The New Sudoku Players' Forum

[JPF]

If a selection criteria is needed (say, the day you should decide to publish a collection), then rather than the artificial "100 first submitted", maybe the "15 or 20 best from each symmetry type, at time of publication" would be more natural.

Agree, it’s fair … even if my “handicapped” generator will not enable me to be in the final list

I think the one-, two-, three-steppers, etc. belong to separate classes, and can not be compared directly. For low-steppers the number of clues is crucial: lower number of clues = better quality. For the sake of diversity, it's interesting to divide in symmetry types: what is the best we can achieve for each symmetry type.

I’m a bit confused.
Would it be possible to set up the updated low-steppers list with the required ranking of the different criteria ?

JPF

[Ocean]

Agree, it’s fair … even if my “handicapped” generator will not enable me to be in the final list

Well... you have already produced several quality puzzles, with all kinds of symmetry. And if a generator has a 'handicap', it might only be a question of time before it's fixed. The new 'rule' (only submit puzzles that are strictly better that one's own personal record for a particular symmetry), should make room for many contributors - ideally any 'final list' should contain as many contributors as possible.

Would it be possible to set up the updated low-steppers list with the required ranking of the different criteria ?

I thought of something like this:

Code: Select all

Lowest known number of clues for Low-steppers:

#------------------------------+----+----+----+----+----+----+----+----+
Number of steps:               |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |
#------------------------------+----+----+----+----+----+----+----+----+
Symmetric + absolute minimal:  | -- | -- | -- | -- | 20 | 20 | 18 | 18 |
Symmetric + minimal symmetric: | 44 | 32 | 28 | 24 | 20 | 20 | 18 | 18 |
Symmetric:                     | 40 | 32 | 28 | 24 | 20 | 20 | 18 | 18 |
Minimal:                       | -- | -- | -- | -- | 20 | 19 | 18 | 17 |
Any sudoku:                    | 38 | 32 | 28 | 24 | 20 | 19 | 18 | 17 |
#------------------------------+----+----+----+----+----+----+----+----+
#------------------------------+----+----+----+----+----+----+----+----+
Type I symmetry:   (M)         |    |    |    |    |    |    |    |    |
                   (SM)        |    |    |    |    |    |    |    |    |
                   (not M)     |    |    |    |    |    |    |    |    |
#------------------------------+----+----+----+----+----+----+----+----+
Type II symmetry:  (M)         |    |    |    |    |    |    |    |    |
                   (SM)        |    |    |    |    |    |    |    |    |
                   (not M)     |    |    |    |    |    |    |    |    |
#------------------------------+----+----+----+----+----+----+----+----+
Type III symmetry: (M)         |    |    |    |    |    |    |    |    |
                   (SM)        |    |    |    |    |    |    |    |    |
                   (not M)     |    |    |    |    |    |    |    |    |
#------------------------------+----+----+----+----+----+----+----+----+
Type IV symmetry:  (M)         |    |    |    |    |    |    |    |    |
                   (SM)        |    |    |    |    |    |    |    |    |
                   (not M)     |    |    |    |    |    |    |    |    |
#------------------------------+----+----+----+----+----+----+----+----+
Type V symmetry:   (M)         |    |    |    |    |    |    |    |    |
                   (SM)        |    |    |    |    |    |    |    |    |
                   (not M)     |    |    |    |    |    |    |    |    |
#------------------------------+----+----+----+----+----+----+----+----+
Type VI symmetry:  (M)         |    |    |    |    |    |    |    |    |
                   (SM)        |    |    |    |    |    |    |    |    |
                   (not M)     |    |    |    |    |    |    |    |    |
#------------------------------+----+----+----+----+----+----+----+----+
Type VII symmetry: (M)         |    |    |    |    |    |    |    |    |
                   (SM)        |    |    |    |    |    |    |    |    |
                   (not M)     |    |    |    |    |    |    |    |    |
#------------------------------+----+----+----+----+----+----+----+----+
No symmetry:       (M)         |    |    |    |    |    |    |    |    |
                   (SM)        |    |    |    |    |    |    |    |    |
                   (not M)     |    |    |    |    |    |    |    |    |
#------------------------------+----+----+----+----+----+----+----+----+
#------------------------------+----+----+----+----+----+----+----+----+

... which makes 8 x 8 = 64 lists, or a list with 64 groups (with the minimality criteria not separated). The upper part of the table is an extract (best picks) from the lower part. It seems a bit hard to maintain manually though...
Any comments/suggestions?

[Ruud]

I have 3 suggestions:

- You do not need (SM) for the 'no symmetry' class
- I strongly advice to start a new thread on these lowsteppers.
- Compile an indexed list of the sudokus that appear in the table. The table can contain number of clues, followed by the index number. Remaining characteristics (best symmetry, poster, submission date) can then be found in the indexed list.

Ruud.

[gsf]

here's some baseline symmetric minimal #clues by #steps and symmetry class

Code: Select all

     1  2  3  4  5  6  7  8
  I 44 36 32 28 28 28 28 28
 II -- 32 28 28 28 28 24 25
III -- 38 31 28 27 26 26 26
 IV -- -- 30 28 26 24 25 25
  V -- -- 28 26 24 23 22 23
 VI -- -- 30 26 24 24 24 23
VII -- -- 29 25 23 23 23 23


[JPF]

Any comments/suggestions?

I'm ok with this recap presentation.

I have 3 suggestions...

I agree with Ruud suggestions, provided that the puzzles already posted will not be lost and that it doesn't create too much accounting work ...

JPF

[tarek]

I must have missed the Symmetry categorisation bit........

What do they stand for ????

tarek

[JPF]

Look at Red Ed post : Thu May 18, 2006 11:59 pm

JPF

[tarek]

• Type I = Full dihedral symmetry
• Type II = Full rotational symmetry
• Type III = Horizontal and vertical reflection
• Type IV = Diagonal and anti-diagonal reflection
• Type V = 180-degree rotational symmetry
• Type VI = Horizontal or vertical reflection
• Type VII = Diagonal or anti-diagonal reflection

Thanx JPF, I missed that post....

I would have suggested to make these as follows .......

• Type I = Horizontal or vertical reflection
• Type II = Diagonal or anti-diagonal reflection
• Type III = 180-degree rotational symmetry
• Type IV = I+III
• Type V = II+III
• Type VI = 90-degree rotational symmetry
• Type VII = VI+(I or II)

It is the word FULL that seems to cast a shadow of inaccuracy to the terms, but I think that the cast has already set.

tarek

[Ocean]

I have 3 suggestions:

- You do not need (SM) for the 'no symmetry' class
- I strongly advice to start a new thread on these lowsteppers.
- Compile an indexed list of the sudokus that appear in the table. The table can contain number of clues, followed by the index number. Remaining characteristics (best symmetry, poster, submission date) can then be found in the indexed list.

I'm ok with this recap presentation.
(...)
I agree with Ruud suggestions, provided that the puzzles already posted will not be lost and that it doesn't create too much accounting work ...

Thanks for your comments and suggestions.
I could start a new thread, were we collect the lowstepper puzzles submitted in this thread, in addition to new submissions. [Still need some improvement on the accounting part - each submitted puzzle should be verified and classified automatically.]

here's some baseline symmetric minimal #clues by #steps and symmetry class

Seems you have a good start set ready for submission!

Compare this to what we have so far:

Code: Select all

     1  2  3  4  5  6  7  8
  I 44 36 -- -- 24 -- -- --
 II -- 36 -- -- -- -- -- --
III -- 36 32 -- -- -- -- --
 IV -- 38 28 -- -- -- -- --
  V 40 32 28 24 20 20 18 18
 VI -- -- -- 26 -- -- -- --
VII -- -- -- 27 -- -- -- --
  0 38 34 -- -- -- 19 18 17


[gsf]

Still need some improvement on the accounting part - each submitted puzzle should be verified and classified automatically.

updated solver binaries at http://www.research.att.com/~gsf/sudoku/sudoku.html#Downloads
the --man option prints the man page that has example usage for inferior-thread style collation

I also have a ksh script that prints the low-step table from the collated data, which has progressed to:

Code: Select all

     1  2  3  4  5  6  7  8
  I 44 36 32 28 28 28 24 28
 II -- 32 28 28 24 24 24 24
III -- 36 30 28 27 24 26 24
 IV -- 36 30 28 26 24 24 25
  V -- -- 28 26 24 22 22 23
 VI -- -- 27 25 24 24 23 23
VII -- -- 28 25 23 23 18 18


the 18's came from gfroyle's 22M

[tarek]

Code: Select all

     1  2  3  4  5  6  7  8
  I 44 36 32 28 28 28 24 28
 II -- 32 28 28 24 24 24 24
III -- 36 30 28 27 24 26 24
 IV -- 36 30 28 26 24 24 25
  V -- -- 28 26 24 22 22 23
 VI -- -- 27 25 24 24 23 23
VII -- -- 28 25 23 23 18 18


Good work, I don't think we saw a 27 clue symmetrical 3 stepper (Type VI), should we add it to the list ???

tarek

[gsf]

Red Ed pointed me to gfroyle's 22M puzzle 18 clue collection
here are some notes on the collection

Code: Select all

notes on gfroyle's sudoku18

2 days to check 22M puzzles ~39 sec/Ghz

22000000 puzzles, all 18 clues

19949545 minimal
     169 symmetric minimal (antidiagonal)

    1557 symmetric (antidiagonal)
    1388 minimal
     169 symmetric minimal

21808366 solved with { basic constraints + x-cycles + y-cycles }

constraint frequency over all constrained (no guessing) puzzles
constraints applied in this order and repeat from
the beginning when progress is made

    F  Forced cell (naked single): only one value possible.
    N  Only cell (hidden single): only one value in row/col/box.
    B  Box claim (locked candidate): only value in row/col within a box.
    Tn (naked) tuple: order <= n (4) N exact N-tuples in row/col/box.
    Hn (hidden) tuple: order <= n (4) N hidden N-tuples in row/col/box.
    Wn Row/col claim: order <= n (4) pure x-wing/swordfish/jellyfish.
    X  Singleton cycle: strong and 1-weak edges. Requires B, included in Y.
    Y  Pair cycle: strong, 1-weak and 0-weak (pair) edges. Includes X.

    21808255 F
    21808058 N
     8992275 B
     2224909 T
     1224925 H
      371029 W
     1762036 X
     1570376 Y

307 puzzles solved with F only
 99 puzzles solved with N only

191634 required guessing
751 that required guessing had 1 basic constraint backdoor
(small # backdoors => greater probability of bad guesses)
average 18 basic constraint backdoors for puzzles requiring guessing
all puzzles requiring guessing had singleton basic constraint backdoors

low (<=8) and high (>=21) symmetric (antidiagonal) steppers
#!sudoku cut=5,
VII,7,18,M,070030000800000500000000100000070943500600000000000000034800070000500600000100000,gfroyle,17921852
VII,8,18,M,001400000000200050300000700520000060000010900000000000009080104070500000000000300,gfroyle,747618
VII,8,18,M,002400000000600800700000010130050000000900200000000400090013070004000600000000000,gfroyle,3911523
VII,8,18,M,003200000000500800900000040410070000000600500000000200090041070002000600000000000,gfroyle,6299657
VII,8,18,M,003200000000500800900000040410070000000600500000000200090041070005000600000000000,gfroyle,6299658
VII,8,18,M,009000036020700000800400000036090000000800700000000000000060190700000800400000000,gfroyle,21574539
VII,8,18,M,009000064020700000800300000046090000000800700000000000000060190700000800300000000,gfroyle,21867336
VII,8,18,M,050000630900100000000400000032080000000600100000000400700032080100000900000000000,gfroyle,12728116
VII,8,18,M,080010000500000300000000200000070814300500000000000000014900070000200600000300000,gfroyle,19482472
VII,8,18,M,090100800500000020000400000302060000000700400000000100900032060010000700000000000,gfroyle,21335141
VII,8,18,M,090100800500000030000200000403060000000700100000000200900043060010000700000000000,gfroyle,21335154
VII,8,18,M,090200800500000030000100000403060000000700100000000200900043060010000700000000000,gfroyle,21482277
VII,21,18,M,050000020300090000000008000000060308010700000002000400000205090600000800000100000,gfroyle,11465945
VII,21,18,M,050000408600300000000000000040080900000700030000005000300900160000040500700000000,gfroyle,12515356
VII,21,18,M,200000065010209000000400000035070000000800100060000000000060030900000400400000000,gfroyle,4682684
VII,21,18,M,300000400000006070000050000000230800007400000060000020800900300050007000000000001,gfroyle,6704751
VII,22,18,M,000800030040000600000903000908100000000000705003000000070050200400000080000060000,gfroyle,20051814
VII,22,18,M,030000020800040000000008000000070405010900000002000700000203090500000800000100000,gfroyle,6476378
VII,22,18,M,040000030800050000000002000000070508010900000003000700000304090200000800000100000,gfroyle,9408169
VII,23,18,M,040000030200080000000002000000070205010900000003000700000304090500000800000100000,gfroyle,9191258
VII,23,18,M,107000090000500003800000000020000605000010800000000000000290080400000100050300000,gfroyle,2401417


[Ocean]

updated solver binaries at http://www.research.att.com/~gsf/sudoku/sudoku.html#Downloads
the --man option prints the man page that has example usage for inferior-thread style collation

I also have a ksh script that prints the low-step table from the collated data, which has progressed to:

Thanks! I downloaded the program. It seems to work fine, and also very fast... However, I got one 'trivial' but crucial problem: I can not redirect the output (>) to a file (on my old home-machine running 'milennium'; might try the office machine over the weekend, or possibly find some workaround.)

Anyway, I started a new 'lowstepper thread'. Will prefer to use gsf's program for the book-keeping. Until I get able to catch output from the program, I would be glad if someone else could produce updated 'sorted/accumulated lists' of the submitted puzzles.

Code: Select all

     1  2  3  4  5  6  7  8
  I 44 36 32 28 28 28 24 28
 II -- 32 28 28 24 24 24 24
III -- 36 30 28 27 24 26 24
 IV -- 36 30 28 26 24 24 25
  V -- -- 28 26 24 22 22 23
 VI -- -- 27 25 24 24 23 23
VII -- -- 28 25 23 23 18 18


Good work, I don't think we saw a 27 clue symmetrical 3 stepper (Type VI), should we add it to the list ???

tarek

Right, that's a new 'overall best'! Will be added to the historical list when the puzzle is submitted.

Red Ed pointed me to gfroyle's 22M puzzle 18 clue collection
here are some notes on the collection

Great! A few questions: All the symmetric mentioned have antidiagonal symmetry... Are these all the symmetric 18s, or did you search for this specific symmetry only? And, when searching for symmetry, did you just check the pattern 'as is', or check all isomorphic forms?

[gsf]

Thanks! I downloaded the program. It seems to work fine, and also very fast... However, I got one 'trivial' but crucial problem: I can not redirect the output (>) to a file (on my old home-machine running 'milennium'; might try the office machine over the weekend, or possibly find some workaround.)

-o output-file added and posted

Great! A few questions: All the symmetric mentioned have antidiagonal symmetry... Are these all the symmetric 18s, or did you search for this specific symmetry only? And, when searching for symmetry, did you just check the pattern 'as is', or check all isomorphic forms?

all 22M 18's were checked for symmetry as is
the 18's as is only show antidiagonal symmetry
checking all isomorphic forms will take some thought

[gsf]

here are the low steppers from a background process that's scanned ~250M random symmetric puzzles so far
I don't think these have made it into the table yet

Code: Select all

#!sudoku cut=5,
I,3,32,SM,000030000004508900058090240070105030503000604020306090092050480006409700000020000,gsf,NEW
I,4,28,SM,000789000006000100070030090800405006704000209600203008050060030002000400000127000,gsf,NEW
I,6,28,SM,000000000034020580080607020005030800020809050009040700010204060048060910000000000,gsf,NEW
I,7,24,SM,400000009030000020000517000002060800001203900009040500000792000070000060800000003,gsf,NEW
I,8,28,SM,000010000002769800080050040070000090319000582050000030090040070005687400000030000,gsf,NEW
II,2,32,SM,000183000071002360020900050850000107400000009603000045060001020085200790000574000,gsf,NEW
II,3,28,SM,058007000040000589010002007602309000000000000000705103700800020481000090000600740,gsf,NEW
II,4,28,SM,000000390900004100130620000070206900008000500003105080000063075007800006062000000,gsf,NEW
II,5,24,SM,100000003009000000008709460001050700000602000004030900067905800000000200800000007,gsf,NEW
II,6,24,SM,030600000009700001000001080008070059000804000120090600060100000400005200000008090,gsf,NEW
II,7,24,SM,000300480900070500280000000000010009060408020100020000000000031002050006037004000,gsf,NEW
II,8,24,SM,000000170150070080600002000001080000020904030000020700000800006080050093049000000,gsf,NEW
III,3,30,SM,030416080070000040200000005007903100600708002008201300300000001090000030040372050,gsf,NEW
III,4,25,SM,000509000008000500701000608400060002000324000500090001603000704007000900000801000,gsf,NEW
III,5,25,SM,000509000008010500701000608400000002000324000500000001603000704007030900000801000,gsf,NEW
III,6,24,SM,009608400013000260000000000400060007000201000100050008000000000032000870006409100,gsf,NEW
III,7,26,SM,000000000103000206000125000070080010310906048040050020000892000906000803000000000,gsf,NEW
III,8,24,SM,400000009030000020000517000002060800501000906009040500000792000070000060800000003,gsf,NEW
IV,2,34,SM,005900030004810007896750000451000000028000960000000174000069852500072300040008700,gsf,NEW
IV,4,28,SM,000000060039500078060082000090060200004905300002030050000710030540003810070000000,gsf,NEW
IV,5,26,SM,000005208004070000080003009000708302010000080608209000300500040000030100207400000,gsf,NEW
IV,6,24,SM,000008500008061000042000007000007018090000020710600000300000450000270600004800000,gsf,NEW
IV,7,24,M,000309800000065000000000504700003068010000050360400001504000000000120000009608000,gsf,NEW
IV,8,25,SM,006004300002700000910200007079000002000010000500000840400006035000007400003500600,gsf,NEW
VI,3,27,SM,000000000003409200980205067000000000000791000207000408010080020036000540050010030,gsf,NEW
VI,4,25,SM,034020960020901050000070000700000003000010000400809001350000012600000005000702000,gsf,NEW
VI,5,24,SM,000968000310000048080000020000000000006020500002301900200000003000256000050040080,gsf,NEW
VI,6,24,SM,000000000000156008074000002080700500056000801090300700068000009000592007000000000,gsf,NEW
VI,7,23,M,007000600000935000000000000800000003690000087000102000400607008006403200900000001,gsf,NEW
VI,8,23,M,000000000009406700020301060052090180000000000007000500730000012000000000500609003,gsf,NEW
VII,3,28,SM,020703000500000900000460050084020003050001600360000709400006000000914008007800040,gsf,NEW
VII,4,25,SM,003109600000007430000000081000700056950000000600002007230000009004080000008520000,gsf,NEW
VII,5,23,SM,040013000200000009000007083000090608600100400407000000000230000005000000031700005,gsf,NEW