10.4 SE 10.5.5.6..8..6.385..97.8..7..6.8...96.7.9..1.5.86.6578.9..5..9.76.8..6..8.59.9856.74.  ; 41 skfr 10.4 SE 10.5...6..8..6.378..59.8..5..678...6597.9..1.7.86.6789.5..5..9.67.8..6..8.95.985..64.  ; 41 skfr 10.4 SE 10.57..6..8..6.387..59.8..5..6.9...65.8...71.8.96.6879.5..8..9.76.5.9...6.78.7658.94.  ; 41 skfr 10.6 SE 10.6 new best for skfr 10.6..96..8..6.387..59.8.....678...5679.9..1.7.86.6798.5..5..7..6.8.96..8.75..856.94.  ; 41 skfr 10.4 SE 10.6...6..8..6.389..57.8..7..968...6957....1.7.68..658.9..5..7.86.9..7..6.85.6895.74.  ; 40 skfr 10.4 SE 10.5...6..8..6.387..59.8..9..678...5697....1.7.86.6798.5..5....96.8..6..8.95.9856.74.  ; 40 skfr 10.4 SE 10.5..96.......397..56.6..8..796...9758.9..1.8.67.8756.9..5....96.8..8..6.95.9685.74.  ; 40 skfr 10.4 SE 10.5...6..8..6.389..57.8..7..698...5697....1.7.86..698.5..5..7.96.8.67..8.95.9856.74.  ; 41 skfr 10.4 SE 10.5..96..8..6.389..57.8..7...98...57.9.9..1.6.78..698.5..5..7.89...67..9.85.9856.74.  ; 40 skfr 10.4 SE 10.67.96..8..8.379..56.6..8...99...58.6....1.7.98.8796.5..5..8.69...7...9.85.9857.64.  ; 40 skfr 10.4 SE 10.6...6..8..6.387..95.8..5...78...97.5.9..1.6.78.6758.9..5..9.87....6..5.89.9876.54.  ; 39 skfr 10.5 SE 10.6.5.6..8..6.387..59.8.....675...6879.9..1.7.85.7859.6..8..7..9.6.95..6.78...98.54.  ; 40 skfr 10.5 SE 10.6.5.6..8..8.375..69.6.....7.9...76.8.6.81.5.97.7589.6..5..9..7.6.96..7.58.8.56.94.  ; 40 skfr 10.5 SE 10.67..6.....6.387..59....5..6.9...65.8...71.8.96.6879.5..8..9.76.5.9...6.78.7658.94.  ; 39 skfr 10.5 SE 10.67..6..8..6.387..95.8..5....9...68.5...61.7.89.7859.6..8..7.59...9...6.78.6798.54.  ; 39 skfr 10.6 SE 10.6..96..8..6.387..59.......678...5679.9..1.7.86.6798.5..5..7..6.8.96..8.75...56.94.  ; 39 skfr 10.5 SE 10.65.76.283.6..89.5.7.8..57.6.7..5...8684...695..65.897..9.6..5..8.7..68.95.589..67.  ; 43 skfr 10.4 SE 10.55.76.283.6..98.5.7.8..57.6.7.65...9894...865..58.697..8....5..6.7..96.85.658..97.  ; 43 skfr 10.4 SE 10.55.76.283.6..89.5.7.8...7.6.8..7...5674...698..65.897..9.6.75..8.7..68.95.589..67.  ; 43 skfr 10.4 SE 10.55.76.283.8..95.6.7.6..87.5.7..5...6864.7.8.9..85.697..9.8.76....7..95.86.568..97.  ; 43 skfr 10.4 SE 10.55.76.283.6..98.5.7.8..57.6.7.65...9894.7.8.5..58.697..8...75....7..96.85.658..97.  ; 43 skfr 10.4 SE 10.559.6.283.6..78.5.9.8..59.6.7.69...8594.5.8.7..58.679..8.9.75....7..96.58.658..79.  ; 44 skfr 10.4 SE 10.55.76.283.6..89.5.7.8..57.6.8.67....574.9.5.8..5..867..9.5.78....7..69.58.685..97.  ; 42 skfr 10.4 SE 10.55.76.283.6..89.5.7.8...7.6.9.67...8584...697..75.896..7...65..8.5..78.96.689..75.  ; 43 skfr 10.4 SE 10.55.76.283.6..98.5.7.8...7.6.9.67...8584...967..75.689..7.8..5..6.5..76.98.6.8..75.  ; 42 skfr 10.4 SE 10.559.6.283.6..78.5.9.8...9.6.7.69...5884...679..59.786..9.8.67..5.7..95.86.658..97.  ; 44 skfr 10.4 SE 10.55.76.283.6..98.5.7.8..75.6.9.67...5874...869..58.697..8....7..6.7..96.85.6.8..97.  ; 42 skfr 10.4 SE 10.659.6.283.6..7..9.5....59.6.7.65...9894...657..58.976..8.9.75..6.7..68.59.659..78.  ; 43 skfr 10.4 SE 10.559.6.283.6..7..9.5....59.6.7.65...9894...657..58.976..8.9.75..6....68.59.659..78.  ; 42 skfr 10.4 SE 10.55..6.283.6..78.5.9.8..59.6.7.69...8594.5.867..58.769..8.5..7..6.7..65.98.6.8..75.  ; 43 skfr 10.4 SE 10.559.6.283.6..78.5.9.8..95.6.7.69...5884...679..59.786..9.8..7..6.7..69.85.658..97.  ; 44 skfr 10.4 SE 10.55..6.283.6..87.5.9.8..59.6.9.67...5884...567..75.689..7.8..6..5.5..87.96.6.5..78.  ; 42 skfr 10.4 SE 10.65.76.283.8..95.6.7.6..87.5.7..5....664...859..5..697..9.6..5..8.8..96.75.758..96.  ; 41 skfr 10.5 SE 10.6..76.283.8..79.5.6.6..58.7.7..8...6564.5.9.8..85.679..9.6.85.......76.98.789..65.  ; 41 skfr 10.4 SE 10.55.76.283.6..98...7.8..57.6.7.65....884.7.9....5..687..9.8.75....7..96.85.658..97.  ; 40 skfr 10.5 SE 10.65.76.283.6..98...7.8..57.6.7.65...9894.7.8....58.697..8...75....7..96.85.658..97.  ; 41 skfr 10.4 SE 10.659.6.283.6..78...9.8..59.6.7.65...9884.9.7....59.687..9.8.75....7..96.85.658..97.  ; 42 skfr 10.4 SE 10.6..76.283.6..89.5.7.8..57.6.9.67...8584.5.9.7..75.689..7...85.......76.98.689..75.  ; 41 skfr 10.4 SE 10.55..6.283.6..78.5.9.8..59.6.7.69...8594.5.8.7..58.679..8...75....7..96.58.658..79.  ; 42 skfr 10.4 SE 10.5.9.6.283.6..78.5.9.8..59.6.7.69...5894.8.5.7..58.769..8...97....7..68.9..695..78.  ; 41 skfr 10.4 SE 10.65..6.283.6..78.5.9.8..59.6...65...7874.9.8.5..58.679..8...75....7..96.85.658..7..  ; 40 skfr 10.5 SE 10.559.6.283.8..7..5.6.6...8...9.68...7574...968..58.679..6.9.75..8.7..86.59.859..76.  ; 42 skfr 10.4 SE 10.559.6.283.6..7..5.9.....9.6.7.69...5884...679..59.786..9.8.67..5.7..95.86.658..97.  ; 42 skfr 10.4 SE 10.659.6.283.6..7..5.9.....9.6.7.69...5884...679..59.786..9.8.67..5....95.86.658..97.  ; 41 skfr 10.4 SE 10.65.76.283.6..9..5.7.....7..69.67...5884...697..75.986..7.8.65....6..79.85.598..76.  ; 41 skfr 10.5 SE 10.55..6.283.6..87.5.9.8...9.6.8..7...5674...698..65.987..9.6.87..5.7..65.98.589..67.  ; 42 skfr 10.4 SE 10.65..6.283.8..57.9.6.6..98.5.6.57....874...956..8..567..9.6..7..5.7..65.89.589..67.  ; 41 skfr 10.5 SE 10.65..6.283.8..75.6.9.6..89.5.6..5...7874.9.8.6..85.679..9.8.76....7..95.86.568..79.  ; 42 skfr 10.4 SE 10.55.76.283.8..97.5.6.6..58.7....7....874...569..8..697..9....7..5.5..96.87.785..9..  ; 38 skfr 10.5 SE 10.65..6.283.6..78...9.8..59.6.7.65....884.9.7....5..687..9.8.75....7..96.85.658..97.  ; 39 skfr 10.5 SE 10.65..6.283.6..78...9.8..59.6.9.65...7874.9.8....58.679..8...75....7..96.85.658..79.  ; 40 skfr 10.5 SE 10.6...6.283.6..87.5.9.8..95.6.9.67...8584.5.9.7..75.869..7...58.......67.98.689..75.  ; 40 skfr 10.4 SE 10.5.9.6.283.6..78.5...8..59.6.7.69...5894.8.5.7..58.769..8...97....7..68....695..78.  ; 39 skfr 10.4 SE 10.6...6.283.6..87.5.9.8..59.6.7.69...5884.7.5.9..59.687......87....7..96.8..685..97.  ; 39 skfr 10.4 SE 10.65976.283.6..78.5...8..59.677.69...5894.8.5.7..58.769..8...97....7..6.....695..7..  ; 40 skfr 10.5 SE 10.65976.283.6..7..5...8..59.677.69...5894.8.5.7..58.769..8...97....7..6.....695..7..  ; 39 skfr 10.5 SE 10.65.76.283.6..89.5.7.8...7.6.9..7...8584...967..75.689..7....5..6.5..76.98...9..75.  ; 39 skfr 10.5 SE 10.65.76.283.6..9..5.7.....7...8.67...9574...968..59.687..9.8.75....7..96.58.658..97.  ; 40 skfr 10.5 SE 10.55..6.283.6..9..5.7.....7.6.8.67...9574...968..59.687..9.8.75..6....96.58.658..97.  ; 40 skfr 10.4 SE 10.55..6.283.6..87.5.9.8...9.6.9.67...8584...697..75.986..7....5..6.5..67.98.6.9..75.  ; 40 skfr 10.5 SE 10.65..6.283.6..78.5.9.8...9.6.7..9...8594...867..58.769..8.5..7..6.7..65.98...8..75.  ; 39 skfr 10.5 SE 10.65..6.283.8..75.9.6.6..89.5....5...7874.8.6.9..58.976..9...78....7..65.89.859..7..  ; 39 skfr 10.5 SE 10.55..6.283.8..75...9.6..89.5.6..5...7874.9.8....85.679..9.8.76....7..95.86.568..79.  ; 40 skfr 10.5 SE 10.659.6.283.6..78.5...8..59.6.7.69...5894.8.5.7..58.769..8...97....7..6.....695..7..  ; 38 skfr 10.5 SE 10.65976.283.6..78.5...8..59.677.69...5894.8.5.7..58.769..8...9........6.....695..7..  ; 38 skfr 10.5 SE 10.659.6.283.6..7..5...8..59.6.7.69...5894.8.5.7..58.769..8...97....7..6.....695..7..  ; 37 skfr 10.5 SE 10.65976.283.6..7..5...8..59.677.69...5894.8.5.7..58.769..8...9........6.....695..7..  ; 37 skfr 10.6 SE 10.65..6.283.6..87.5.9.8...9.6.9..7...8584...697..75.986..7....5..6.5..67.98...9..75.  ; 38 skfr 10.5 SE 10.687.6..9..61..8..57..9..7.869...4687.7....86.5.6857...959..6.7.8.378..56..867.5.9.  ; 42 skfr 10.4 SE 10.587.6..9..61..5..78..9.87.6.9...4678.7....85.6.8657...959..6.8.7.378..65..687.5.9.  ; 42 skfr 10.4 SE 10.587.6..9..61..5..78..9.87.6.9...4678.7....85.6.8657...959..6.8.7.378..6...687.5.9.  ; 41 skfr 10.4 SE 10.587.6..9..61..9..57.....7.865...4687.7....56.9.6897...595..6.7.8.367..59..875.9.6.  ; 41 skfr 10.4 SE 10.5.756..9..6....9.75.49.57..895...678.72.9..5...6857...959..6.8.7..789..5...67.5.91  ; 41 skfr 10.4 SE 10.5.756..9..6...59.7..49.87..595...678.72.9.85...6857...959..6.8.7..789..5...67.5.91  ; 42 skfr 10.4 SE 10.5.756..9..6....9.75.49.57..895...67..72.9..5...6857...959..6.8.7..789..5...67.5.91  ; 40 skfr 10.4 SE 10.6.756..9......59.7..49.87..659...678.72.9.86...8657...995..6.8.7..789..6...87.5.91  ; 41 skfr 10.4 SE 10.576.85.9..95.6.48.7..8.97.56.7.9...8.....8.7.9.897...615.7..869.83..69.7..9657...8  ; 42 skfr 10.4 SE 10.576.85.9..98.7.46.5..5.69.78.5.9...6...6.758.9.796.8.516....759.53..96.8..9.5....6  ; 42 skfr 10.4 SE 10.576.85.9..89.7.45.6..5.96.7865.9...8...9.786.5.78..5.919....785.53..89.6..8.5....9  ; 42 skfr 10.4 SE 10.576.85.9..89.7.45.6..5.96.78.5.9...8...9.78..5.786.5.919....785.53..89.6..8.5....9  ; 41 skfr 10.4 SE 10.576.85.9...5.9.47.6..9.76.58.8.7...9.....98..7.976.5.815.6..987.93..87.6..7.56...9  ; 41 skfr 10.5 SE 10.676.85.9..59.7.46.8..8.69.75.5.9...6...6.....9.796...816.5..789.93..86.5..8.59...6  ; 40 skfr 10.5 SE 10.6.5.79....67.5.49.8..9.68.5798.6.5.7.7..8.3.95..5.798..5.7.8..69.9..5678....9.75.2  ; 42 skfr 10.4 SE 10.5.5.7..6..76.5.48....9..6.75.7.8.9.5.9.56.3.8...8..59..5.7.6..98.9..5876..869.75.2  ; 40 skfr 10.5 SE 10.456...97..7.815.9.6..97.6.5.89...56.76.5..7..2....6.58.98..7..653.659.8...5.6.8...  ; 39 skfr 10.4 SE 10.5.759.2.1.9..7...25..8.5..7956...978.78..6593...987..568...9.56..9.5.8.4..5.6.7.98  ; 42 skfr 10.4 SE 10.5.7.9.2.1.9..6...27..8.7..6956...798.78..5963...986..758...9.75..975.8.4..5.7.6.98  ; 42 skfr 10.4 SE 10.5..5982.1.8..6..529..9.5..8675...689.98..7563...689..575...6.97....5.9.4..9.7.8.65  ; 42 skfr 10.4 SE 10.5.7.9.2.1.9..7...26..8.6..7956...978.78..5693...987..658...9.65..9.5.8.4..5.6.7.98  ; 41 skfr 10.4 SE 10.5..96..8..6.389..57.8..7...98.1457.9.9....6.78.6798.5..5..7.89....6..9.85.9856.7..  ; 40 skfr 10.4 SE 10.57.96..8..6..87..59.8......78.1..7.9.93...6.78.6798.5..5..7.89...76....85.9856.7.2  ; 39 skfr 10.5 SE 10.6..598....8..6.75.9..9.53.6875...689.98..756.1..689..575.7.6.9....87.9..549.5....6  ; 41 skfr 10.4 SE 10.5`

to "fill in the gap" with skfr ratings, here are the skfr 10.4's with 45+ clues and the skfr 10.3's with 46+ clues. the only puzzle in common to both these lists is the top one, which is dobrichev's first puzzle with the 5-template swapped out for another one and 3 clues removed
15 puzzles: Show
Code: Select all
`.956..8..61..89.5..48.57.9695.7.8.6.82.56.97..76.9.5.856.8..7.9.3.9.568..89.76..5  ; 46 skfr 10.4 SE 10.585.79.63.67.5..9.8..9.68.57.6.8.5.7.5.794..86..8.765..7.6.8..9518..5976..956.78..  ; 46 skfr 10.3 SE 10.357.96.8..68...5.793.97.856.75.68..9...8..76.51.659..878..259746.678..95...5.76..8  ; 47 skfr 10.3 57.96.8..68...5.793.97.856.76.85..9...5..76.81.869..578..276945..65..78..57.89..6  ; 47 skfr 10.3 57.96.8..68...5.793.97.856.96.57..8.7.8..96.51.568..978..25.946.968...5..5..96..8  ; 46 skfr 10.3 57.96.8..68...5.793.98.756.86.57..9.9.5..87.61.7.9..857..25.948.987...5..5..89..7  ; 45 skfr 10.4 SE 10.457.96.8..69...8.573.87.596.96.85..7...7..96.51.567..897..296548..65..79..59..7..6  ; 46 skfr 10.3 57.96.8..68...5.793.98.756.76.58..9...5..67.81.879..568..279645..76..98...6..8..7  ; 45 skfr 10.4 SE 10.3.7.96.8..68...5.793.97.865.75.89..6...8..67.51.657..988..257946..76..58..6..89..7  ; 45 skfr 10.4 SE 10.35976.283.6..89.5.7.8..57.697.69...5884.7.5.9..59.867..9.5.78....7..69.85.685..97.  ; 46 skfr 10.4 SE 10.495..6.8..6....8.59..85.96..59..8.7.6..765..98.869.75..8154932677.9826..5.6.17598.  ; 48 skfr 10.3 SE 10.4 new best for skfr 10.395..6.8..6....8.59..85.96..58..9.7.6..765..98.968.75..719483265..5926..7.6.1759..  ; 46 skfr 10.3 95..6.8..8....5.69..68.9...68..9.7.5..567..98.975.86..719453286..8926..7.6.1879..  ; 45 skfr 10.4 SE 10.495..6.8..8....9.56..65.89..68..9.7.5..567..89.978.56..719453268..8926..7.6.187.9.  ; 46 skfr 10.3 7659..8..8.3.6..79.94.78.566517.9..89.28.65.7.78.5.69.5.769..8..89...76...6.879.5  ; 47 skfr 10.4 SE 10.4 new best for skfr 10.4`

the next step at this point is to take the hardest puzzles obtained so far and move the 1,2,3,4's around the grid and rate them with skfr in the hope to find new hardest puzzles and hopefully a SE 10.7 or higher. that will take a day or so. i'll make another post once i'm done with that
999_Springs

Posts: 591
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

### Re: Maximum number of clues for a given SE rating

well.

so i took the hardest 500 or so puzzles generated using the method in the previous post and moved the 1,2,3,4 clues everywhere in the puzzle (keeping either any 3 or all 4 in a 1110 or 1111 distribution, but the 1110 gave a much greater yield), then did the same method again to remove the 56789 numbers from all possible 5-templates. this gave 73 skfr 10.5+'s (i think only 1 came from the 1111 distribution, the rest from the 1110)

i then iterated this process once more using the new skfr 10.5+'s as seeds, moving the 1234's everywhere else, then removing 56789's again. this gave 15 more skfr 10.5+'s (i was also going to do the new skfr 10.4's as seeds too but didn't, maybe i will come back to that)

the skfr rating distribution of all the new puzzles is
skfr 11.1 x 1 (clues: 42)
skfr 11.0 x 0
skfr 10.9 x 2 (most clues: 39)
skfr 10.8 x 1 (clues: 40)
skfr 10.7 x 2 (most clues: 39)
skfr 10.6 x 22 (most clues: 42 + 2 extra)
skfr 10.5 x 60 (most clues: 44)

the SE rating distribution is
SE 11.1 x 2 (most clues: 42)
SE 11.0 x 1 (clues: 40)
SE 10.9 x 1 (clues: 39)
SE 10.8 x 4 (most clues: 39)
SE 10.7 x 15 (most clues: 42)
SE 10.6 x a lot (most clues: 44)

here are all the new skfr 10.5+ puzzles, split by first and second iteration, sorted by skfr then clues then SE
first pass (73 puzzles): Show
Code: Select all
`59.86.7...8...5.96.467.9.8.6.59..8.78...76.5..7..5861.92.68..7..5..9..68.685.79..  ; 42 skfr 11.1 SE 11.1 oh my god this is amazing..96..8..61.87..59.8.....6782..5679......7.86.6798.5..54.7..6.8..6..8.75..856.9..  ; 39 skfr 10.9 SE 10.9 new best for skfr 10.9 and SE 10.9...6..8..6..58..97.8..7...5921.58.7.5....6.89.68.9.5..8..9.57...96..7.58...86.94.  ; 37 skfr 10.9 SE 11.17.96..8..8.379..56.6..8...99.1.58.6......7.98.8796.5..5.28.69...7...9.85.9857.6..  ; 40 skfr 10.8 SE 11.0 new best for skfr 10.8 and SE 11.07..6.....6.387..59....5..6.9.1.65.8...7..8.96.6879.5..8.29.76.5.9...6.78.7658.9..  ; 39 skfr 10.7 SE 10.7 new best for skfr 10.77.96..8..8.379..56.6..8...99...58.6....1.7.98.8796.5..5.2..69...7...9..5.9857.6..  ; 38 skfr 10.7 SE 10.857.96.8..69...8.57..87.569.75.69..8..36..75.91.9.5..769..2.6..5..75..96..65..9..8  ; 42 skfr 10.6 SE 10.4 (*)7.96..8..6.387..59.8.....6.8.14.6.9.9....7.86.6798.5..5..7..6.8.96..8.75.7856.9..  ; 40 skfr 10.6 SE 10.7..96..8..6.387..59.......678.1.5679.9....7.86.6798.5..5.27..6.8.96..8.75...56.9..  ; 39 skfr 10.6 SE 10.77..6..8..61.87..95.8..5....92..68.5...6..7.89.7859.6..84.7.59...9...6.78.6798.5..  ; 39 skfr 10.6 SE 10.7.5.6..8..6..58..97.8..7...5921.58.7.5....6.89.68.9.5..8..9.57...96..7.58..586.94.  ; 39 skfr 10.6 SE 10.67..6.....6.387..59....5..6.9...65.8...71.8.96.6879.5..8.29.76.5.9...6.78.7658.9..  ; 39 skfr 10.6 SE 10.67..6.....61.87..95....5....92..68.5...6..7.89.7859.6..8..7.59...9...6.78.6798.54.  ; 37 skfr 10.6 SE 10.8...6..8..6..58..97.8..7...5921.58.7.5....6.89.68.9.5..8..9.57...96.47.58...86.9..  ; 37 skfr 10.6 SE 10.7...6..83.6..58..79.8..7...58.1..7.5.9....6.87..685.9..5....87...672.5.98.9876.5..  ; 37 skfr 10.6 SE 10.77..6.....6.387..95....5....9.1.68.5...6..7.89.7859.6..8..7.59...9...6.78.6798.54.  ; 37 skfr 10.6 SE 10.77..6.....61.87..95....5....92..68.5...6..7.89.7859.6..84.7.59...9...6.78.6798.5..  ; 37 skfr 10.6 SE 10.77..6.....6.387..95....5....9...68.5...61.7.89.7859.6..8.27.59...9...6.78.6798.5..  ; 37 skfr 10.6 SE 10.77..6.....6.387..95....5....9.1.68.5...6..7.89.7859.6..8.27.59...9...6.78.6798.5..  ; 37 skfr 10.6 SE 10.759761.83.6..7..5...8..59.677.69...5894.8.5.7..58.769..8...9........6.....695..7..  ; 37 skfr 10.6 SE 10.659761.8.46.37..5...8..59.677.69...589..8.5.7..58.769..8...9........6.....695..7..  ; 37 skfr 10.6 SE 10.559.86.7..78...5.96.467.9.8.6.59..8.78...76.5..7..5861.92.68..7..57.9..68.685.79..  ; 44 skfr 10.5 SE 10.6 new best for skfr 10.5 and SE 10.676..5.8..89.6....5..5.78.69673..598.158..6..742978.65.9.7.6.5.85.68.7.9..8.5....6  ; 44 skfr 10.5 SE 10.5 only puzzle with all 4 of 12345.76.28..6..89.5.7.8..57.6.7..5...8684...695..65.897..9.6..5..8.7..68.95.589.367.  ; 43 skfr 10.5 SE 10.67..6..8..61.87..59.8..5..6.92..65.8...7..8.96.6879.5..8..9.76.5.9...6.78.7658.94.  ; 41 skfr 10.5 SE 10.67..6..8..6.387..59.8..5..6.9...65.8...71.8.96.6879.5..8.29.76.5.9...6.78.7658.9..  ; 41 skfr 10.5 SE 10.67.96..8..6.387..59.8.....678.1.5679.9......86.6798.5..5.....6.8.96..8.75.7856.94.  ; 41 skfr 10.5 SE 10.57.96..8..6.387..59.8.....6.8.1..6.9.9....7.86.6798.5..5.27..6.8.96..8.75.7856.9..  ; 40 skfr 10.5 SE 10.67596..8..8.359..76....78...5....7.6.9..1.5.87.8796.5..6....97...752.6.98.9875.6..  ; 40 skfr 10.5 SE 10.6.5.6..8..6.387..59.8.....675.1.6879.9....7.85.7859.6..8.27..9.6.95..6.78...98.5..  ; 40 skfr 10.5 SE 10.67.96..8..81.79..56.6..8...992..58.6......7.98.8796.5..5..8.69...7...9.85.9857.64.  ; 40 skfr 10.5 SE 10.67.96..8..8.379..56.6..8...99...58.6....1.7.98.8796.5..5.28.69...7...9.85.9857.6..  ; 40 skfr 10.5 SE 10.67.96..83.8..79..56.6..8...99.1.58.6......7.98.8796.5..5.28.69...7...9.85.9857.6..  ; 40 skfr 10.5 SE 10.6..96..8..6.389..57.8..7...98.1.57.9.9....6.78.6798.5..5..7.89....6..9.85.9856.74.  ; 40 skfr 10.5 SE 10.6.5.6..8..6.378..59.8..5...75.1.78.9.9....6.85.6859.7..8..9.75...96..5.78..586.94.  ; 40 skfr 10.5 SE 10.65.76.283.6..9..5.7.....7.6.8.67....57.1..968..5..687..9.8.75..6.7..96.58.658..97.  ; 40 skfr 10.5 SE 10.5.5.6..8..6..78..59.8..5...7521.78.9.9....6.85.6859.7..8..9.75...96..5.78..586.94.  ; 40 skfr 10.5 SE 10.55..61.8..6.39.45.7.....7..69.87...657....698..65.987..8.6.75.......69.58.598..67.  ; 39 skfr 10.57..6..8.46..87..95.8..5....9...68.5...61.7.89.7859.6..8.27.59...9...6.78.6798.5..  ; 39 skfr 10.57..6..8..61.87..95.8..5....92..68.5...6..7.89.7859.6..8..7.59...9...6.78.6798.54.  ; 39 skfr 10.57..6..8..6.387..95.8..5....9...68.5...61.7.89.7859.6..8..7.59...9...6.78.6798.5.2  ; 39 skfr 10.57..6..8..6.387..95.8..5....9...68.5...61.7.89.7859.6..8.27.59...9...6.78.6798.5..  ; 39 skfr 10.57..6.....6..87..59....5..6.9...65.8...7..8.96.6879.5..8429.76.5.9...6.7837658.9..  ; 39 skfr 10.57..6.....6.387..59....5..6.9.1.65.8...7..8.96.6879.5..8..9.76.5.9...6.78.7658.94.  ; 39 skfr 10.57..6.....6..87..59....5..6.921.65.8...7..8.96.6879.5..8..9.76.5.9...6.78.7658.94.  ; 39 skfr 10.57..6.....61.87..59....5..6.92..65.8...7..8.96.6879.5..8..9.76.5.9...6.78.7658.94.  ; 39 skfr 10.5...6..8..6.387..95.8..5...78.1.97.5.9....6.78.6758.9..5..9.87....6..5.89.9876.54.  ; 39 skfr 10.5...6..8..6.378..59.8..5...78.1.75.9.9....6.78.6789.5..5..9.87...96..7.85..856.94.  ; 39 skfr 10.5...6..8..6..78..59.8..5...7821.75.9.9....6.78.6789.5..5..9.87...96..7.85..856.94.  ; 39 skfr 10.5...6..8..6..78..59.8..5...7821475.9.9....6.78.6789.5..5..9.87...96..7.85..856.9..  ; 39 skfr 10.5...6..8..61.78..59.8..5...782..75.9.9....6.78.6789.5..5..9.87...96..7.85..856.94.  ; 39 skfr 10.5...6..83.6..78..59.8..5...78...75.9.9..1.6.78.6789.5..5.29.87...96..7.85..856.9..  ; 39 skfr 10.55..61.8..6.3..45.9.......6.7.69...588....679..59.786..9.8.67..5....95.86.658..97.  ; 38 skfr 10.55.761.8.46.37..5...8..59.677.69...589..8.5.7..58.769..8...97....7..6.....695..7..  ; 38 skfr 10.55..61.8..6.39.45.7.....7..69.87...657....698..6..987..8.6.75.......69.58.598..67.  ; 38 skfr 10.55976.283.6..78.5...8..59.677.69...589.18.5.7..58.769..8...9........6.....695..7..  ; 38 skfr 10.5...6..8..6.378..59.8..5...75.1.78.9.9....6.85.6859.7..8..9.75...96..5.78...86.94.  ; 38 skfr 10.5...6..8..61.78..59.8..5...752..78.9.9....6.85.6859.7..8..9.75...96..5.78...86.94.  ; 38 skfr 10.5...6..8..61.78..59.8..5...752..78.9.9....6.85.6859.7..84.9.75...96..5.78...86.9..  ; 38 skfr 10.57..6...3.6..87..95....5....92..68.5...6..7.89.7859.6..8..7.59...9...6.78.6798.54.  ; 37 skfr 10.57..6.....6..87..95....5....9...68.5...61.7.89.7859.6..8427.59...9...6.78.6798.5..  ; 37 skfr 10.57..6.....6..87..95....5....921.68.5...6..7.8947859.6..8..7.59...9...6.78.6798.5..  ; 37 skfr 10.57..6.....61.87..95....5....92..68.5...6..7.89.7859.6..8..7.59...9..46.78.6798.5..  ; 37 skfr 10.57..6.....6.387..95....5....9...68.5...6..7.89.7859.6.18.27.59...9...6.78.6798.5..  ; 37 skfr 10.57..6....46..87..95....5....9...68.5...61.7.89.7859.6..8.27.59...9...6.78.6798.5..  ; 37 skfr 10.57..6.....6.387..95....5....9...68.5...61.7.89.7859.6..8..7.59...9...6.78.6798.5.2  ; 37 skfr 10.57..6.....6..87..95....5....9...68.5...6..7.89.7859.6..8427.59...9...6.7836798.5..  ; 37 skfr 10.559.61.8..6..7..5...8..59.6.7.69...5894.825.7..58.769..8...97....7..6.....695..7..  ; 37 skfr 10.55..6.28.46..78.5...8..59.677.69...589.18.5.7..58.769..8...9........6.....695..7..  ; 36 skfr 10.5...6..8..6..58..97.8..7...5..1497.5.9....6.7..7685.9..5..9.87...6...5.89.9.76.5.2  ; 36 skfr 10.55.761.8.46.37..5...8..59.677.69...589..8.5.7..58.769..8...9........6.....695..7..  ; 36 skfr 10.55.761.83.6..7..5...8..59.677.69...5894.8.5.7..58.769..8...9........6.....695..7..  ; 36 skfr 10.559.6.28..6.37..5...8..59.6.7..9...589..8.5....58.769..8...97....7..6.....695..7.1  ; 35 skfr 10.5`

second pass (15 puzzles): Show
Code: Select all
`59.86.7...8..45.96..67.9.8.6.59..8.78...76.5..7..5861.92.68..7..5..9..68.685.79..  ; 42 skfr 10.6 SE 10.7 new best for SE 10.759.86.7...6..45.98..87.9.6.8.59..6..6....8.5..7..5681.92.68..7..5..9..86.865.79..  ; 40 skfr 10.6 SE 10.759.86.7...6..45.98..87.9.6.8.59..6..6...78.5..7..5681.92.68.....5..9..86.865.79..  ; 40 skfr 10.6 SE 10.759.86.7...8..45.96..67.9.8.8.59..6..6...78.5.27..5681.9..68.....5..9..68.685.79..  ; 40 skfr 10.6 SE 10.759.86.7...8..45.96..67.9.8.8.59..6..6....8.5.27..5681.9..68.....5..9..68.685.79..  ; 39 skfr 10.6 SE 10.8 new best for SE 10.859.86.7...6..45.98..87.9.6.6.59..8..8....6.5..7..5861.92.68.....5..9..86.865.79..  ; 39 skfr 10.6 SE 10.8.5.6..8..6..58..97.8..7...5921.58.7.5....6.89.68.9.5..8..9.57...96.47.58..586.9..  ; 39 skfr 10.6 SE 10.659.86.7...8..45.96..67.9.8.6.59..8.78...76.5.27..5861.9..68..7..5..9..68.685.79..  ; 42 skfr 10.5 SE 10.659.86.7...8..45.96..67.9.8.6.59..8..8....6.5.27..5861.9..68..7..5..9..68.685.79..  ; 40 skfr 10.5 SE 10.77.96..8..6.387..59.8.....6.8....6.9.9..1.7.86.6798.5..5.27..6.8.96..8.75.7856.9..  ; 40 skfr 10.5 SE 10.57..6...3.61.87..95....5....92..68.5...6..7.89.7859.6..8..7.59...9...6.78.6798.5..  ; 37 skfr 10.57..6.....6..87..95....5....9.1.68.5...6..7.89.7859.62.8..7.59...9..46.78.6798.5..  ; 37 skfr 10.57..6.....6.387..95....5....9...68.5...61.7.89.7859.6..8..7.59...9...6.78.6798.54.  ; 37 skfr 10.55.76128.46..7..5...8..59.677.69...589..8.5.7..58.769..8...9........6.....695..7..  ; 36 skfr 10.55.76.283.6..7..5...8..59.677.69.1.589..8.5.7..58.769..8...9........6.....695..7..  ; 36 skfr 10.5`

i have posted the 4 hardest puzzles to the hardest sudokus thread. i finally beat Mauricio's record for the most clues for any puzzle with SE 11+ he had it for 14 years with his SE 11.2 with 37 clues

the puzzle marked (*) is skfr 10.6 with 42 clues, but skfr rates it 10.6/10.5/2.6 indicating that it is not maximal, and in fact, adding the two missing 7's gives a skfr 10.6 with 44 clues. strangely, SE doesn't find the 7's, it finds 4r8c6 as the first cell instead and the puzzle is rated 8.3 after that
44-clue skfr 10.6: Show
Code: Select all
`57.96.8..69...8.57..87.569.75.69..8..36..75.91.9.5..769..2.67.5..75..96..65.79..8  ; 44 skfr 10.6 SE 10.4 new best for skfr 10.6`

with these new ratings, that means i have successfully closed the gap between Mauricio's 37 and dobrichev's 48's - or even to the 1.0 SE rating that started this entire thread 13 years ago! that was one of my original goals when i created this thread - to have something nice for every rating. me at age 14 would be proud, even though it took so long

here is the new table for maximum clues for each SE rating in that range
10.5 | 46 | .956..8..61..89.5..48.57.9695.7.8.6.82.56.97..76.9.5.856.8..7.9.3.9.568..89.76..5
10.6 | 44 | 59.86.7..78...5.96.467.9.8.6.59..8.78...76.5..7..5861.92.68..7..57.9..68.685.79..
10.7 | 42 | 59.86.7...8..45.96..67.9.8.6.59..8.78...76.5..7..5861.92.68..7..5..9..68.685.79..
10.8 | 39 | 59.86.7...8..45.96..67.9.8.8.59..6..6....8.5.27..5681.9..68.....5..9..68.685.79..
10.9 | 39 | ..96..8..61.87..59.8.....6782..5679......7.86.6798.5..54.7..6.8..6..8.75..856.9..
11.0 | 40 | 7.96..8..8.379..56.6..8...99.1.58.6......7.98.8796.5..5.28.69...7...9.85.9857.6..
11.1 | 42 | 59.86.7...8...5.96.467.9.8.6.59..8.78...76.5..7..5861.92.68..7..5..9..68.685.79..

and the equivalent table for skfr in this range - because they seem to be mostly different puzzles to the SE ones
10.3 | 48 | 95..6.8..6....8.59..85.96..59..8.7.6..765..98.869.75..8154932677.9826..5.6.17598.
10.4 | 47 | 7659..8..8.3.6..79.94.78.566517.9..89.28.65.7.78.5.69.5.769..8..89...76...6.879.5
10.5 | 44 | 76..5.8..89.6....5..5.78.69673..598.158..6..742978.65.9.7.6.5.85.68.7.9..8.5....6
10.6 | 44 | 57.96.8..69...8.57..87.569.75.69..8..36..75.91.9.5..769..2.67.5..75..96..65.79..8
10.7 | 39 | 7..6.....6.387..59....5..6.9.1.65.8...7..8.96.6879.5..8.29.76.5.9...6.78.7658.9..
10.8 | 40 | 7.96..8..8.379..56.6..8...99.1.58.6......7.98.8796.5..5.28.69...7...9.85.9857.6..
10.9 | 39 | ..96..8..61.87..59.8.....6782..5679......7.86.6798.5..54.7..6.8..6..8.75..856.9..
11.0
11.1 | 42 | 59.86.7...8...5.96.467.9.8.6.59..8.78...76.5..7..5861.92.68..7..5..9..68.685.79..
999_Springs

Posts: 591
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

### Re: Maximum number of clues for a given SE rating

To fill in the top of the table a bit:

11.6 | 29 | ........1.....2.3...4.5..624...67.....65...4778..246....2..5.7..4.2..9..1...4.32. (mith 27c + singles)
11.7 | 28 | 98.76.5..7.5..9.8..4.5..7.98.7..53.....2..............5.8..3..731....8...74....3. (GP;2016_04_23;1835324 26c + singles)
11.8 | 26 | 98.76.5..7.54..6....3.58...5..6..4......2...........1.4...7..59...5...64.5....7.. (PAQ;2019_04_28;2345626 24c + singles)
11.9 | 23 | 98.7.....6.....87...7.....5.4..3.5....65...9......2..1..86...5.....1.3.......4..2 (GP;kz0;11523 + 2 others)

Given that I just found the 11.6 27c this week, I'm hopeful to find some higher clue counts soon.
mith

Posts: 950
Joined: 14 July 2020

### Re: Maximum number of clues for a given SE rating

i filled in all the singles from the 11.3+ puzzles from champagne's hardest list (which i didn't realise was an old version from 2019 until i was done) and got these. each (non-minimal) puzzle is unique for its clue count here. the small puzzles underneath each one are the minimal versions

11.7 | 28 | 98.76.5..7.5..9.8..4.5..7.98.7..53.....2..............5.8..3..731....8...74....3. (same as above)
98.76.5..7.5..9.8..4.5..7.98.7..53.....2..............5....3..731....8....4....3.;11.70;1.20;1.20;GP;2016_04_23;1835324;26;

11.6 | 31 | 98.7..6..75..6..9...6......5...86..9..89...5669..4.3..26......18.96...7...58...6. (sorry mith, you didn't make it)
98.7..6..75.....9...6......5...8...9..89...56....4.3..2.......1..96...7...58...6.;11.60;1.20;1.20;PAQ;2018_12_06;2210346;25;

11.5 | 32 | 98.7..6..7.4.86.59..6..9...69...74....34....6.47.6...246..7.9....1....6...96....4
98.7..6..7...8..5...6..9...69...74....34.............24...7.9....1....6....6....4;11.50;1.20;1.20;PAQ;2018_12_06;2210330;23;
98.7..6..7...8..5......9...69...74....34.........6...246..7.9....1.........6....4;11.40;1.20;1.20;PAQ;2018_12_01;2123981;23; <- this one only completes to 30 clues after singles
98.7..6..7...86.5......9...69...74....34.............246..7.9....1....6....6....4;11.30;1.20;1.20;PAQ;2019_01_13;2316259;24;
98.7..6..7...86.5......9...69...74....34.........6...246..7.9....1....6.........4;11.30;1.20;1.20;PAQ;2019_01_13;2316260;24;
98.7..6..7...86.5......9...69...74....34....6........246..7.9....1.........6....4;11.30;1.20;1.20;PAQ;2019_01_13;2316261;24;
98.7..6..7...8..5...6..9...69...74....34....6........246..7.9....1.........6....4;11.30;1.20;1.20;PAQ;2019_01_13;2316258;24;

11.4 | 33 | 98.7.56..57.4.......6.8..757...5..69.6....7.3...6.72..6....15.7.5..7..86..75..3..
98.7..6..5..4.......6.8..757...5...9.6......3...6.72..6....1....5.....86..7...3..;11.40;1.20;1.20;PAQ;2019_01_07;2236784;25;

11.3 | 34 | 98.7..6..7.5....9..4..9...763.9...7...4.7.9.6.97.62...37.6....9..9..786.....1973.
98.7..6..7.5.......4..9....63.9...7...4...9.6.....2...3..6....9..9..78......1.73.;11.30;1.20;1.20;PAQ;2019_03_16;2317691;25;
98.7..6..7.5....9..4.......63.9...7...4.7...6.9...2...37.6....9..9...8......1.73.;11.30;1.20;1.20;GP;2019_01_07;2240426;26;

i have no idea why some of the minimal versions for 11.5 have a lower rating. maybe they are skfr ratings... i can't check right now

this finally completes the entire rating catalogue by giving one example for every SE rating, which was the main goal of this thread when i first began this 13 years ago mission accomplished!

i still have more ideas for generation in the 10.5+ range but haven't been able to get around to doing them. hopefully soon

--- edit ---

i re-ran the singles check on the latest versions of champagne's database, rather than the early 2019 version.

no new records showed up compared to the above but there are A LOT of ties. i didn't check the solution grids for isomorphism, and my guess is that most of these are isomorphic, but now there are:
11.9 | 23 x 5
11.8 | 26 x 2
11.7 | 28 x 1
11.6 | 31 x 38
11.5 | 32 x 1
11.4 | 33 x 9
11.3 | 34 x 103
here are all of them. i didn't check which minimal puzzles they all came from
11.3 and higher: Show
98.7.....6.....87...7.....5.4..3.5....65...9......2..1..86...5.....1.3.......4..2 11.9 23
12..3....4....1.2...52..1..5..4..2......6..7......3..8.5....9....9.7..3......8..6 11.9 23
........1....23.45..51..2....25...1..6...27..8...9......42....7.3...6...9...8.... 11.9 23
..3..6.8....1..2.6....7...4..9..8.6..3..4...1.7.2.....3....5.....5...6..98.....5. 11.9 23
5.6...7...1.3.....8.3.5.9.....1...2.....8.6.7.....2.4.7...9...6.3...42....5...... 11.9 23

98.76.5..7.54..6....3.58...5..6..4......2...........1.4...7..59.5....7.....5...64 11.8 26
98.76.5..7.54..6....3.58...5..6..4......2...........1.4...7..59...5...64.5....7.. 11.8 26

98.76.5..7.5..9.8..4.5..7.98.7..53.....2..............5.8..3..731....8...74....3. 11.7 28

98.7..6..75..6..9...6......5...86..9..89...5669..4.3..26......18.96...7...58...6. 11.6 31
98.76....5.7..48...3.58....8.6.5.4...4...8.2..5.4....84.58..7...9.....84..8.4...1 11.6 31
98.76....75.4.......3.587..5...793...3.5...7...73....2.7..358.....6...373....7.1. 11.6 31
98.7..6..5..8..94...4.95.836..5..8...25.8......8..1....5.9...78.....85..8...5..69 11.6 31
98.76.5..5.7..9.6...4..3.7947.6...9.39...7..6..6.9......9..6.4.....2.9.....9..6.1 11.6 31
98.7..6.4..5.94.3...4.8..974..8.2....1.4.......8.3..4..4.....8...9..84.58...4.9.3 11.6 31
98.7..6..5.6.84.....3.96...79..6.8...6...7.2...5....7664...97....76....1..9.7..6. 11.6 31
98.7.465.75...84....4.5..878...7..94.4...3......84.2...9..8..454..5.1......4..... 11.6 31
98.7..6..5..96.4...63..8.797......6..596....7.46.7.9..6..5..7......27..6.....6.1. 11.6 31
98.7..6..7....8.5...4....8769..8.7...476.3.....29.7...37...98....98...7...8.7...1 11.6 31
98.7..6..7...8..5...4....8769...87...4763......297....37..9.8....98...7...8..7..1 11.6 31
98.7..6..75..6..9...6......46...3.....86...5.5.79...6...58.6.7.67..2.1..8....75.6 11.6 31
98.76.5..5.7..9.6...4..3.7947.6...9.39...7..6..6.9......9..6.4....9..6.2....1.9.. 11.6 31
98.76....5..49.....47..39..8......93.349..7....9.3...24..3....9.96.4.3..3....9.1. 11.6 31
98.7..6..5..94.8....4.83.957..8..5...25....8...8.....1...5....88...79.5..5..689.. 11.6 31
98.76....5.7..48...3.58.....9.....844.58..7....8.4...2.4...8.1.8.6.5.4...5.4....8 11.6 31
98.76....5.7..48...3.58....8.6.5.4...4...8.2..5.4....8.9.....844.58..7....8.4...1 11.6 31
98.76....75.4.......3.587..5...793...3.5...7...73....23....7.1....6...37.7..358.. 11.6 31
98.76....5.7..48...3.58....8.6.5.4...5.4....8.4...8.2.4.58..7...9.....84..8.4...1 11.6 31
98.7..6..5..94.8....4.83.957..8..5...25....8...8.....1.5..689.....5....88...79.5. 11.6 31
98.7..6..75..6..9...6......67..4.3....58.6.7.8....75.626...1.....86...5.5.79...6. 11.6 31
98.7..6....7.5..9...6..9..74.9...8.363.9...7...2...9.6.9...17..76.3....9..4.97... 11.6 31
98.7..6..75..6..9...6.....747...39.6.396...7...897..5...78...6.....267.......7..1 11.6 31
98.7..6..5.6.84.....3.96...64...97....76...2...9.7...679..6.8...6...7..1..5....67 11.6 31
98.76....5.7..48...3.58....4.58..7...9.....84..8.4...2.4...8.1.8.6.5.4...5.4....8 11.6 31
98.76....75.4.......3.587..5...793....73...2..3.5....73....7..1.7..358.....6...73 11.6 31
98.7..6..75...6.9...6.9....49..67..3.379...6...58..97...96...5.....2...9.....91.6 11.6 31
98.7..6..75..6..9...6......46......38.96...7...58...6...89...565...86..969..2.1.. 11.6 31
98.7..6..5..94.8....4.83.597..8..5...25.....8..8....1..5..689.....5...8.8...79..5 11.6 31
98.76....75.4.......3.587..5...793...3.5...7...73....2...6...37.7..358..3....7.1. 11.6 31
98.7..6..75...6.9...6......46..3......86...5.5.79...6...586..7.8...7.5.667...21.. 11.6 31
98.7..6..75...6.9...6......8...7.5.6..586..7.67...43..26..1......86...5.5.79...6. 11.6 31
98.7..6..75..6..9...6......69..4.3....89...565...86..926......18.96...7...58...6. 11.6 31
98.76.5..5.7..9.6...4..3.7947.6...9.39...7..6..6.9.......9..6.2....1.9....9..6.4. 11.6 31
98.7..6..7...8..5...4....8769...87...4763......297....37..9.8....8..7..1..98...7. 11.6 31
98.76....5.7..48...3.58....4.58..7...9.....84..8.4...28.6.5.4...5.4....8.4...8.1. 11.6 31
98.76....75.4.......3.587..5...793....73...2..3.5....73....7..1...6...73.7..358.. 11.6 31
98.76....75.4.......3.587..5...793...3.5...7...73....23....7.1..7..358.....6...37 11.6 31

98.7..6..7.4.86.59..6..9...69...74....34....6.47.6...246..7.9....1....6...96....4 11.5 32

98.76.5..7.4.95.6...5..3.9.5....63.9...9...5...9.5.4.6.9..2.6...5.6..9.1..6..9.3. 11.4 33
98.7.56..57.4.......6.8..757...5..69.6....7.3...6.72..6....15.7.5..7..86..75..3.. 11.4 33
98.7..6..56..8..7...7..6...7..8.4.63..867.94...6.5.7..62...8..7..5.6.8..8..1....6 11.4 33
98.7.46..7.5.69.4...6.3..9.6...4.3.9..9..65.4...9...6..6.4..9.2..4.9..3..9...14.. 11.4 33
98.76.5..76..4......5..8.676....7.59.5....6.3...65.2..5..1..7.6.7...6.85..6.7.3.. 11.4 33
98.7.46..7.5.69.4...6.3..9.6...4.3.9...9...6...9..65.4.9...24...6.4..9.1..4.9..3. 11.4 33
98.74.6..74..5......6..8.476..3..7.4.7...4.86..4.7.2..4....7.69.6....4.2...46.1.. 11.4 33
98.7.56..75.4.......6.9..576.....73....6.72...7..5..865...7..69.6...157...75..3.. 11.4 33
98.76.5..4...9.8...578.3.9.8...5.4...2...8.5...5..9.815..9...48.9..8..65..8...9.. 11.4 33

98.7..6..57.64......6..9.757....6.59.69.7.3.....29.76..9...7.86..7.6..3.6.....1.7 11.3 34
98.7..6..7.5....9..4..9...763.9...7...4.7.9.6.97.62...37.6....9..9..786.....1973. 11.3 34
9876..5..64..9..87..57..6..7..8...65.6..7.8....8..6.732...67..8..63..7...7..1...6 11.3 34
98.76.5..5.7..4.9..3..958..3.59....21......59.9..5.3....9.3..65..35..9...5...9.38 11.3 34
98.76....7..54...9..4..967.34.....97.7.9.4..2..9.7.46..9...7.2...74..95.....9.7.1 11.3 34
9876..5..6..5..9...45.89.7.8...93..5.5.8...9...9.568..5..9..3...9...5.2...1..8.59 11.3 34
98.76.5..5.7..4.9..3..958..2......59.9..5.3..3.59....1..9.3..65..35..9...5...9.38 11.3 34
98.76....7..54.9....4..9.6734....7.9.7.9.42....9.7..46..74...95....9.17..9...7..2 11.3 34
9847..6..56..94.8...76..4..6..9...4..4..679....9.43..64....6.2..1...9.64..64..3.. 11.3 34
98.76.5..5.7..4.9..3..958..2......593.59....1.9..5.3....9.3..65..35..9...5...9.38 11.3 34
98.7..6..5.....7.8..7.8..9.84...3..7..9.78.2.7.241..8..7..9.8.1.9.8...7...8..72.9 11.3 34
98.7..6....7.56..8....89.4769...87...78....63..267..8.75..6.8...2.8...7.8.1..7... 11.3 34
98.76.5..756..4.8...4..8.6..6.84..7...763...88....76...2..7.8.6..8..6.3.6...8.1.. 11.3 34
98.7..6..7...9......5..4.7949..537....74...93....794..2....79.6.7.9..1.4..9.4..37 11.3 34
98.7..6.575.6.......6.85.7.6...78.5...546...7.7.53.2...6..57.9...73..5.15.....7.. 11.3 34
98.76.5.447.........5.49.7.5...74.8...76..4.3.4....7...5..97.4...42.5..77..4.61.. 11.3 34
98.7..6.55.76..4....3.5..877..4..5...5...2.74....75..14...97.5..7.5...4...5.467.. 11.3 34
98.7..6..56..9..7...7..6.9.7..4...36..867.9....6.538.7.2...7.69..9.6.7..67......1 11.3 34
98.76.5..7.5.4.6....35.8.7.5...7.4...7.4.5..2...1...574....7.95.5...47....7.5..46 11.3 34
98.76.5..7.5.4.6....35.8.7.4....7.95.5...47....7.5..46...2...575...7.4...7.4.5..1 11.3 34
98.76.5.474.........5.48.7.5...87.4..7.4.63....42.5..7.5..74.9...76..4.14.....7.. 11.3 34
98.7..6..57..6...9..6..97..4....697.69.....3...79....6.6..2.19...569...7..98.1.65 11.3 34
98.76....54.8..7....7..5.988....7.59.75.8.3.....25.8.77.....18..5...8.74..8.7...3 11.3 34
98.7..6.557.6.......6.95.7.6...57.8..5....7....74..5.3.6..79.5...526...77..54.1.. 11.3 34
98.76.5..756..4..8..4..8..66...8.3...2..7.86...8..6..1..761..8..6.84...78....76.. 11.3 34
9876..5..64..9..87..57..6..3...67..8.7..2...6..61..7...6..7.8....8..6.717..8...65 11.3 34
98.7..6....7..8.95...94.7.87..8....6.9...7.83..8...27..39.7.8...7518....8....9.57 11.3 34
98.76.4..5...849...47..3.8.8...4.5...548....2.1.....484....8.59..8.5..64..54..8.. 11.3 34
98.76....54.9....7..7..498.7.4.9...3.9...784....24.7.94....957..7.....91..9.7.3.. 11.3 34
98.76.5..756..4.8...4..8.6.8....76....763...8.6.84..7.6...8.2...1..7.8.6..8..6.3. 11.3 34
98.76.5..756..4.8...4..8.6.8....76...6.84..7...763...86...8.2...1..7.8.6..8..6.3. 11.3 34
98.76.5..7.5.4.6....35.8..75...7.4...7.4.5.2....1...754....7.59.5...47....7.5..64 11.3 34
98.7..6..7...9......5..4.7949..537....74...93....794..2....79.6..9.4..37.7.9..1.4 11.3 34
98.76.5.475.........4.58.7.4...87.5..7.5.6..3..52.47...4..75.9...76..1.55.......7 11.3 34
98.76....7..5..9.6..6.49.7.6...5.7.....3.7.6...7.26..916.....47.7.6...92..9.746.. 11.3 34
98.76.5..756..4..8..4..8..68....76....763..8..6.84...76...8.2...1..7.86...8..6..3 11.3 34
98.76.5..4...859...57..3.8.5....8.49..8.4..65..45..8...2.....58.458....18...5.4.. 11.3 34
98.7..6..56..9..7...76....94..9.6..779...3.....6.7.9...7.2.9.1...5.6.79...9.578.2 11.3 34
98.76.5..756..4.8...4..8.6.8....76...6.84..7...763...8.2..7.8.6..8..6.3.6...8.1.. 11.3 34
98.7..6..56..9..7...76....94..9.6..7..6.7.9..79...3....7.2.9.1...9.578.2..5.6.79. 11.3 34
98.7..6....7.56.9.....98.7486...97....367...97.9....2657..6.9..3..9....7.91..7... 11.3 34
98.7..6..7.5....9..4..9...763.9...7...4.7.9.6.97.62...37.6....9....1973...9..786. 11.3 34
98.76....7..54.9....4..9.6734....7.9..9.7..46.7.9.42...9...7..2..74...95....9.17. 11.3 34
98.7..6.55.76..4....3.5..877..4..5......75..2.5...1.744...97.5..7.5...4...5.467.. 11.3 34
98.7..6..7.5....9..4..9...763.9...7..97.62.....4.7.9.637.6....9....1973...9..786. 11.3 34
98..6.5..7..9.4..8.3485.9...9..8.6....86.9.2....1...89.6...8.938...9..56..9..68.. 11.3 34
98.7..6..56..4...77.3..6.9.3.6..79...9.....76.7.69..23.5.16.7..6.7..2..9....7..6. 11.3 34
98.7..6.557.6.......6.95.7.7..54.3...6..79.5...526...76...57.8..5....7....74..5.1 11.3 34
9876..4..6..4..9...54.89.7.8...93..4.4.8...9...9.468....2..8.494..9..3...9...4.1. 11.3 34
9876..5..6..5..9...45.89.7.8...93..5.5.8...9...9.568..5..9..3....2..8.59.9...5.1. 11.3 34
98.76.5..5.7..4.9..3..958..3.59....21......59.9..5.3....35..9....9.3..65.5...9.38 11.3 34
98.76.4..5...849...47..3.8.8...4.5...2.....48.548....14....8.59..54..8....8.5..64 11.3 34
98.7..6.557.6.......6.95.7.6...57.8...74..5.3.5....7...6..79.5...526...77..54.1.. 11.3 34
9876..5..6..5..9...45.89.7.8...93..5..9.568...5.8...9.5..9..3...9...5.2...1..8.59 11.3 34
98.7..6.55.76..4....3..5.877..4..5......57..2.5..1..744...79.5..7.5...4...5.647.. 11.3 34
98.76.5..7.5.4.6....35.8.7.4....7.95.5...47....7.5..46.7.4.5..2...1...575...7.4.. 11.3 34
98.7..6..56..9..7...7..6.9.7..4...36..867.9....6.538.767......2.1...7.69..9.6.7.. 11.3 34
98.76.5..7.5.4.6....35.8..75...7.4.....2...75.7.4.5.1.4....7.59.5...47....7.5..64 11.3 34
98.76.5..7.5.4.6....35.8.7.5...7.4.....2...57.7.4.5..14....7.95.5...47....7.5..46 11.3 34
98.76.5..756..4.8...4..8.6.8....76...6.84..7...763...8.2..7.8.66...8.1....8..6.3. 11.3 34
98.76.5.447.........5.49.7.7..4.63...5..97.4...42.5..75...74.8...76..4.1.4....7.. 11.3 34
98.76.5..4...859...57..3.8.5....8.49..8.4..65..45..8...458....2.1.....588...5.4.. 11.3 34
98.76.5..7.5.4.6....35.8..75...7.4...7.4.5.2....1...754....7.59..7.5..64.5...47.. 11.3 34
98.7.46....5.96.4..463..7..6...3.4...3..4..86..46...374...63..2.....1.64.6.4..3.. 11.3 34
98.76.3..7.3.5.6....43.8.7.5....7.93.3...57....7.3..56...2...373...7.5...7.5.3..1 11.3 34
98.7..6..5..68......6..9..884..6..3...9..2.866.2..84.1.6.81...9..829..6..9...68.. 11.3 34
98.76.5..7.5.4.6....35.8.7.5...7.4.....2...57.7.4.5..14....7.95..7.5..46.5...47.. 11.3 34
98.7..6.575.6.......6.85.7.6...78.5..7.54.3....526...7.6..57.9...74..5.15.....7.. 11.3 34
98.76.5..5.7..4.9..3..958..2......59.9..5.3..3.59....1..35..9....9.3..65.5...9.38 11.3 34
98.7..6.55.76..4....3.5..874...97.5..7.5...4...5.467...5...2.747..4..5......75..1 11.3 34
98.7..6..75..6..8...6..87..86......4.3...68.7..78...6.6...2.1.8..568..7...89.1.56 11.3 34
98.7.46....5.96.4..463..7..6...3.4...3..4..86..46...374...63..2.6.4..3.......1.64 11.3 34
98.76....54.9..7....7..4.987.4.9.3...9...7.84...24.97.4....9.57.7....1.9..9.7..3. 11.3 34
9876..4..6..4..9...54.89.7.8...93..4..9.468...4.8...9.4..9..3...9...4.2...1..8.49 11.3 34
98.76.5..4...859...57..3.8.8...5.4...458....2.1.....585....8.49..45..8....8.4..65 11.3 34
98.7..6..7.5....9..4...9..763.9...7...4..79.6.97.26...37.6....9..9.7.86.....9173. 11.3 34
98.7..6..75...6.8...6.8.7..86......4.3..6.8.7..78...6...56.8.7...892..566....12.8 11.3 34
98.7..6.55.76..4....3.5..874...97.5..7.5...4...5.467..7..4..5......75..2.5...1.74 11.3 34
98.7..6..5..6.8.....6.9..8..6.8.4.9...83.9..6.9..6.8..82...6..1..9.3..686.3.8.24. 11.3 34
98.76....53.9..7....7..3.983....9.57.7....2.9..9.7..1..9...7.837.3.9.1.....43.97. 11.3 34
98.76.5..4...859...57..3.8.8...5.4...2.....58.458....15....8.49..8.4..65..45..8.. 11.3 34
98.76.5..4...859...57..3.8.8...5.4...458....2.1.....585....8.49..8.4..65..45..8.. 11.3 34
98.76....7..54.9....4..9.6734....7.9..9.7..46.7.9.42....74...95....9.17..9...7..2 11.3 34
98.7..6....7.9..85...8.47.98...7..93.7.9....6..9...27.3.8..79...9..8..577.51.9... 11.3 34
98.76.5..4...859...57..3.8.8...5.4...2.....58.458....15....8.49..45..8....8.4..65 11.3 34
98.7..6.575.6.......6.85.7.6...78.5...546...7.7.53.2..5.....7...6..57.9...73..5.1 11.3 34
98.7..6.55.76..4....3..5.877..4..5...5..2..74....57..14...79.5..7.5...4...5.647.. 11.3 34
98.7..6.575.6.......6.85.7.6...78.5..7.54.3....526...75.....7...6..57.9...74..5.1 11.3 34
98.76.4..5...849...47..3.8.8...4.5...2.....48.548....14....8.59..8.5..64..54..8.. 11.3 34
9847..6..56..94.8...76..4..6..9...4..4..679....9.43..6.2...9.64..64..3..4....6.1. 11.3 34
98.76.5..7.5.4.6....35.8.7.5...7.4...7.4.5..2...1...574....7.95..7.5..46.5...47.. 11.3 34
98.76.5..7.5.4.6....35.8..75...7.4.....2...75.7.4.5.1.4....7.59..7.5..64.5...47.. 11.3 34
98.7..6....7.56.9.....98.7486...97..7.9....36..267...957..6.9..2..9....7.91..7... 11.3 34
98.76....7..54.9....4..9.6734....7.9.7.9.42....9.7..46.9...7..2..74...95....9.17. 11.3 34
9847..6..56..94.8...76..4..6..9...4...9.43..6.4..679..4....6.2..1...9.64..64..3.. 11.3 34
9876..5..64..9..87..57..6..3...67..8.7..2...6..61..7....8..6.717..8...65.6..7.8.. 11.3 34
98.76.5..756..4.8...4..8.6.6...8.3...2..7.8.6..8..6.1..6.84..7...761...88....76.. 11.3 34
98.7..6..57.64......6..9.757....6.59.69.7.3.....29.76.6.....1.7.9...7.86..7.6..3. 11.3 34
9876..5..6..5..9...54.79.8.7...93..5.9..567....57...9..2...7.595..9..3....9..5.1. 11.3 34
98.76.5..756..4.8...4..8.6.6...8.3...2..7.8.6..8..6.1...761...8.6.84..7.8....76.. 11.3 34
98.76....7..54..9...4..96.734.....79.7.9.4.2...9.7.4.6..74..9.5....9.71..9...7..2 11.3 34
98.76.5.474.........5.48.7.5...87.4...43.5..7.7.4.62...5..74.9...76..4.14.....7.. 11.3 34
98.7..6..5..6.8.....6.9..8.84...6..3..9.2..686.2.8.41..6.8.1.9...82.9..6.9..6.8.. 11.3 34
999_Springs

Posts: 591
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

### Re: Maximum number of clues for a given SE rating

That's ok, I can at least claim 11.5:

11.5 | 33 | ........1.....2..3..4....5..6.57..8.54.6.87.28.7.24..5.86.45...42.8.75..7.526....
........1.....2..3..4....5.....678.2..8..4....6..5..7..764.....42..785..8.562....;11.50;1.20;1.20;mith;;;26
........1.....2..3..4....5...6..4....4..786.2.7..5..8..2..865...874.....6.572....;11.50;1.20;1.20;mith;;;26
........1.....2.3....45.2.6.12.6.7.363.....288.7.......63....8.17.......2.8..71..;11.50;1.20;1.20;mith;;;27
........1.....2.3....45.2.6..1.......72..81..63.....78.87......12..6.8.33.6....27;11.50;1.20;1.20;mith;;;27
........1.....2.3....45.2.6.12.6.7.363......88.7.......63....8.17......22.8..71..;11.50;1.20;1.20;mith;;;27 (only expands to 31 with singles)
........1.....2.3....45.2.6..1.....2.72..81..63.....78.87......12..6.8.33.6.....7;11.50;1.20;1.20;mith;;;27 (only expands to 31 with singles)

(I can tie 11.4 and 11.3 as well, with 33 and 34 respectively - at least, the minimals they were generated from are new, I'll check the maxed versions at some point to see if they are truly new. 29 is still my high for 11.6, sadly.)
mith

Posts: 950
Joined: 14 July 2020

### Re: Maximum number of clues for a given SE rating

The 11.4s you gave are all isomorphic, and mine is as well - just some extra minimals that were missing from the database (I've actually been running scripts to expand and then minimize to check for this exact thing, so that's not too surprising):

........1..1..234..3..1.25......4..3.56.31...7..62..1.....8..2..2...3..41.....9..;11.4;1.2;1.2;mith;;;26
........1..2..3.4..4..5.63.....3..14.5...4.7.3.......8.6.3...5.4...67..39...45...;11.4;1.2;1.2;mith;;;26
........1..2..3.4..5.46...........3.47.5..8..8.9..2.5......54....492...55..34..2.;11.4;1.2;1.2;mith;;;26
........1....23.45..56.437...7....8..1..7...49.45......5.......4.1..5..77.2.4..5.;11.4;1.2;1.2;mith;;;27
........1....23.45..56.437...74...8..1..7....9.45......5....4..4.1..5..77.2....5.;11.4;1.2;1.2;mith;;;27

There are three essentially different 11.3s:

.....1..2..3.2..4112.5..6....27.6.15..51.2...71..5.2..27...51..3.12....85.9.1..2. (31)
.....1.23..1.2.4...2.5..61...215...4.1...275.8.5...1.2.5..1.27.1.92.7...2..6.5..1 (67)

A few of my minimals are from the 67 (23 new ones), but the rest are from two new ones:

.......12..1.234..24.1.5.63..2.31.4..7.25...11..84.2....6.12..4.1.....2.92.5..1.. (7 minimals - a relative to the first one above)
.....1..2..3.2..4112.5..6....27.6.15..51.2...71..5.2...312....8.59.1..2.27...51.. (107 minimals - a relative to the second)
mith

Posts: 950
Joined: 14 July 2020

### Re: Maximum number of clues for a given SE rating

I haven't done a new exhaustive search, but the 31c minimal 11.6 allows 4 singles, so 11.6 is now at least 35.
mith

Posts: 950
Joined: 14 July 2020

### Re: Maximum number of clues for a given SE rating

well done mith on finding the 35 clue 11.6:
11.6 | 35 | ........1.....2.3..34..5....41.6..736.34.781.78....6.4.78...1.631..86.4.4.67..38.
your 11.7 from one page earlier in the thread is a new record too, starting with 5 hidden singles:
11.7 | 34 | .....62.1....23.....21.4.....5....62.27.6.18.68....5.7.76....1521....8.65.86.172.
edit: mith just broke Mauricio's 14 year old record for the hardest puzzle with 37 clues:
11.3 | 37 | .3......1....23....24....35.673.4.8.3.2.86...84.27.6.3.76.38...28.74.3.64.3..2.7.

a few weeks ago i asked 1to9only for more details about clue counts in the solving paths for all the patterns game puzzles when certain techniques were applied. i was looking for stuff in the subsets/UR/BUG range because i don't have much of a strategy for those other than "try lots of puzzles and see what happens". thanks to 1to9only for doing this for me. results were a bit disappointing in that all the high clue counts for the subsets were only there to set up a higher rated BUG, rather than solve the puzzle with singles, so no new records were found there. the only record i got was these two new 6.1's. the same puzzle for the 6.2 record also showed up; i'd originally found it as an arkietech's daily puzzle, but it's PG 68 #91 with the digits relabelled

6.1 | 61 | ..2186974947325618618497253....3184.....58....8.249..5129573486.7.862391863914527 (PG 176 #122)
6.1 | 61 | 164852397329617..4875394.6...7168.....2475.....12397..5437269..716983425298541673 (PG 372 #56)

i had a look at some of the 4.9's that were UL6+naked quad to see if i could turn more of them into 5.3's but found nothing from the next 6 puzzles with the most clues other than the two i already found, but i'll keep looking

edit: just remembered this one. it isn't a new record but deserves a place here as an "honourable mention". here is a 46-clue 10.2 by ssxsssxs that has a completely different structure to anything else in that range in this thread, and not based on a 999991110 digit distribution or anything close to that, unlike the dobrichev puzzles. this suggests that there may be a new interesting area to look into for the 8.5+ range that doesn't come from that digit distribution
Code: Select all
`+-------------------+-------------------+-------------------+| 1     2     3     | 78    9     4     | 78    5     6     || 7     456   569   | 18    56    2     | 149   3     489   || 8     456   569   | 17    3     56    | 149   2     479   |+-------------------+-------------------+-------------------+| 9     1     4     | 3     2     8     | 6     7     5     || 6     378   278   | 4     57    15    | 29    18    389   || 5     378   278   | 9     67    16    | 248   148   348   |+-------------------+-------------------+-------------------+| 2     578   578   | 6     4     3     | 78    9     1     || 4     9     1     | 5     8     7     | 3     6     2     || 3     678   678   | 2     1     9     | 5     48    478   |+-------------------+-------------------+-------------------+`
999_Springs

Posts: 591
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

### Re: Maximum number of clues for a given SE rating

Just ran the expander on all of mine 11.2+:

My 11.8s top out at 23
11.7 (34) - ..2.....1.....2.3...1...2451.3.26....678.13..82.73.1...386.....2.6.87..371.2.3... is another, these are the only two expanded puzzles from 26 minimals.
11.6 (35) - six of them, from 22 minimals:
Code: Select all
`..............1..2.13....454.6.7.1.8.718.4...83.16..74.68.174..14.63..8.3.74.8...........1.....2.3...4....5.4.1.26....2718...486.4.71..6.82..71..1287..4674..61.8...............1..2.13....454.6.7.1.883.16..74.718.4....68.174..14.63..8.3.74.8...........1.....2.3...4...25..2678.1..4.7.21...81.4.6..2.4..7861.68.1.4.277.126............1.....2.3...4....5.84..61.7.6.72..81..1278..46.2817...44.1.26...76.4.81..........1.....2.3..34..5....41.6..736.34.781.78....6.4.78...1.631..86.4.4.67..38.`

11.5 (37) - a ton of these:
Code: Select all
`........1....12.3..13.45....34...16.1.74.63.886..31..4.81.6...33.61.48.747....61.........1....12.3..13.45....34...16.1.74.63.886..31..447....61..81.6...33.61.48.7........1....12.3..13.45....34...61.1.74.63.886..31..4.81.6...33.61.48.747....16.........1....12.3..13.45....34...61.1.74.63.886..31..447....16..81.6...33.61.48.7........1....12.3..13.45...1.64.73.8.34...17.87..31..43.71.48.646....71..81.7...3........1....12.3..13.45...1.64.73.8.34...71.87..31..43.71.48.646....17..81.7...3........1....12.3.1.3.45...3.4...16..174.63.868..31..4.361.48.774....61.8.1.6...3........1....12.3.1.3.45...3.4...61..174.63.868..31..4.361.48.774....16.8.1.6...3....2.........1.23.12....45.26.1..7.4.82.7...17.68.2.4.417.2...28.16.4.76.7.4..12....2.........1.23.12....45.26.1..7.4.87.2...17.68.2.4.412.7...28.16.4.76.7.4..12...2..........1.23.12....45.41.26...27.81.4.68.64...12.281...6.16.78.2.44.7.62......2..........1.23.12....45.41.62...27.81.4.68.64...12.281...6.16.78.2.44.7.26.....4.....1.....2.34....4..5...6.24..7.286.741.47.81.....624.817.74..61...8.127..46..4.....1.....2.34....4..5...6.24..7.286.741.74.81.....624.817.47..61...8.127..46.1...6....56..1.23..4.5..164.578...1.681.4...17..65..4.81.47...5.76...4.64.5.8....1...6....56..1.23..4.5.1.64.517..6..678.4...18..65..7.71.486..5.86.....64.5.7....1...6....56..1.23..4.5.1.64.517..6..678.4...18..65..7.71.486..54.6.7...6.85......1...6....56..1.23..4.5.1.64.517..6..678.4...18..65..76.85......71.486..54.6.7....1...6....56..1.23..4.5.1.66.75......81.476..54.6.8....687.4...17..65..84.518..6..3......1..21.3.4..4156...3.17...8.22.4.1.37.38.7...14.73..1.281.8...4..42....1.7.3......1..21.3.4..4156...3.17...8.22.4.1.37.38.7...14.73..1.2812....4.74.8...1...3......1..21.3.4..4156...3.17...8.22.4.1.37.38.7...1412....4.7.73..1.284.8...1...3......1..21.3.4..4156...31.7...4...83..1.2742....1.8.18...7.22.4.1.38.37.8...14.3......1..21.3.4..4156...32.4.1.37..17...8.238.7...14.73..1.281.8...4..42....1.7.3......1..21.3.4..4156...32.4.1.37..17...8.238.7...14.73..1.2812....4.74.8...1...3......1..21.3.4..4156...32.4.1.37..17...8.238.7...141.8...4...73..1.2842....1.7.3......1..21.3.4..4156...32.4.1.37..17...8.238.7...1412....4.7.73..1.284.8...1...3..4......1..2.34.24.3.5.6.4781....1.23.74..38..24..7.73.81.4.2.84.....41.27.....3..4......1..2.34.24.3.5.6.4781....1.23.74..38..24..7.73.81.4.21.47....4.82......3..4......1..2.34.24.3.5.61.23.74...4781....38..24..7.73.81.4.2.84.....41.27.....3..4......1..2.34.24.3.5.61.23.74...4781....38..24..7.73.81.4.21.47....4.82......3..4......1..2.34.24.3.5.61.23.74...4781....38..24..74.82......73.81.4.21.47.....3..4......1..2.34.24.3.5.64.72......83.71.4.21.48.....4871....1.23.84..37..24..8.4......1.61.23..4..54.1.6.1.7...6...841...5765....1.8.18...7.547...8.165.6.1.48..4......1.61.23..4..541..6.5.6..147..17...8.548..7..16.741...581.8...6..65....1.7.4......1.61.23..4..541..6.5.6..147..17...8.548..7..16.741...5815....6.76.8...1...4......1.61.23..4..541..6.5.6..147..17...8.548..7..161.8...6...741...5865....1.7.4..3......1..2.34.23.4.56.1.24.73...3781....48..23.7.3.82......74.81..321.37.....4..3......1..2.34.23.4.56.1.24.73...3781....48..23.7.31.27.....74.81..32.83......4..3......1..2.34.23.4.56.3.72......84.71..321.38.....3871....1.24.83..47..23.8..4..3......1..2.34.23.4.56.31.27.....74.81..32.83......3781....1.24.73..48..23.7..4..3......1..2.34.3..145.63.82.14...1437...872..48....72.83.4.18.42....4..1.7....4..3......1..2.34.3..145.63.82.14...1437...872..48....72.83.4.48.12....1..4.7...1....6...5.6..1.23..4.5..16.1578...46.81.4...74..65..1.576...4.46.5.8...8.1.47...1....6...5.6..1.23..4.5..16.4578...16.81.4...71..65..4.576...4.46.5.8...8.1.47...1....6...5.6..1.23..4.5.1.6.4517..6.6.78.4...81..65..7.586.....46.5.7...7.1.486..1....6...5.6..1.23..4.5.1.6.4517..6.6.78.4...81..65..7.685.....45.6.7...7.1.486..1....6...5.6..1.23..4.5.1.66.78.4....4517..6.81..65..7.586.....46.5.7...7.1.486..1....6...5.6..1.23..4.5.1.66.78.4....4517..6.81..65..7.685.....45.6.7...7.1.486..2.......1.....2.3...4....254.2..6.7..67.482.338.27.....28.643.76.372....74.8.3.622.......1.....2.3...4....254.2..6.7..67.482.338.27.....28.643.774.8.3.626.372....2.......1.....2.3...4....254.2..6.7..67.482.338.27....6.372.....28.643.774.8.3.622.......1.....2.3...4....254.2..6.7..67.482.338.72.....28.643.76.327....74.8.3.622.......1.....2.3...4....254.2..6.7..67.482.338.72.....28.643.774.8.3.626.327....2.......1.....2.3...4....254.2..6.7..67.482.338.72....6.327.....28.643.774.8.3.622..46.15.....12.34..15.32.6.....5..2.52.4.6..7.8.26..5...2.4.61...63..2..2..514.32..46.15.....12.34..15.32.6.....5..2.52.4.6..7.8.26..5...23..6....6.4.21.2..514.33.......1..21.3.4.4.156...31.7...8.2.24.1.37.83.7...14.48...1..21....4.77.3..1.284.......16.1.23..4..541..6.1.7...8.5.56..147.84..7..16.18...6..56....1.77.41...584.......16.1.23..4..541..6.1.7...8.5.56..147.84..7..16.68...1..51....6.77.41...584...3......1..2.342.3.4.56.3.781.....124.73..84..23.7..283.....13.27....7.4.81..34..36.25.....12.34..34.56.1.....4..6.645...2.7.8..6.45....4.51.....534.2.4.2.1.634..36.25.....12.34..34.56.1.....4..6.645...2.7.8..6.45....435.2....5.41..4.2.1.63`

11.4 (37 as well)
11.3 (38):
Code: Select all
`...53..122.3.145.6.5.2.634....35.62..6...2.313.2.614.5..76.3....2......383.1.5.....3..2..1..2..3.4..5..6.23.5.73.6....68.27.5332.5...76.356.8...2.6.753..78.23......3..2..1..2..3.4..5..6.23.52.3...76.68.27.533.75.6....356.8...2.6.753..78.23......3..2..1..2..3.4..5..6.23.52.3...763.75.6....68.27.53.356.8...2.6.753..78.23.....2......1....23.4.....567.21.32.5....5836.12.26..1...3.3568.21.61.5.2...8.2.31..5.2......1....23.4.....567.21.32.5....5836.21.26..1...3.3568.12.61.5.2...8.2.31..5.2......1....23.4.....567.23.12.5....62.1...385.36.12..165.2...2.8.31..553.68.21..2......1....23.4.....567.23.12.5....62.1...385.36.21..165.2...2.8.31..553.68.12..2......1....23.4.....567.23.15.2....62.1...385.36.12..162.5...2.8.31..553.68.21..2......1....23.4.....567.23.15.2....62.1...385.36.21..162.5...2.8.31..553.68.12..2...6..1.6...2.3...4.5.2.64.26...5767.4.5....85.27.64.465.8...25..746..7.826.....2...6..1.6...2.3...4.5.26.4.26...75.85.27.4667.4.5....465.8...25..746..7.826.....2...6..1.6...2.3...4.5.26.4.26...7567.4.5....85.27.46.465.8...25..746..7.826.....2...6..1.6...2.3...4.5.6.24.62...5727.4.5....85.67.24.425.8...65..742..7.862.....2...6..1.6...2.3...4.5.62.4.62...75.85.67.4227.4.5....425.8...65..742..7.862.....2...6..1.6...2.3...4.5.62.4.62...7527.4.5....85.67.42.425.8...65..742..7.862.....5......1....23.45....567..6.12.5....35.1...682.63.15..135.2...26.38.51.5.8.61..2.5......1....23.45....567..6.12.5....35.1...682.63.51..135.2...26.38.15.5.8.61..2.5......1....23.45....567..6.15.2....35.1...682.63.15..132.5...26.38.51.5.8.61..2.5......1....23.45....567..6.15.2....35.1...682.63.51..132.5...26.38.15.5.8.61..22.......1....23.4.....567.2.132.5...5.836.12.62..1...3.82.31..516.5.2...3.568.21.2.......1....23.4.....567.2.132.5...5.836.21.62..1...3.82.31..516.5.2...3.568.12.2....6..16....2.3...4.5.26..2678....5.72.46..84..65....5.62..7446.5.7...7.2.48.562....6..16....2.3...4.5.26..2678....5.72.46..84..65...45.6.7....6.52..747.2.48.562....6..16....2.3...4.5.26.46.5.7....5.62..747.2.48.56.2678....5.72.46..84..65...2....6..16....2.3...4.5.6.2.264...5774.2.5...8.5.67.24.7862....4.25.8...56..742..2....6..16....2.3...4.5.62..2.56..7445.2.7...7.6.48.52.6278....5.76.42..84..25...2....6..16....2.3...4.5.62..264...7574.2.5...8.5.67.42.7862....4.25.8...56..742..2....6..16....2.3...4.5.62.42.5.7....5.26..747.6.48.52.6278....5.76.42..84..25...`

11.2 (also 38)

I'll run some lower ratings later.
mith

Posts: 950
Joined: 14 July 2020

### Re: Maximum number of clues for a given SE rating

11.1 (39)
11.0 (40)
10.9 (41) - ...45..616...2354...56.1..2.5...62..26.5...1.789142635...3.4.56.3..65.2.5.62....3
10.8 (40) - ....246.16.2..345..1456..32..6.3152..2.45..635.32.61.4..7...2.6..86.2...26.....4. (among others)
10.7 (40)
10.6 (40)
10.5 (40)
10.4-10.2 (48)

The 48 clue puzzles are exclusively from 19c minimals - it has the least restrictive first filter, so all the higher clue counts are throwing out these puzzles. They have a 999991110 distribution (where the singletons are in different houses). 20c has some 46 clue 10.1 (skfr) puzzles, with a somewhat less restricted than normal filter. I'd probably need to relax my filters for other counts to get higher rated 42+ clue puzzles.
mith

Posts: 950
Joined: 14 July 2020

### Re: Maximum number of clues for a given SE rating

11.8 is up to 29c now: ........1......23......4..5...26.....23.784..86.4.3....7863....34.8.2...6.2.47.8. (two minimals, 26c and 27c)
mith

Posts: 950
Joined: 14 July 2020

### Re: Maximum number of clues for a given SE rating

11.8 makes a big jump to 32c (with 29c and 30c minimals)
mith

Posts: 950
Joined: 14 July 2020

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