Max number of clues 2

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

Postby ravel » Mon Jul 02, 2007 2:57 pm

It seems. that last time i even was lucky to find 12 37's in 7 days. This time in a week i only found these 4 lonely 37's:
Code: Select all
1.34.678.4........698.3714...46.3.5.......4..935..461.3.1.6587.5....8..1.89....6.
1.3456..94....9.36..9......2.8.613.43..5.8....1..4...8....9....8.2.14.939.18356.2
12..5..89.....9......2.7.51.6189..47.7..64192.4.....68..4.2.....16.48.25..2.7..14
12.4.67.94..1.9..6.96372..4.4...73...618.3..7.3.9.....3..7.16.2.1.2.8.73..2......


gsf,

unlike for low clue search, for max clues generation only minimal puzzles are of interest (this is one point, why it is harder). Is there an option for that ?
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Postby coloin » Mon Jul 02, 2007 7:07 pm

Well done, Yes I agree it is very much harder.......

gsf is on the beach for 2 weeks so he may have more thoughts on his return.
I think the latest program from gsf adds ALL the clues in a +2 as opposed to a somehow selected few as it was before - so my search for a minimal stepup takes much longer.

As you say the minimality issue is not addressed with gsfs , it has to be done as a second stage.

I have mentioned to gsf that I think the probability is very high that out there there is a grid with a 38. Also the 37s that we have are far from "full" in terms of number of grid solution per clue.

The grid with the most likely prospect is the PT grid as RW mentioned.
Code: Select all
123456789457189326689327154231645897745891632896732541318264975574918263962573418

However although I struggled initially to find a 34 in this grid I have now easily with a {-0+2} search option managed to find over 7000 34s and well over 100 35s......which isnt surprising in itself, except that there appears to be no sign of the 34s or 35s tailing off - spreading out throughout the regions of the grid.

A "region" in a grid might well be a maximal pseudopuzzle [with 2 solutions] plus one [solving] clue.

The maximal pseudopuzzle that I have in mind might have 41 clues with the unavoidable set associated with the pseudopuzzle containing 40 clues in this instance.

The resultant region [in effect a non-minimal puzzle] will have 41+1 =42 clues.

These 42 clues [if taken from one of the above 34s or 35s - or other 36s or 37s] we know will have a large minimal puzzle within.

This might be better than a random search [10^9 grids*10^20 regions per grid] !

We might just have to admit defeat on this one !

C
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Postby ronk » Mon Jul 02, 2007 8:01 pm

coloin wrote:I think the latest program from gsf adds ALL the clues in a +2 as opposed to a somehow selected few as it was before - so my search for a minimal stepup takes much longer.

As you say the minimality issue is not addressed with gsfs , it has to be done as a second stage.

I don't know whether it would be faster, but I think you can add the minimal 37 clue requirement with ... -m1 -e"C==37"
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Postby ravel » Mon Jul 02, 2007 8:39 pm

ronk wrote:... -m1 -e"C==37"
Thanks, Ron, i will try it in the next days (compared to my non optimized program).

When i look at Ocean's (almost) not biased puzzle distribution from here:
Ocean wrote:
Code: Select all
#
# Distribution of minimal puzzles per grid, as calculated from the sample set.
# Average based on 10000 random grids, one random path per grid.
#
           Minimal Puzzles
Clues  Percentage     Counts
>30   ???        %
 29   7.01864390 %   4,44E+14
 28  29.00737012 %   1,84E+15
 27  41.60557541 %   2,63E+15
 26  18.85143698 %   1,19E+15
 25   3.30430984 %   2,09E+14
 24   0.20779917 %   1,31E+13
 23   0.00483095 %   3,06E+11
 22   0.00003352 %   2,12E+09
 21   0.00000011 %   6,77E+06
<21  <0.0000001  %
#

It seems that the number of minimal puzzles above 27 is decreasing faster than below 27 (no 30's listed). On the other side in my test i needed about 1000 18's for one 17 with 2off/1on, and i have about 1500 36's, from which i found 16 37's with 1off/2on and 2off/2on for the 37's (no statistical relevance, of course).
So i start to believe that there are much more 17's than 37's, but i still see a chance for a 38 clue.
Only the off/on method to find 37's is all but effective (more a patience training).
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Postby ravel » Tue Jul 03, 2007 10:57 am

ronk wrote:... -m1 -e"C==37"
Dont use this option. In the time my program found 2 37's and 44 new 36's (from a list with 39 36's), -goc{-1+1} -m1 -e"C==36" only gave me 2 36's.
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Postby ravel » Fri Jul 06, 2007 11:31 am

Some more 37's.
I think, this one is the hardest so far with ER 8.8:
Code: Select all
.2345.7894.7.8.....9.3......49578.6....63.9.8..6....7...284569..6.79382.....6....
This one is very nice to solve (x,xy,xyz and W[or Y] wings).
Code: Select all
1..45..8.4.718...38..3271.427.63.4.53...7..26......3...1......2..271....78.26.5.1


Here is the whole list of known 37's:
Coloin Fri Jun 08, 2007
..34....945..8.2..8.932.4..28.713...3....21.....8.....54..3..9.732.9854.9.85.4.2.
..34....945..8.2..8.932.4..28.713...3....21.....8.....54.23..9.73..9854.9.85.4.2.
..34....945..8.2..8.932.4.528.713...3....21.....8.....54..3..9.732.985..9.85.4.2.
..34....945..8.2..8.932.4.528.713...3....21.....8.....54.23..9.73..985..9.85.4.2.
.234....945..8.2..8.93..4..28.713...3....21.....8.....54..3..9.732.9854.9.85.4.2.
.234....945..8.2..8.93..4..28.713...3....21.....8.....54.23..9.73..9854.9.85.4.2.
.234....945..8.2..8.93..4.528.713...3....21.....8.....54..3..9.732.985..9.85.4.2.
.234....945..8.2..8.93..4.528.713...3....21.....8.....54.23..9.73..985..9.85.4.2.
Havard Fri Jun 08, 2007
.2.45...9.5..89.3...92.3..42...98.45..53.29.89.8.4132...6..45..........3....35461
.2.45...9.5..89.3...92.3..42...98.4...53.29.89.854132...6..45..........3....35461
.2.4....9.5..89.3...92.3.542...98.45..53.29.89.8.4132...6..45..........3....35461
.2.4....9.5..89.3...92.3.542...98.4...53.29.89.854132...6..45..........3....35461
.2.45...9.5..89.3...92.3..42...98.45.98.4132...53.29.8..6..45..........3....35461
.2.4....9.5..89.3...92.3.542...98.45.98.4132...53.29.8..6..45..........3....35461
.2.45...9.5..89.3...92.3..42...98.4..9854132...53.29.8..6..45..........3....35461
.2.4....9.5..89.3...92.3.542...98.4..9854132...53.29.8..6..45..........3....35461
Havard Mon Jun 11, 2007
.2345.789....8..3...9..25.4....9.8....18.4973.......423...784.5..52...98.9.54.32.
.2345.789....8..3...9..25.4....9.8....18.4973.......423..9784.5..52....8.9.54.32.
..3......45..8.2...8..23.45.148....636...15..59863.41.63..98.....5.1..6.94136....
..3......45..8.2...8..23.45.148....636...15..59863..1.63..98..4..5.1..6.94136....
1..4.67....6......78.1....4.175...9.69.3.1..58.596.4..37169...85.8..39..96...5..7
...4567.945.7..1..7........2.......353.6.291..673...2.34.56729.6.293.4.....2.43..
...4567.94..7..1..7........2.......353.6.291..673...2.34.56729.6.293.4....52.43..
Coloin Fri Jun 15, 2007
..3......45..8.2...8..23..5.148....636...15..59863.41.63..98..4..5.1..6.94136....
..3......45..8.2...8..23..5.148....636...15..59863.41.63..98..48.5.1..6..4136....
..3......45..8.2...8..23..5.148....636...15..59863.41.63..981..8.5.1..6..4136....
ravel Sat Jun 16, 2007
12.4.6...4571.92.6....27..121.6....88.6..2...9758.46.2....4.9..59....1.47..9.1...
...45.7...571892.6.....7..5....1.8.4.8.....6..6489.....759614.88..54.6.7.4..7..51
...45.7...57189..6.....7..5....1.8.4.8.....6..6489...3.759614.88..54.6.7.4..7..51
...45.7...571892.6.....7..5....1.8.4.8.....6..64.9.....759614.88..54.6.7.4..78.51
...45.7...57189..6.....7..5....1.8.4.8.....6..64.9...3.759614.88..54.6.7.4..78.51
.........4.7...2.66..72.5..2.893.4..37...8..296427.8.3.3.......74659.3.88.23..6.5
1.3456.89.5.1.9.36..9...1.......5.98..68.4...8.....6..3.1548.625.29.1..3....32.1.
.2.......4.7..92.6..9..7.412.8....65.75...4.89468.5.27.6.......7.4....128.2.71654
ravel Sun Jun 17, 2007
12.4.67..4.71.9....6972.1..2.69..45..4.......9..2.561..3.......6.23...7.7945.236.
12.4.67..4.71.9....6972.1..2.69..45..........9..24561..3.......6.23...7.7945.236.
ravel Mon Jul .2, 2007
1.34.678.4........698.3714...46.3.5.......4..935..461.3.1.6587.5....8..1.89....6.
1.3456..94....9.36..9......2.8.613.43..5.8....1..4...8....9....8.2.14.939.18356.2
12..5..89.....9......2.7.51.6189..47.7..64192.4.....68..4.2.....16.48.25..2.7..14
12.4.67.94..1.9..6.96372..4.4...73...618.3..7.3.9.....3..7.16.2.1.2.8.73..2......
ravel Fri Jul 06, 2007
.2345.7894.7.8.....9.3......49578.6....63.9.8..6....7...284569..6.79382.....6....
1..45..8.4.718...38..3271.427.63.4.53...7..26......3...1......2..271....78.26.5.1
1..4.6..9..7..9.36..973.145.3.5.....5..9...1..9136..523.42.5.61.156...24....4....
1.34.678.4........689.3714...46.3.5.......4..935..461.3.1.6587.5....8..1.98....6.
1.34.6..9..7..9.36..973.145...5....75..9...1.7.136..523.4..5.61.156...24....4....
1.34.678.4........689.3714...46.3.........4..935..461.3.196587.5....8..1.98....6.
12.4.67.94..1.9..6.69372..4.4...73...918.3..7.3.6.....3..7.19.2..2.......1.2.8.73
12.4.67.94..1....66..72314.2.63.549..3.2946........3..3.25.79.........7.7....25.3
.....6....5.18.....68.7251..456......81.4795.....1.4...9476..25516.24.9..729...4.
1234..7.94....9......23...42985.34.73719.48.5.4.........2...9..71.392..8.3.8...7.
.2..5....45..891.2.8.2..5...349.78.557...8293..8..54.73.........4..923.1..2..39.4
.23.....94...89.....92371.42.58439.1....9....9.4712..5342.71..8.....84......2..13
......7...571.92.6..97.2.15.159..6.8.98.1.........8..1.368...2...239..679712..8.3
.2....7.94.7..9.3..892.3.54.......1..14.38927.98.12.43....27..1.42..1.75..13.....
.2345.7894.7.8..3..9........49578.6....63.9.8..6....7...284569..6.79382.....6....
.2......94.7..9.3..89273.54.......1..14.38927.98.12.43....27..1.42..1.75..13.....
.....6....571...366..2.7514...7..1.33...2..5.57.8...427.63.84258.56.2.71.......6.
.....6....571...366..2.7514...7..1..3...2..5.57.8.3.427.63.84258.56.2.71.......6.
.2......94.7..9.3..8.273.54.......1..14.38927.98.12.43....27..1.42..1375..13.....
.2......94.7..9.3..89273.54.......1..14.38927.98.12.43....27..1.4...1375..13.....
.2....7.94.7..9.3..8.2.3.54.......1..14.38927.98.12.43....27..1.42..1375..13.....
.2....7.94.7..9.3..892.3.54.......1..14.38927.98.12.43....27..1.4...1375..13.....
1.3.567..4571..2.6........12.456.8..37....6....57...235426.13.87.68..1.2..1......


[Edit: removed an equivalent puzzle]

So after the grid where Coloin found the first 8 37's (its neither MC nor Pt?) this one now is the next best with 6:
Code: Select all
123456789457189236689327541214563897378942615965718423542691378796834152831275964
Last edited by ravel on Fri Jul 06, 2007 10:28 am, edited 1 time in total.
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Postby JPF » Fri Jul 06, 2007 1:27 pm

Interesting to note that there are no singles.
4.4<=ER<=8.8 is correct.

There 2 are equivalent :
Code: Select all
120406000457109206609027001210600708006002000975804602000000000590000107700901000
120056789050109206000072510210037698000001002930020150000000000590000860000065900

JPF
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Postby ravel » Fri Jul 06, 2007 2:30 pm

JPF wrote:There 2 are equivalent :
Code: Select all
120406000457109206609027001210600708006002000975804602000000000590000107700901000
120056789050109206000072510210037698000001002930020150000000000590000860000065900

Thanks JPF,

the first one was not canonicalized, i removed it.
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Postby ravel » Fri Jul 06, 2007 7:41 pm

Since i cannot block my notebook (and sometimes my PC) all the time, i hope that others will join and continue the search for 37's. Here is a more detailed description of my method. I am very sure that much can be improved:

Part 1: Get some 35's with 1off/2on.
Just for fun i started with a 17 clue, more seriously with 94 randomly generated 28's (6 ot the 100 were 29's), this only took an hour. Depending on the number of clues i only took a part (randomly chosen) of the generated puzzles to continue. Up to 32 clues you get more than you need. So for each step i defined a percentage of input lines to take. At the end i had about 15 35's (both times). Of course equivalents have to be eliminated. For this i used a batch file calling gsf's program to canonicalize and the unix commands sort, uniq and grep (and at the end calling the search program for n+1 clues).

Part 2: Get some 36's with 2off/2on and 1off/2on
With 2off/2on slowly, but always i got more 35's. With about 100 i started to search for 36's. When doing the 1off/2on i also saved the minimal 1off/1on puzzles for later use. I continued, until i had about 30 36's (needed about 60 35's for one).

Part 3: Get a 37
Same procedure as in part 2, but it takes longer.

Part 4: Get more from a 37
2off/2on for the 37's. Here i also save minmal 2off/1ons (new 36's) for later use.

The off/on searches for parts 2-4 are automized in the sense, that after an input file is worked through the search is continued with the new found puzzles. The 1off/2on for 36's and 2off/2on for 37's stops, when nothing more can be found. The 2off/2on for 36's is killed by me manually, when i have found enough.

I now have a stock of about 2500 36's, more than 300 new ones for 2off/2on search. Before a new 2off/2on i define a percentage, for how much it should do it (like in step one). This way i expect not to run out of 36's for a long time.
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Postby coloin » Sat Jul 07, 2007 7:04 pm

Very good..

We might just chance on our 38 if we keep this up !

I found over 100 36s in my original grid with 8 37s.

Gsfs program throws up so many puzzles it is extremely difficult to go up a level. Well done for sorting it.

The Pt grid might seem a good grid to look at - except, as with grids with 17s it is fairly difficult to pinpoint puzzles in individual grids.

It was possible with grids with a high density of 17s in a particular region - but even then it was difficult to [statistically] highlight individual clues. I think the background noise of other puzzles will be even more pronounced in max clue puzzles.

dukuso wrote a program to do this which was partially effective
However as oceans data demonstrate - generating, by random deletion of clues from a region in a grid, max clue puzzles is progressivly more difficult.

I have loads of 35s in the Pt grid - and no way of singling out the region which may have 36s or higher...........

C
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Postby coloin » Fri Jul 13, 2007 11:07 pm

I looked back at some old data on number of clues in minimal puzzles - generated by randomly removing clues from a specific full valid grid. Here are the average puzzle size with the size distribution of 1M minimal puzzles, in a random puzzle and others selected.

This, because of a statistical bias tends to preferentially give puzzles with approx 1 clue less on average.
Code: Select all
Ran6         Coloin37      Havard37        MC             PT           
24.5         24.83         24.80           25.71          25.56   
                                                                     
                                                                       
18 0         18  0         18  0           18 0           18  0       
19 0         19  0         19  0           19 0           19  0       
20 53        20  8         20  8           20 5           20  0       
21 2281      21  409       21  489         21 56          21  9       
22 33020     22  11093     22  12231       22 1797        22  1051     
23 169240    23  93587     23  97379       23 21631       23  22174   
24 340913    24  281228    24  284695      24 116439      24  137344   
25 299993    25  351640    25  348769      25 287167      25  323361   
26 124899    26  198947    26  195332      26 330392      26  324568   
27 26439     27  54898     27  53222       27 184541      27  152286   
28 2966      28  7571      28  7338        28 50751       28  35032   
29 190       29  587       29  518         39 6735        29  3931     
30 6         30  31        30  19          30 466         30  239     
31 0         31  0         31  0           31 20          31  5       
32 0         32  1         32  0           32 0           32  0   

Not as dramatic as I had hoped, however the 32 which "happened" to be produced was more similar to our 37s than could be expected.
Code: Select all
coloin37
123456789457189236869327415285713964374962158691845372546231897732698541918574623
..34....945..8.2..8.932.4..28.713...3....21.....8.....54..3..9.732.9854.9.85.4.2.
..34....945..8.2..8.932.4..28.713...3....21.....8.....54.23..9.73..9854.9.85.4.2.
..34....945..8.2..8.932.4.528.713...3....21.....8.....54..3..9.732.985..9.85.4.2.
..34....945..8.2..8.932.4.528.713...3....21.....8.....54.23..9.73..985..9.85.4.2.
.234....945..8.2..8.93..4..28.713...3....21.....8.....54..3..9.732.9854.9.85.4.2.
.234....945..8.2..8.93..4..28.713...3....21.....8.....54.23..9.73..9854.9.85.4.2.
.234....945..8.2..8.93..4.528.713...3....21.....8.....54..3..9.732.985..9.85.4.2.
.234....945..8.2..8.93..4.528.713...3....21.....8.....54.23..9.73..985..9.85.4.2.


.234.6.8..5...9...8.93..4.52..7.........6..5...18.....5...3..9..32..8.4.9.8574.23  random32

I have tried to work out a "factor" for the bias, but have failed.

EDIT I have just found Ocean's explanation here.

The puzzle generation method removes clues to minimality - this must bias against large puzzles.

A 21 clue puzzle will probably be minimal but unlikely to be valid.....
A 27 clue puzzle has had more ways for clues to be removed than a 28 clues puzzle.
A 27 clue puzzle has approx 0.5% chance of being valid although probably not minimal .....
A 35 clue puzzle has a 10% chance of being valid [but very unlikely to be minimal].......

C
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Postby ravel » Tue Jul 17, 2007 9:36 am

Now the harvest time started for what i have seeded weeks ago. In this list of 37's there are 13 puzzles with the same solution grid, some with ER 9.0 and with M2 (singles backdoor size). I am still optimistic for a 38.

ravel Tue Jul 17, 2007
.........45.1.92.66.9.3.5.1..8.4.3..3..9.8...59432.1.8.4.6..8..8.6...9..9358.46.2
.........45.1.92.66.9.3.5.1..8.4.3..3..9.8...59432.1.8.4.69.8..8.6...9...358.46.2
.........45.18..36.8...714..3..1..7.59..73.617..86539..7..9....86....95.94..38.17
.........4571.9..66.93.7.4.2.6...95..7.....2494...26175..9...72794..356...2..54..
......7...5.18.2.668..275.1..48.1..3.3..6....76853...2376.481.58.....3.4.45.1....
.....6......18..368...3.14.28.61739..1.89..27.9...3....7.9....36...7.91.94.361.78
.....6...4.7.8..366.8.7314.2.4.3.918.......2.8.9.2.3..3.276.4.17........946.12.73
.....6..94..1.92.66..32.1.52.8965.13..6.1.......2.3..8..5......8.2.91.549.45.28.1
.....6..94..1.92.66..32.1.52.8965.133.6.1.......2.3..8..5......8.2.9..549.45.28.1
.....6..94.71.9.36.96237.142.53.1.47.7........1.7.53.2..19.3.2...95.2..3..2....9.
...4.....4..18..3686..321..2..3..617.1....49.79..4...3.7...39..6..91..7.98..74361
...4....94.71.9.36.96237.142.53.1.47.7........1.7.53.2..19.3.2...95.2..3..2....9.
...4.6.....7.8....689.72..42.4.1.....61....4797864..21.1.2.....79683..12..2.61..3
...4.6.....7.8....689.72..42.4.1.....61.2..4797864..21.1.......79683..12..2.61..3
...4.6..9..71.9.36..9237.412.83....7.7........147.83.2.468.21.3..16.3.2...2....6.
...4.6..94...8..3.869.23.142.4.37.6..8.....4393.8...273986.1..2.........6.2..8.91
...4.67.9.......3.69..37145.4.3....75...714..7..9.4513....9....8.56.39..96...8351
...4.67.9.....9.3.69..37145.4.3....75...714..7..9.4513.........8.56.39..96...8351
..3...7.9457.89.3......3.5..94.38.17.3.......785.61.93.48.1.975..6.9.....7.8.5.6.
..3..6..94...8..3.869.23.142.4..7.6..8......39368...27....9.....986.1.726.2.78..1
..3..6..94...8..3.869.23.542.4..1.6..8.......9368.4.21.4.......6.2..8..5.98645.12
..34....9.5..8.13..8923.546.........5...2.9..94186.25.3.56..4..61....39..943..6.5
..34...8.45.....36869..31...........586....719.1.7546.3....86..69..37814.1..4..53
..34...8.45.....36869..314..........586....719.1.7546.3....86..69..3781..1..4..53
..34.6..94...8..3.869.23..42.4.35.6..8.....4.9368.4.25...2......98..1..26.2..8.91
..34.6..94...8..3.869.23..42.4.35.6..8...2.4.9368.4.25..........98..1..26.2..8.91
..34.6..94...8..3.869.23.142.4.37.6..8......39..8.4.273986.1..2.........6.2..8.91
..34.6..94...8..3.869.23.142.4.37.6..8.....4.93.8.4.27..........92..8.716.8.7..92
..34.6..94...8..3.869.23.142.4.37.6..8.....439..8...273986.1..2.........6.2..8.91
..34.6..94...8..3.869.23.142.4.37.6..8.....439..8...273986.1..2....9....6.2..8..1
..34.6789...........8..3.6...5..7.91.1.5..8..9876.135.5793.4.18.319...4.8..1.5...
..34.6789...........8..3.6...5..7.91.1.5..87.98.6.135.5793.4.18.319...4.8..1.5...
..345..894.....2..6.9.321.42.6..34.534..2.....9564...256231.9.8.........93..6...1
..345.78.....8..3.7..2..4.62.5.4896............456.82.342.7569.59..34.7...792....
.2......94.7..9.3..9.273.54.......1..14.38927.89.12.43....27..1.42..1375..13.....
.2....7..4.7.892.686.72...4.........64..9.1..9.83146.23.467...1.8.93...77...483..
.2....7..45718.2.68...2...4........5.4569.87.76.8..4..5.296.14.61..7.9....421...7
.2....7..45718.2.68...2...4........5.4569.87.76.8..4..57296.14.61..7.9....421....
.2....7..45718.2.68...2..14........5.4569.87.76.8..4..5.2.6.14.61..7.9....421...7
.2....7..45718.2.68...2..14........5.4569.87.76.8..4..572.6.14.61..7.9....421....
.2....7.94.7..9.3..9.2.3.54.......1..14.38927.89.12.43....27..1.42..1375..13.....
.2...6.8..5718.23..8..725..23......5.7861.92.9.1.2.8...........79.83..5..15.6739.
.2..5.......1.9....9823.41521596.34..4932..6...6.......81.9.6....261.8.4.6.8..15.
.2..5..8..5.78912...........6..94.7...45..6..97526.84..4261.9..5.....4..697.4521.
.2..5..8..5.78912...........6..94.7...457.6..9.526.84..4261.9..5.....4..697.4521.
.2..5..8..5718.2.668.2..5.1.........79.5..162.659..37...6..18...7289.613...3....7
.2..5.78..571..2.668.2..5.1.........79.53.162.659..37...6..18...7289.613...3.....
.2..5.78..5718...668.2..5.1............91.4..79.54.162.7289.61.8..7...24..6.2.8..
.2..5.78..5718...668.2..5.1.6.9..37..........79.5..162.7289.6138..3.......6.218..
.2..5.78..5718...668.2..5.127.89.6138..3...2...6...8............6.9..37.79.53.162
.2..5.78..5718.2.668.2..5.1............91.4..79.54.162.7289.61.8..7....4..6.2.8..
.2..5.78..5718.2.668.2..5.1.........73....162.6531.47.....2.8...7283.6.481...5...
.2..5.78..5718.2.668.2..5.1.6591.37.........579.5..162..6..18..8..3......7.8..61.
.2..5.78..5718.2.668.2..5.127.89.613..6..18.....3......6.9.237.79.53..62.........
.2..5.78..57189......7......75.91.48..48...5...1.4567.....6..94.4291856...6..48..
.2..5.78.4.718.2.68..2..5.4..........4.96.175.6..1.4..57269.84.68.7..9....482....
.2..5.78.45718.2.68..2....4..........4.96.175.6..1.4..57269.84.68.7..9....482....
.2..5678..571..2..6.82.7.1.2....1...3158.264...65...2.5...1487.8.17.54.....3.....
.2.4....9..7..9.3..89273.452.4397.18....2...4..18.4..77.5.32..1..........127.8.53
.2.4....94.7..9.3...9273.452.4397.18....2...4.918.4..77.5..2..1..........127.8.53
.2.4....94.7..9.3..89273.452.439..18....2...4.918.4..77.5..2....3........127.8.53
.2.4....94.7..9.3..89273.452.439..18....2...4.918.4..77.5.32....3........127.8.5.
.2.4..78.4...8...368.2374...6.97.3.1........2...3.267.7..89.1..84...3...91.72483.
.2.4..78.4...8...368.2374..26.97.3.1........2...3..67.7..89.1..84...3...91.72483.
.2.4..78.4...8...368.2374..26.97.3.1........2...3..67.7..89.1.484...3...91.72.83.
.2.4.6..94...8.2..896.32..4..........39..81.768..1.9.334..216....8...4..9628.43.1
.2.4.6..94...8.2..896.325.4..........39..81..68..1.9.334..216....8...4..9628.43.1
.2.4.6.8...7......68.27..4.2..69741.....2.59..1.5.46...94.6285.56.9...7..72..59..
.2.4.6.8...7......68.27..4.2..69741.....2.59..1.5.46...9476285.56.9...7...2..59..
.2.4.678...7......68.2...4.2..6.741...6.2159..1.5.46...94..285.5..9...7.872..59..
.2.4.678...7......68.2...4.2..6.741...6.2159..1.5.46...947.285.5..9...7.8.2..59..
.2.4.678...7......68.2...4.2..69741.....2.59..1.5.46...94.6285.56.9...7..72..59..
.2.4.678...7......68.2...4.2..69741.....2.59..1.5.46...9476285.56.9...7...2..59..
.2.4.678..5718.2.668.2..541.........73.5..1.2.6.31.47.....2.8...728..61481.......
.2.45...9......2..96..2.1.429..3..4.73..94521....7.9.337..6541.5........61.74.3.5
.2.45...9......2..96.32.1.429..3..4.73..94521....7.9.337..6541.5.........1.74.3.5
.2.45...9.....92...6.32.1.429..3..4.73..9452.....7.9.337..6541.5........61.74.3.5
.2.45...94..1..23.....2...523.59..71.7..12.9.9..37.52.36..4..57.........74.93516.
.2.4567.9.57.892.6...........1.9.........4..1874.15.92.12.47.68.8..61.24..6...1.7
.23...7..45..89.368...3...4..........65824...78.59..6257..48.23.4.3....7.38.72.4.
.23...7..45..89.368.6.3...4...........5824...78.59..6257..48.23.4.3....7.38.72.4.
.23...7..45..89.368.6.3...4..........65824...78.59..6257..48.23...3....7.38.72.4.
.23...7..457.89.368.6.3...4..........65824...78.59..625...48.23...3....7.38.72.4.
.23..6...45..89.368.6.3...4...........5.24.7.78.59..6257..48.23.4.3....7.38.72.4.
.23..678.4.7.8..3..98..3..4.............6..27786.2149..31..7.42....3.9.19.4.1237.
.234....9..7..9....89273.412.4.97.58.958.4..7...52......27.8.1.731.42..5.4.......
.234....9..7..9....89273.412.43.7.58.958.4..7...52......27.8.1.731.42..5.4.......
.234....9..7..9....89273.412.4397.58.958.4..7...5.......27.8.1.731.42..5.4.......
.234....94.7..9....89273..12.4.97.58.958.4..7...52..9...27.8.1.731..2..5.4.......
.234..7...5..89.368.6.3...4..........65824...78.59..6257..48.23...3....7.38.72.4.
.234..7...57.89.368.6.3...4..........65824...78.59..625...48.23...3....7.38.72.4.
.234..7894.7....3..9..3...42...7.....695.....7.526.89...6....42.7.34.96.9.462.37.
.234.6..94...8....896.3.5.4.896.51.3..1......63..18..534...1.....8...4.2.628.43.1
.234.67.94.7.892............84.635..5.9.4...2.3...5..83.5.94.2..426389.5..85.....
.234.67.94.7.892............84.635..5.9.4...2.3...5..83.5.9482..4263.9.5..85.....
.234.67.94.7.892............84.635..5.984...2.3...5...3.5.9482..4263.9.5..85.....
.234.67.94.7.892............84.635..5.984...2.3...5..83.5.94.2..4263.9.5..85.....
.234.678...7......68.27..4.23.69.45.....25.9....3..6..3725.89...947628...6.9.....
.2345..89.57...26...92......365.8.47...69483...........6294..787..8.2.9..9.7..42.
.2345..894.....2..6.9.321.4..6..34.534..2.....9564...256231.9.8.........93..6...1
.2345..894.7.8.....9.2....4.........3.5.1..27.195..3.8..2..14.3.3174..929.4.2..71
.2345..894.718.....9.2....4.........3.5....27.195..3.8..2..14.3.3174..929.4.2..71
.2345..894.718.....9.2....4.........3.5.1..27.195..3.8..2...4.3.3174..929.4.2..71
.2345.789.57...26...92......365.8.47...69483...........6294...87..8.2.9..9.7..42.
.2345.7894.7.8.....9.3......49875.6....63.9.8..6....7...254869..6.79382.....6....
.2345.7894.7.8..3..9........49875.6....63.9.8..6....7...254869..6.79382.....6....
.2345678..5..8..63......4..23..41.7..1.6.....846.7513....5...1.562.1..4..81.64...
1.........57..92...9..7251.26.79.45..74...1..9.5.4.....4961732..3..24.7....93.64.
1.........57.8.2.6698.7251..6...895...5.6...1981..5..7.......7..7.8.31.2819.273..
1......8...71...6368.2.7.15.3.7.1...7.58...4.8165.437.3....58265.86.2.34.........
1.....7...57.8.2.6698.7251..6...895...5.6...1981..5..7..........7.8.31.2819.273..
1...5.78..5718.2.668.2..5.127.89.6.3....2.8...1.3......6.91237.79.53.16..........
1...567...57.8.2..68..725.1..5.6.81..6......5891.4567..78.941...........91..2.4.8
1...5678..57.8.2..6...725.1..5.6.81..6......5891.4567..78.941...........91..2.4.8
1..4.....4.71.9.36.96237.142.53.1.47.7......1...7.53.2..19.3.2...95.2..3..2....9.
1..4....94.71.9.36.96237.142.53.1.47.7..........7.53.2..19.3.2...95.2..3..2....9.
1..4....94.71.9.36.96237.142.53.1.47.7........1.7.53.2...9.3.2...95.2..3..2....9.
1..4.6..94..18..3668..3..14...897.65..86....396...3.....4......59..78.4181.9.4.5.
1..4.67.94.71.9.36..............1..48..5.....91.6.8.57341..59.859.8.4.737.89....5
1..4.67.94.71.9.36..9...........1..48..5.....91.6.8.57341..59.85..8.4.737.89....5
1..456.8....1.....68.237.4127.3.1.5...6....1791.7.5.24...6..47.7625.4........3..2
1.3....8.45.....36869..31...........586..4.719.1.7546.3....86..69..37814....4..53
1.3....8.45.....36869..314..........586..4.719.1.7546.3....86..69..3781.....4..53
1.3..678.4.678.1.28....1.6.23..64...6.51.72....1.2.6..3...754.15.43.287..........
1.3.56.8............823.514..4..5.9.3.9.24.58..691...2...59..61....4.92.9.1.62.45
1.3.56.8............823.514..4..5.9.3.9624.58..691...2...59..61....4.92.9.1..2.45
1.3.567.9.5......66.92.7...2...613...159.26.8..65.3..253...89.7...3.....9.17.58..
1.3.567.9.5......66.92.7...2...613..3159.26.8..65....253...89.7...3.....9.17.58..
1.3.567.9.5...92..6.92.7...2...613..3159.26.8..65....25.17..9.3.........93...58.7
1.3.5678..5....26.6.82.7.1.2...61...3158.264...65...2.5.1..48..8..3154...3.......
1.3.5678..5....26.6.82.7.1.2...613...1.8.264...65.3.2.5.13.48..8...154...3.......
1.3.5678..5....26.6.82.7.1.2...613..31.8.264...65...2.5.13.48..8...154...3.......
1.3.5678..57.8.2..6..27.51..1...5....36.1.45...562.1..36..428............7286.34.
1.3.5678.4..18..368....7.14..8745.616..8....7..4.6.85.3.1.74.2.5...1..73.........
1.3.5678.4..18..368....7.142.8745.616..8....7..4.6.85.3.1.74...5...1..73.........
1.34.678..........6.8.371.42.5.7.6..8...245.7..46.5.2.3.25..4..5.1743.6......2..5
1.345...9...........93...1.2...6.94...65...219.524.3.63.2.1.6.8.6183..9289.62....
12......9..7..9....892731..2.139.4.8....249.1..48.1...7.5.328.48...4.....427.85..
12......9..7..9....892731..2.139.4.8..8.249.1..48.1...7.5.328.4....4.....427.85..
12......9..7..9....892731..2.13974.8....249.1..48.1...7.5.328.48...4.....42..85..
12......9..7..9....892731..2.13974.8..8.249.1..48.1...7.5.328.4....4.....42..85..
12..56..9.5....2.66.92.7...2...613..3159.26.8..65....2531..89.7....9....9..7.5..3
12..56..9.5...92.66.92.7...2...613..3159.26.8..65....25..7.8..3.........931..58.7
12..56..9.5...92.66.92.7...2...613..3159.26.8..65....2531..89.7.........9..7.5..3
12..56..9.571..2.6..92.3...2...67...7.59.26.8..65....2.........57..189.39.13.58.7
12..567.9.5....2..6.9..7...2...613..3159.26.8..65....253..189.7.........9.17.58.3
12..567.9.5....2.66.9..7...2...61...3159.26.8..65....253..189.7.........9.17.58.3
12..567.9.5....2.66.9..7...2...613..3159.26.8..65....253..189.7.........9.17..8.3
12..567.9.5...92.66.9..7...2...61...3159.26.8..65....253...89.7.........9.17.58.3
12..567.9.57...2..6.92.7..12...613..31.9.26.....5.3..25..3189.7...6.....9.1..58..
12..567.9.57...2..6.92.7..12...613..31.9.26.8...5.3..25..3189.7...6.....9.1..5...
12..567.9.57...2.66.92.7..12...613..31.9.26.....5.3..25..3189.7.........9.1..58..
12..567.9.57...2.66.92.7..12...613..31.9.26.8...5.3..25..3189.7.........9.1..5...
12..5678..57...2..6.82.7.1.2....1...3158.264...65...2.5...1487.8.17.54.....3.....
12..5678..57...2..6.82.7.1.2...613..31.8.2.4...65.3.2.56..1487.8.1..54...........
12..5678..57...2..6.82.7.1.2...613..31.8.2.4...65.3.2.56.31487..........8....54..
12..5678..571..2..6.82.7.1.2...6.3..31.8.2.4...65.3.2.56.31487..........8....54..
12..5678..5718.2..6.8....1.23..1.45....63.1...1..25.3..72.6..4.56..4287....5.....
12.4.........8..6.86.2.7.142...1.4...3...2.7191.74382.39..786..68.3.4.97...6.....
12.4.......71.92.66897...41.......6.36.89..72.9.6..8.3....4...88..9.7.2494.2.8..7
12.4.....4..1.92.66897...41.......6.36.89..72.9.6..8.3....4...88..9.7.2494.2.8..7
12.4..7.94..1.9..66..72314.26.3.549...4......93.2.4...3.25.796.7....25.3.......7.
12.4.6.89.5..8.2.....2..1.428.7.4...6..92..7.97.56842..9..4.61.51.69..4.........5
12.4.678..5.1.....6.......123.67.4..7....5....6.34...731.5.48..5728.31.4.8.71...3
12.4.678.4..1.....6..7231.426.3.54.8..4...3...3.2.46..3.28.7..67..5.283.........7
12.4.678.4..1...6.6..7231.426.3.54.8..4...3...3.2.4...3.28.7..67..5.283.........7
12.456.8...71..2...8..72...24...8..5.7861..2.9.1.248...1..6749.79.841.5..........
12.456.8...718.2...8..72...24......5.7861..2.9.1.248...1..6749.79.841.5..........
12.4567.......9...69.23714.2467.53..3....24.7...3...6.......9...629....49..52467.
123..67.9..67.91.3.9.......2613.89.4....4.....4.6..8.26....34...1..643.7.348.72..
123.56..9.5......66.92.7...2...613..3159.26.8..65....25...189.....3.....931..58.7
123.56.8.4.6..91...8.....6.21..6483.3...2..166.8..34..5.1.923488..3.5..1.........
123.56.8.4.6..91...8..3..6.21..6483.3...2..166.8...4..5.1.923488..3.5..1.........
123.56.8.4.6..91...8..3..6.21..6483.3...2..166.8..34..5.1.923488....5..1.........
123.567...5....2.66.9..7..12...6....3159.26.8..65.1..2.3..189......9....9.17.58.3
123.567...5....2.66.9..7..12...6....3159.26.8..65.1..253..189......9....9.17.58..
123.567...5...92.66.9..7..12...6....31...26.8..65.1..253...8..7....9.1..9.17.58.3
123.567...5...92.66.9..7..12...6....3159.26.8..65.1..2.3..189...........9.17.58.3
123.567...5...92.66.9..7..12...6....3159.26.8..65.1..253..189...........9.17.58..
123.567.9.5......66.92.7...2...613..3159.26.8..65....25.17.89.....3.....9....58.7
123.567.9.5....2..6.9..7...2....13...159.26.8..65.3..253..189.7.........9.17.58.3
123.567.9.5....2..6.9..7...2....13..3159.26.8..65....253..189.7.........9.17.58.3
123.567.9.5....2..6.9..7...2...613...15..2..8..65.3..25..7189.3.........9316.58.7
123.567.9.5....2..6.9..7...2...613...15..2..8..65.3..25316.89.7.........9..7158.3
123.567.9.5....2..6.9..7...2...613..3159.26.8..65....25.17.89.3.........93...58.7
123.567.9.5....2.66.9..7...2........3.59.26.8.965.1...53..189.7......1..9.17.58.3
123.567.9.5....2.66.9..7...2....1...3159.26.8..65....253..189.7.........9.17.58.3
123.567.9.5....2.66.9..7...2....13..3159.26.8..65....253..189.7.........9.17..8.3
123.567.9.5....2.66.9..7...2....13..3159.26.8..65....253..189.7........19..7.58..
123.567.9.5....2.66.9..7...2...61...3159.26.8..65....25.17.89.3.........93...58.7
123.567.9.5...92.66.9..7...2...61...315..26.8..65....253...89.7.........9.17.58.3
123.567.9.5...92.66.9..7...2...61...315..26.8..65....253...89.7....9......17.58.3
123.567.9.5...92.66.9..7..12...6....31...26.8..65.1..253...8..7......1..9.17.58.3
123.5678..5.....6.6.82.7.1.2...613...1.8.264...65.3.2.5.13.48..8...154...3.......
123.5678..5.....6.6.82.7.1.2...613..31.8.264...65...2.5.13.48..8...154...3.......
123.5678..57.8....68..7.51.236.1..5.....25.....56.81..361.92.7......7....7..6.39.
123.5678..57.8....68..7.51.236.1..5..1..25.....56.81..36..92.7......7....7..6.39.
123.5678..57.8.2..6......1.23671.95..1..2......56..1..36..9287..7286..9....3.....
123.5678..57.8.2..6.....51.236.1.45...56..1...1..2....36..4287..7286..4....3.....
123.5678..57.8.2..6.....51.23671.95..1..2......56..1..3.........6.89237..72.6..9.
123.5678..57.8.2..6...7.51..1...5....36.1.45...562.1..36..428............7286.34.
123.5678..57.8.2..6...7.51.23671.4...1...5.....56.....36..4287..7286..4.8........
123.5678..5718.2..6.....5..23671..5..1..25.....56.81..362.9..7...........7..6239.
123.5678..5718.2..6.....5..23671..5..1..25.....56.81..372.6..9...........6..9237.
1234.678.4........6892.714.2..8..3....8....6.9.13628..392..461...462.........34..
1234.678.4........6892.714.2..8..3...38....6.9.1.628..392..461...462.........34..
1234.678.4........6892.714.2..8..3.1..8....6.9.13628..392..46....462.........34..
1234.678.4........6892.714.2..8..3.1.38....6.9.1.628..392..46....462.........34..
ravel
 
Posts: 998
Joined: 21 February 2006

Postby ravel » Tue Jul 17, 2007 9:40 am

Hey, another look and here it is:
Code: Select all
 +-------+-------+-------+
 | 3 1 2 | 6 7 . | . 5 4 |
 | 7 . . | 4 . . | . 3 6 |
 | . 4 6 | 5 . . | . . 2 |
 +-------+-------+-------+
 | . 7 1 | 3 . . | . 6 8 |
 | . 6 . | 2 . 7 | . . 3 |
 | . . 3 | . 6 . | . . . |
 +-------+-------+-------+
 | . . . | . 2 . | . 4 . |
 | 1 . 7 | 8 . . | . . 5 |
 | . 2 4 | 7 . 5 | . 8 1 |
 +-------+-------+-------+
[Edit: scrambled it - thanx Ron]
Last edited by ravel on Tue Jul 17, 2007 7:19 am, edited 1 time in total.
ravel
 
Posts: 998
Joined: 21 February 2006

Postby Havard » Tue Jul 17, 2007 9:49 am

ravel wrote:Hey, another look and here it is:
Code: Select all
 +-------+-------+-------+
 | 1 2 3 | . 5 6 | 7 8 . |
 | . 5 7 | . 8 . | 2 . . |
 | 6 . . | . 7 . | 5 1 . |
 +-------+-------+-------+
 | . 1 . | . . 5 | . . . |
 | . 3 6 | . 1 . | 4 5 . |
 | . . 5 | 6 2 . | 1 . . |
 +-------+-------+-------+
 | 3 6 . | . 4 . | 8 . . |
 | . . . | . . 2 | . 7 . |
 | . 7 2 | 8 6 . | 3 4 . |
 +-------+-------+-------+


congratulations!:)
Havard
 
Posts: 377
Joined: 25 December 2005

Postby ronk » Tue Jul 17, 2007 10:02 am

ravel wrote:Hey, another look and here it is:

Congrats on the first known minimal 38:!:

It looks like it's in row-order minlex form ... but gsf's canonicalization yields a different result. What "normalization" did you use?

BTW I think you should scramble it. Why make it easy for people to simply guess that r1c4=4?
ronk
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