The New Sudoku Players' Forum

[Havard]

some exciting news!

If we first take these:

Code: Select all

1...26.........38.............8.....6.....45....3....1.3.74......2.....6.......1.
...8.5.1..2....6...........81..3........7.9.45.........4..2..........7.......3.8.
..62...4.1...7......5......3.........48..........51....3.8..........45........1.6
.3..6............1..6....5.....25....9....4.....7.1...2...4.8..1..........5...6..
...2....6.1.....5..........3..8...4.......17.2........6....5..2.....73...5..1....
.7.2.............1.36.4....1....8.2.....3....9..............78.5..1........6..3..
.2....4.....3..5......1....7.1.........2..6..4.........4.6...3...8....1.....4...7
.....2..4.75.1......8......3..4.6......3..8........1..2.......1....8...9...7.....
.7...9.68..3.............2..9....4.....25.1......6.......7..3..2.6......5........
.1.....7.....4.5.....2............815.6......2........4.......2..7.3.......1..6.8
.....36..5.9...............8.....71....29.......5......1...8.......4.2.9.3......5
......12......43...5.6.........2.4.....57.....8.......3.4..1......7...5.2........
......1.2.....43...5.6.........2.4.....57.....8.......3.4..1......7...5.2........
....2....8......3.1............5.7.8......2.....9......753......6.4...9..2.....5.
....3..5.7.......2..8.5....1.....8.....7......3..4.......6..3.1.542..............
.4..31.........8.2.........3.7.........8..4..1..............637...21....6......9.
....7.2...8....6...........5..6.3.4....8.....7.............6.35.2.4......1....7..
....73....21..........4.......9..2.17...........1..8..3......7.....6...5.4.8.....
....783....1..........3.....6.5...1....4.....7.......3.5.1...6.8.....7......2....
....8...18....4...2.........15.3..........24..........6.....7.5...1...6....9.3...
....8.7.159...................4..35..19......6.........4.5.1...2.....8.....9.....
...1....3..7....8.2...........2..7..6..4......3........1..78.....5...2......5.6..
...2..61.4........3.....5...1.93........8...4......7..8.4....3.............6....9
...3..2...4...2.....6.....1...6.4....5....8..2.....5..3..1...7............9....4.
...3.19..5...................3...24..8...5....9.......6..7....11......58...2.....
...3..9..5...4...............3...24..8...5....9.......6..7....11......58...2.....
...43...671..............3.2....7..5...1..6...........5.8.2...........4....3..1..
...43...681..............3.2....8..5...1..6...........7.5.2...........4....3..1..
...5...4.................262.....38.1.6.........4..5...3..7.1......62....5.......
...58.4...91...............81........5.7........3...2.....1...55.....7....2..9...
...62.4...........3.5.......4..52.......1..7..2.......1..7..........68.....3..2..
...64..5.3.1..........1.2..7...2.4..8.......3..........5.....1....8.9........3...
...8.....6...4......3.....5.1....62......5.4.....3....4..6..2.......7..3...1.....
...8..1...2.........3...7...5.....247..1..............19.6.....8.......7....2..3.
...8..2..54.......1..4.........5.72.8....6...4...1...........41.7.3..............
...8.52.....7..9...1.......8.24.....9...............6.....36.1.2.....8......1....
..2...47.....13....6..........2..9..3.....1....74.....1........54..........8...2.
..4.1.2..3..6..............6..75..........32........1.81..........43...5..2......
..4.1.2..3..9..............6..75..........32........1.81..........43...5..2......
..4.1.2..7..9..............6..75..........32........1.81..........43...5..2......
..4.1.2..9..6..............6..75..........32........1.81..........43...5..2......
..8....6......65..3..1......6....2......3.......5......5..82.........4.17......3.
.2.65............1....7........2.75.8.6..1............1..8.3.........5........24.
.21.........4..8...............15.2.3..6......7.......4..7....38.....6.4....2....
.24.7....6.......3...5...1..5.........72........6.1.8.....4.2..1.............3...
.6....8......5.9.2.1..........4...1.3..7...........5.6...1...7.9.2......5........
.56.............84....9.......6.2.3..7....1..4....8......1..6.5..8............2..
.6..2....4.....7...........9.57..1.....36....1.........9.....628..1........4.....
.7.....89...1............3.....8.5....3.9....1......7.5..6..2.......31...2.......
.7...83..8...3.........2....695....4......2...1..........6...1.3...4....2........
.7.4..........82.....2.........791..54.........3..........1..478......3.2........
.7.4...3......82...............791..54.........3.........1...478........2....6...
.7.8..4...26.............1.1..4.9.....3.....25........3.....9.....65........2....
.76.........1......2..8....48.....3.....71............5....96..1..3...........7.2
.8......1...34......75...........46.12.............3.....2.8.....4...53......6...
......39.7816..............23.4............81.........5..3.....6.....2....7.8....
.8...........3..5..31......7..5...6.2.....4.....8.....5..62............1....4.8..
.8.97.......5..4.........1.....31..794......................2..3.......176.4.....
.81.........49.6...........42......8...1..5......3....6.....39......21.....8.....
.81..........9.6....4......42......8...1..5......3....6.....39......21.....8.....
.87...5......1.....2.......4..3...........2......9.71....8.2...1......4.3..6.....
.96.5...........87.........1.82...........6......3.9...5.7..3.......1......8....6
1............3..542..7......579....3...1......3..........6..1......5..8.4........
1...2...........3...9....7.37..4.......5..4.98........2.....1.....8.3......7.....
14.....6.6.......5...9.....3.8...2.....7....9......3......3..1...9.2.....7.......
71.5.....2......8....6....458....16....3.........4....3.....7.......1.......8....
57....3.....94.......8.....61...7.5........24.........2.45...........1....9......
38..1........8..2.......5...6.4.2.....5.....1......3.....5.7.4.1...........6.....
38..1........8..9.......5...6.4.2.....5.....1......3.....5.7.4.1...........6.....
4............7.32....5......3..2.5...7......4...6.....6..4.9.........27.......1..
5.......12...6..8..4.7........3..7.....8.....1.......4....152...3...........4....
5..3...6.....1..............7..2.....12.6..........8..4..5...2.......71.8..4.....
5..3...6.....7..............7..2.....12.6..........8..4..5...2.......71.8..4.....
5..2.....3.65...4...........8..17..........56..........1..3.7..2..6...........1..
.3.2.........5..8.4...........1..3.7......2....8..........7..432.6..4....1.......
56...2.......1.8..............83...........45.1.......7..4.....6.8...3.......1..2
56.47..........9..3........6..24.......3..1............18........9.........5...42
6......4......53......1...2......1..2..6........4..56..35.........7....8.1.......
6.....4.....3...1.............7...93.16......2............562....94......3.....8.
6...1.5....5.87...2...........4..2...8........3.........9...18....2........3....7
9..3.....7.....5........1..21......7....58......4........67..3..58..........9....
6..4.2..........79..........7.8.......9....5......36...5627....3.....4...........
6.3.54......1..7..2.....8...9...8..........32.....5....7....9......3.......6.....
64......9....7..6............7...1.2.3.6........9.....9........8.1.2.7.........3.
5.....3.....12.......8.....48.6...........73..6.....5...3.45.........8.1.........
7.....5.....4...1.............8...43.17......2............672....35......4.....9.
7...3.8....9...1......1....6..4......4.9...........5.....2...46.15.....3.........
7..3..1.................5.4.51.........7...3........9..6..58...2......7.....4...3
7.14..6......3..2.4.........2....1.....7..4...8..........1.4...5...............83
7.6.....9...4.....1........82..9..........54....1......4....81...5..3.......7....
71....6.....54.7......3....1..8..2...54...............2....1..........3...7....4.
.....61......39..4.............58.3..4.1......2......9...8..4..3.9......5........
6.5...........27.8..3.......7..2.........4.5......1.6.........9...5.....1.....2.4
6.59..........27.83.............4.....6....5..7.....6.4..........9.5..........2.4
6.5...........27.83.........9...4..........7...13..56..........7..6...........2.4
6.59..........27.83.................2......5.8..3.4.6............96......7....2..
6.59..........27.83............4..........95...9....6..........9..6......7....2.4
6.59...........7.8..1.......7..2...........5.....3..6....8.....1..6......3....2.4


that will bring the Gordon list up to 39999 17 sudoku...

and then...

Nr 40000:

Code: Select all

6 . 5|. . .|. . .
. . .|. . 2|7 . 8
3 . .|9 . .|. . .
-----+-----+-----
. 7 .|. . .|. . .
. . .|. . 1|. 5 .
. . .|. . .|. 6 1
-----+-----+-----
. . 1|. . .|3 . .
. . 9|6 . .|. . .
. . .|. . .|2 . .

This sudoku is a tribute to one of the greatest puzzlemakers I know, Deano! This 17 was made from an 18 he handmade: http://www.sudokuarchitect.com/forum/viewtopic.php?t=375

And a few more for fun and giggles:

Code: Select all

6.5...........47.83.........7........1...8.52.......6.....7....9..63............4
6..35........4.7.8.........27..........98..5........6......7..43.............82..
6.5..3........47.81.........7..4.........8.5........6.....7....3..5...........2.4
6.53..........27.81.........7...4.........35......9...5...1............7......2.4
6.59..........71.83.........7...1..........5........6.5..8.......96...........7.4
6.3...........2..8..........8..47......3...5..4.....6..........5.96.........8.2.4
6.5...........27.89........27..........1...5........6.....7.3..1..6..........82..
6.59..........27.84.........7...3......1...5.................6.5.98.....1.....2..
6.5.9........2.7.8..1.......7...4..........59.......6........3...96..........82..
6.5.9.........47.8..1.......7.3..........1.5........69.........3.96...........2..
6.5..........2.7.8.........87..3..........95........6...1....4.3..6..........82..
6.59..........27.8..1.............5.........9.7...3.6.........44.9...........72..
6.59..........27....1.......7..........5....12....346............96......3....2..
6.59..........27.8..1.......7..........6...5...3...4.9.........5.9...........72..
6.59..........27.8..1......27..............5....3....6.4....2....96.........8....
6.59.........2.7.8........1.7.......21..........34..6............96...........2.7
6.5..9........27.1..3.......1..2...........5......7.6.....1.......6.......9...2.4
6.51..........27.8..3.......7..............5......1.6.....8....3..5.....4...7.2..
6.5..9........27.8..3...................2..5.98.....6.....7....3..5...........2.4
6.5..........2.7.81.........7....3.....4...5....1...6..........4.16..........82..
6.59..........27.81.........8.......3......5....2...6..........9.6..........8.2.4
6.59...........7.31..........4.2.....7....95........6..........9..6.........8.2.4
6.59..........27.81.........7..2......8....5......1.6....5..3..9.............8...
6.59..........27.8..........74........18...5........6......14..9..6.....5........
6..9..........27.13.........7...4..........5..4.....6.......8..5.96..........7..4
6.59..........47.83.........7..2.......6...5........6..........5.91...........2.4
6.5...........27.8..3.......7.........2....5.....1..6....2........6.3...1......94
6.59..........27.8..3.......4..............5.....71.6..7....2......6.......5....4
6.59.....9....4..8..3.......7..4.......3...5........6.........73..6...........2.4
6.5.1.........27.8..3.......7......2...3...5......4...........93..56..........2..
.4..31.........8.2.........3.7.........8..4..1...............37...216...6......9.
...1....3..7....8.2........5..2..7..6..4......3........1..78.........2......5.6..
...43...671..............3.2....7..5...1..6...........5.8.2................3..14.
...62.4...........7.5.......4..52.......1..3..2.......1..7..........68.....3..2..
..3...1...2..........8..7...5.....247..1..............19.6.....8.......7....2..3.
...62.4...........3.5.......4..5........13.7..2.......1..7.5........68........2..
..4...2..75.9..............6..7.5.........32........1.81..........43...5..2......
.21.........4..8...............15.2.3..6......7.......4..7....38.....6......24...
.6....8......5.2.9.1..........4...1.3..7...........5.6...1...7.9.2......5........
.8......1...34......75...........4..12.............36....2.8.....4...53......6...
.7.8..4...26........5....1.1..4.9...........2..7......3.....9.....65........2....
1.............3.542..7......579....3...1......3..........6..1......5..8.4........
.96.5...........87.........1.82.........3.6........9...5.7..3.......1......8....6
6...1...........3...9....7.37..4.......5..4.98........2.....1.....8.3......7.....
......39.7816..............23.4............81.........5....3...6.....4....7.8....
56.47..........8..3........6..24.......3..1............18........9.........5...42
6.....4.....3...1.............7...93..6......21...........562....94......3.....8.
6...1.5....4.87.....2.........4..2...8........3.........9...18....2........3....7
7.....5.....4...1.............8...43..7......21...........672....35......4.....9.
.1....6.....54.7......37...1..8..2...54...............2....1..........3...7....4.
71....6.....54.7......3....6..8..2...54...............2....1..........3...7....4.
.1....6.....54.7......37...6..8..2...54...............2....1..........3...7....4.
8...3........2...7.....95.....6...2195.8.....3.............89...1.7..............
8..1..2.....3..7....6........5.74.........1......8.......9....5.1.....4.4......8.
8..1..2.....3..7....9........5.74.........1......8.......9....5.1.....4.4......8.
8..5........7..2.........1.....13..57.8......4........61...9.4....8..7...........
8.2.4.......7..9.13........6.....48..3.5............2.....8.2...1..........3.....
9.......1....5........4....7.....35.4..1............6.35....6.....47.....6.8.....
9....84..............6..2...7.....8..6.....7......1......76..3.4.1...5.....2.....
...5...6.21....3...8.......1......79....32......8......3....2....54.........6....
9.5.3..........21..6....4......4...571..................2..1.4.3..7........9.....
94............5.27..8......5...2.......8..6..1.........3.....54...68.......1.....
6.59...........7.31..........4.2.....7....95........6..........9..5.........8.2.4
5.69.....9....4..8..3.......7..4.......3...5........6.........73..6...........2.4
6.59.....9....4..8..3.......7..4...........5....3...6.........73..6...........2.4


making the total 40065!

Havard

[gfroyle]

that will bring the Gordon list up to 39999 17 sudoku...

and then...

Nr 40000:

Code: Select all

6 . 5|. . .|. . .
. . .|. . 2|7 . 8
3 . .|9 . .|. . .
-----+-----+-----
. 7 .|. . .|. . .
. . .|. . 1|. 5 .
. . .|. . .|. 6 1
-----+-----+-----
. . 1|. . .|3 . .
. . 9|6 . .|. . .
. . .|. . .|2 . .

Congratulations...

Only took a week since I claimed that it would be difficult!!


Now for the next 10K puzzles....


Who will be the lucky discoverer of Number 50000?

Cheers

Gordon

[JPF]

Based on the data as of today (40095) here is the distribution of digits over the boxes.
See here for the last one made by Ocean a while ago (32930).

Code: Select all

                                                                                       
      2   001122344                                                             
      7   001222334                                                             
      4   001223333                                                             
      2   002222234                                                             
     17   002222333                                                             
      1   011112335   xxx                                                             
      8   011112344                                                             
     10   011113334                                                             
      2   011122235                                                             
     20   011122244                                                             
    225   011122334                                                             
    146   011123333                                                             
      2   011222225                                                             
    445   011222234                                                             
   1176   011222333                                                             
    103   012222224                                                             
   1187   012222233                                                             
    208   022222223                                                             
      1   111112235                                                             
     28   111112244                                                             
    613   111112334                                                             
    169   111113333                                                             
   1606   111122234                                                             
   3886   111122333                                                             
    748   111222224                                                             
  13886   111222233                                                             
  13899   112222223                                                             
   1694   122222222 
  ------                                                           
  40095



This distribution xxx is new , #, puzzle :

Code: Select all

011112335
#15746
010800000000000460000000030706000000000200000400000000600534000000060200000007001


JPF

[JPF]

Here is the list of the non isomorphic (minlex) grids with more than 5 17-puzzles :

Code: Select all

                                                                             
  29    123456789456789123798231564234675918815943276967812435379164852582397641
  20    123456789456789123789132564264918357875324691931675248392861475547293816
  14    123456789457189263689237451275613948348975612961842537534798126712364895
  12    123456789456789123798132546215648937864973215937215468342567891581394672
  11    123456789456789123798231564237615948864973215915824637342567891581392476
   9    123456789456789123798132546237915468864273915915648237342567891581394672
   8    123456789456789123789132546231864975864597231975321468347918652592643817
   8    123456789457189326689237451261374895378591642594628137742865913836912574
   8    123456789456789231789231564214895673395627418867143952531974826648512397
   7    123456789456789123798231564264975318875143296931628457349812675582367941
   7    123456789457189236698327154269715843745863921831942567376298415584671392
   7    123456789457189236689732154245698317361275948978341562594817623736524891
   7    123456789456789132789231546247193658368574291591862374635928417812347965
   7    123456789457189236869732154218367495394528617675914823542873961781695342
   7    123456789457189263689273451276815394395764128814392576538647912741928635
   7    123456789456789132789213456271594863638127945945638217397845621514962378
   6    123456789456789123789132564267314958531968247894527316342675891675891432
   6    123456789457189326689732541236945178874613295915827463342598617568271934
   6    123456789456789132789123546231867954675941328948532671367294815592318467
   6    123456789457189236689273154278935641394617528516842973761324895842591367
   6    123456789456789123798213564274835916381692475965147238537928641619374852
   6    123456789456789123789132465215967348347518296698324517561843972874295631
   6    123456789456789231789231564215347896378695412964128357537914628692873145
   6    123456789456789123789132465217895346394627851568341297642513978835974612
   6    123456789457189236689732514264973851718524963935618427341295678576841392
   6    123456789456789123798213564245361978379548612681972345562194837837625491
   6    123456789456789123798231645284597361517643892639128457365914278872365914
   6    123456789456789123798213564267345918385691247914827356572968431649132875
   6    123456789456789123798231564261548397845973612937162845314697258582314976
   6    123456789456789132789123546275348961638291475941567328392675814567814293
   6    123456789456789123798213564247598631539167842861324975385641297672935418
   6    123456789456789132789132546267593418391847625845621973532974861678215394
   6    123456789456789132789231546278314695395678214641592378534967821862143957
   6    123456789456789132789213456214895673538627941967341825392174568671538294
   6    123456789456789132789231546295814673674392815831675924367928451548163297
   6    123456789456789132789132564234875691598361427671294358362917845847523916


and the number N of non isomorphic grids with n non isomorphic 17s :

Code: Select all

 n      N     n x N                                                             
                                                                               
29      1        29                                                             
20      1        20                                                             
14      1        14                                                             
12      1        12                                                             
11      1        11                                                             
 9      1         9                                                             
 8      3        24                                                             
 7      7        49                                                             
 6     20       120                                                             
 5     18        90                                                             
 4     81       324                                                             
 3    236       708                                                             
 2   1599      3198                                                             
 1  35487     35487
              ------                                                             
              40095                                                             


JPF

[gfroyle]

This distribution xxx is new , #, puzzle :

Code: Select all

011112335
#15746
010800000000000460000000030706000000000200000400000000600534000000060200000007001


JPF

Darn.. I didn't think of keeping this information in the DB... now I should add another field...

What I keep is the frequency of each DIGIT

Gordon

[daj95376]

Here is the list of the non isomorphic (minlex) grids with more than 5 17-puzzles :

Interesting. In the Canonical Forms thread, you indicate that [r2c3]=6 should occur only 28.9% of the time from random samples. Seems to me there's a higher success rate with these 17's.

[RW]

Here is the list of the non isomorphic (minlex) grids with more than 5 17-puzzles :

How many of these include both old and recently discovered puzzles?

RW

[JPF]

In the Canonical Forms thread, you indicate that [r2c3]=6 should occur only 28.9% of the time from random samples. Seems to me there's a higher success rate with these 17's.

In the actual list (40095):
[r2c3]=6 ; 55.1 %
[r2c3]=7 ; 44.9 %

I don't know if it's very useful.

Here is the list of the non isomorphic (minlex) grids with more than 5 17-puzzles :

How many of these include both old and recently discovered puzzles?

See here the stats when the list had 36628 17s.
The new puzzles are such that n <=4.
n being the number of non isomorphic 17-puzzles having the same equivalent solution.

JPF

[coloin]

Yes the 17 grids are twice as likely to have a repeating minirow tupel as an average grid. The SF grid has 2.

From another thread, JPF has analysed the clue frequency, and this shows how the more obscure grids have improved most since gfroyle did this analysis originally.

Code: Select all

      7      15    011122334
    175     226    011123333
    197     315    011222234
   5908    7537    011222333
     12      25    012222224
   8377   10028    012222233
    730     850    022222223
     10      15    111113333
     81     121    111122234
   2220    2847    111122333
     13      21    111222224
  11091   13394    111222233
   4104    4696    112222223
      5       5    122222222
-------  ------             
  32930   40095     

[gfroyle]

Code: Select all

      7      15    011122334
    175     226    011123333
    197     315    011222234
   
<snipped>

   4104    4696    112222223
      5       5    122222222
-------  ------             
  32930   40095     

I wonder if we could ever complete the analysis of all the 17-s with the 122222222 clue frequency profile...

Are those 5 the only ones?

Cheers

Gordon

[Pat]

So what I do is to keep any pseudo-puzzle that has "few" completions (say less than 10 or maybe 20) hoping that a subsequent "move" from one of those will land us back onto a real puzzle with a unique completion...

a small number of answers
may be irrelevant --
see: Megaclue

~ Pat

[Pat]

please clarify the 17-2+2

are the 2 clues added in any of the 66 holes,
or only in the original 64 holes ??

[Havard]

please clarify the 17-2+2

are the 2 clues added in any of the 66 holes,
or only in the original 64 holes ??

The one that I have been doing creates a "15-subgrid", and tries all possible ways to complete it. Or 66 holes if you like!

Havard

[ravel]

In the last time i had played around with "distances" between puzzles.
My own definition for the distance between 2 puzzles was (see Sudoku Space thread) the minimum number of "operations" needed to get from one to an equivalent of the other puzzle, where these operations are:
- change a given
- remove a given
- add a given.


I called a set of puzzles a family with distance n, when all puzzles have a pairwise distance less equal n.

Similar to Gordon's idea above i also thought about clusters of puzzles, where a cluster of distance n could be defined this way:
1. Any set A with a single puzzle is a cluster
2. Set A remains to be a cluster of distance n, when a puzzle is added, that has distance less equal n to any puzzle in A.

Now i wondered, what distance the cluster of known 17-clues has. To get a feeling, i looked at Ocean's puzzle May 16, where he mentioned, that it does not have another 17 within 2 off/2 on. I found 4 puzzles in the old list with the lowest distance 6 and 31 with highest distance 16.
I picked out one of the distance 16 puzzles in order to try to get closer to Ocean's, but with no success so far. The 6 puzzles (in the old collection) i found, had still distance 15 or 16, and when i tried it with one of the 15's, i did not find a new one.

Code: Select all

.3.....1....7..5....4..2...1.......2...4..6....8.3....54............3.8.....1....
...1...382....5.............5....4..4...3.......7....6..1....5.....6.2...6...4...
...6...453....7............6.......7.....25...4..8......1.5.....2.....6....7..3..
.7..4......2.....1.....1.3....3..5.......84..1.4.......5..6....3......8....2.....
2.......5.....16....8.3.....3.....2......74....15......1..2.......3...8.4........
3.......2...4..6....8..1....1.....3....7..5....4.2....54............3.8.....1....
3.7...........87......1.5...6.7..........3..1..2....3..5.4.....1......8.....2....



They also build a "17-clue 3off/3on" cluster. Maybe someone with more time and computer power can determine, if it is "closed" or other 17 clues can be added.

[gfroyle]

a small number of answers
may be irrelevant --
~ Pat

Absolutely correct.... I have no reason, other than blind hope, to assume that "few solutions" = "close to 1 solution" but empirically it has worked to some extent.

But there may well be other measures that are more effective in winkling out the remaining 17s by local search (or indeed, other mechanisms than local search)... it might need someone else to think of it though, because my brain is sort of stuck on the "counting solutions" mode.

But I enjoyed the megaclue thread.. I hadn't seen it, and it's pretty amazing how much effect one clue can have!

Cheers

Gordon