The New Sudoku Players' Forum

[gfroyle]

OK, here is a list of 17, 3 of which are not new,
but I don't know which

Three not new.. and also three duplicates...

But that gave me 11 more to add to the growing list, now at 9500+ 17s.

Thanks

gordon

[flagitious]

I can send my solver by email (sterten(at)aol.com) to anyone who is interested
(except those from the running programming contest ;-) )

What contest is this? I'm interested.

[dukuso]

I can send my solver by email (sterten(at)aol.com) to anyone who is interested
(except those from the running programming contest ;-) )

What contest is this? I'm interested.

http://www.vbforums.com/showthread.php?t=351477

[dukuso]

OK, here is a list of 17, 3 of which are not new,
but I don't know which

Three not new.. and also three duplicates...

But that gave me 11 more to add to the growing list, now at 9500+ 17s.

Thanks

gordon

You mean less than 14 were new to the 7611- list ?
Then I'll have to check for another bug :-(

The list is growing at about 700 per day. Do you confirm the
estimate that there are about 500000 of these ? (equivalence-classes)

[gfroyle]

You mean less than 14 were new to the 7611- list ?
Then I'll have to check for another bug

The list is growing at about 700 per day. Do you confirm the
estimate that there are about 500000 of these ? (equivalence-classes)

Not a very sophisticated bug - the list you posted has duplicate lines.... no need to search deeply for a bug in your equivalence routines!

I would not like to hazard a guess at the number of 17s at the moment.. just heuristic searches so far, so I have no basis on which to generalize the data.

Gordon

[dukuso]

delete

[dukuso]

here is the gangster-statistics for the solution-grids of Gordon's
7611 17-clue-sudokus :
(6 gangsters per grid)


1,6
2,124
3,326
4,88
5,48
6,119
7,143
8,715
9,1094
10,567
11,2279
12,453
13,373
14,1039
15,1480
16,199
17,996
18,1902
19,508
20,372
21,451
22,1067
23,950
24,926
25,2011
26,574
27,956
28,1420
29,724
30,340
31,2094
32,2507
33,2223
34,1483
35,4590
36,2144
37,4783
38,965
39,1236
40,37
41,666
42,185
43,463
44,40



to compare, here are the numbers of a random(?) sudoku generation:

2,22
3,52
4,29
5,8
6,8
7,24
8,96
9,62
10,28
11,273
12,31
13,62
14,52
15,148
16,23
17,128
18,179
19,28
20,20
21,25
22,42
23,57
24,58
25,122
26,25
27,57
28,125
29,29
30,13
31,167
32,190
33,206
34,76
35,204
36,124
37,195
38,45
39,57
40,6
41,50
42,26
43,19
44,1


can someone make a graphics, to compare these ?



=============================================







and here the gangsters again:



gang of the 44
================

(1) (allowed sudoku-) 9-tupel of 3-sets for the 3 entries in the 9 columns
(2) lfd.nr
(3) number of compatible 3*9 sudokus
(4) number of classes of compatible sudokus (from the gang of 416)
(5) number of 9-tupels from T in the class
(6) (5)/1680/36
(7) number of sudokus with a band from (4) as upper band / 9!/6^4/2^7
--------------------------------------------------
123456789123456789123456789,1,1728,2,60480,1,13546872
123456789123456789123457689,2,576,3,4898880,81,346083192
123456789123456789124357689,3,192,3,29393280,486,668815056
123456789123456789124378569,4,192,2,9797760,162,225521136
123456789123456789147258369,5,96,2,6531840,108,72962040
123456789123457689123458679,6,576,4,6531840,108,455091264
123456789123457689123468579,7,864,7,6531840,108,688823352
123456789123457689124356789,8,192,6,58786560,972,1334816064
123456789123457689124358679,9,192,8,117573120,1944,2639418048
123456789123457689124367589,10,192,6,58786560,972,1322892864
123456789123457689124368579,11,288,24,235146240,3888,7997419008
123456789123457689124389567,12,192,6,58786560,972,1333594368
123456789123457689126345789,13,192,3,29393280,486,671794992
123456789123457689126347589,14,192,8,117573120,1944,2665795968
123456789123457689126348579,15,288,16,117573120,1944,3983962320
123456789123457689145267389,16,96,1,29393280,486,330914376
123456789123457689145268379,17,144,8,117573120,1944,1987093296
123456789123457689146258379,18,168,14,235146240,3888,4596811128
123456789123457689148259367,19,144,3,58786560,972,975856572
123456789124357689125348679,20,192,5,39191040,648,871266816
123456789124357689125367489,21,144,4,58786560,972,989360244
123456789124357689125368479,22,168,9,117573120,1944,2299821930
123456789124357689125378469,23,264,13,117573120,1944,3652048026
123456789124357689126358479,24,144,8,117573120,1944,1973476872
123456789124357689126378459,25,168,14,235146240,3888,4626249012
123456789124357689126389457,26,144,4,58786560,972,997250292
123456789124357689128345679,27,192,10,117573120,1944,2649236544
123456789124357689128356479,28,168,9,117573120,1944,2318867082
123456789124357689128359467,29,120,4,78382080,1296,1095439500
123456789124357689134258679,30,192,5,39191040,648,869683680
123456789124357689134268579,31,288,28,235146240,3888,7900690752
123456789124357689135268479,32,228,22,235146240,3888,6250718781
123456789124357689135278469,33,276,26,235146240,3888,7604258643
123456789124357689136258479,34,168,9,117573120,1944,2284590420
123456789124357689136278459,35,180,30,470292480,7776,9833024970
123456789124357689137268459,36,216,20,235146240,3888,5918022972
123456789124357689138259467,37,156,26,470292480,7776,8466321474
123456789124357689138269457,38,228,11,78382080,1296,2085113295
123456789124357689158267349,39,120,6,117573120,1944,1613192490
123456789124378569129356478,40,96,2,3265920,54,37222080
123456789124378569135279468,41,192,8,78382080,1296,1758335904
123456789124378569137245689,42,516,9,26127360,432,1595569911
123456789124378569157268349,43,168,6,39191040,648,756792918
123456789147258369159267348,44,120,2,4354560,72,59305360
-------------------------------------------------
sum:11352,416,4741632000,78400,110817071884

60713 out of the 85184=44^3 combinations of 3 gang44-members
can be joined to form a valid 9*9 sudoku.




realizations of the 44 gangmembers as the first band of a sudokugrid:

123456789456789123789123456231674895568291374947538261812945637675312948394867512
123456789456789123789123465271834956395261874648597231812345697567912348934678512
123456789456789132789123546271894653564231897398675214812347965635912478947568321
123456789456789123789123645231574896865291437947368251512837964394612578678945312
123456789456789231789123645261834597837295164594617328942561873318972456675348912
123456789457189623689723154271894536534261897896375241312547968948612375765938412
123456789456789123789132465231945876675218394948673251512864937397521648864397512
123456789456789123789213465231874596564921837978365241812637954345192678697548312
123456789457189263986327514271893645594261837368574921812735496749612358635948172
123456789457189623689723514261974358975238146348615297792341865534862971816597432
123456789456789123789132564261945837937218645548367291312674958894521376675893412
123456789457189623689723415271834596394265178568917234842691357936572841715348962
123456789456789132789231456231947568865123974947568213312674895598312647674895321
123456789457189623896327451281673594564298137379514268632941875715832946948765312
123456789456789123798132546271643895689215437345897261912378654564921378837564912
123456789457298613896317245241863957578921364639574821312785496964132578785649132
123456789456789132789213654231574968865921473947368215612895347574132896398647521
123456789456789132789321564231567948894213675567894213312645897948172356675938421
123456789457189632689723514261974358975238146348615297792341865514862973836597421
123456789457189263968327514281563497374291658596874321812735946749612835635948172
123456789457189632698732541261547398785293164349618257572964813814325976936871425
123456789457189236689372451241635897895247163376918524512763948934821675768594312
123456789457189236968327514271863495584291673396574821812635947649712358735948162
123456789457189623869273451241637598785921346396845217612394875538712964974568132
123456789457189263689273415261938574745621398398547126832764951516392847974815632
123456789457189263689273154271835946945621378368947521512364897894712635736598412
123456789457189236869327514271893645685241973394765821512638497746912358938574162
123456789456789132798231546261947358375128964984365217512874693839612475647593821
123456789457189632968237415271643958549821367386975241712564893894312576635798124
123456789457189236869372415281635974694217853375948621912863547546721398738594162
123456789457189236689273541241635978795821364368947125912364857874512693536798412
123456789456789123798213564231874956549621837687935241312547698864192375975368412
123456789456789123798312564231574896879261345564893217382945671915627438647138952
123456789456789123798231564231845697965127438847963215382674951514392876679518342
123456789457189263689732514231947658568213947794568321912674835375821496846395172
123456789457189236896237514261743895538921467749865123682374951314592678975618342
123456789457189236896372154281934675745268913369517428572643891914825367638791542
123456789456789123798213654231874596549621837687395241912547368864132975375968412
123456789457189263968327145271863954694275318385914627832591476546732891719648532
123456789456789231789312456261578394834291567597634128312867945948125673675943812
123456789456789123789231564231548976695127438847963215562374891314892657978615342
123456789456789123789231645231948576647125938598673214872564391315892467964317852
123456789457189263968372145241638957576294318389517426632945871715823694894761532
123456789456789123897231564231845697965127438748693215582364971314972856679518342

[Moschopulus]

I normalized the data from Gordon's 17s.

Red = Guenter's data from Gordon's 17s, Green = random grids.

There is definitely some correlation in the peaks.

[dukuso]

thanks. Yes that's the picture I wanted to see.
The correlation is bad news for us, since it
shows that a careful selection of certain
grids is not very likely to speed up the
search for 17s a lot.
That's my interpretation at least.

[Addlan]

thanks. Yes that's the picture I wanted to see.
The correlation is bad news for us, since it
shows that a careful selection of certain
grids is not very likely to speed up the
search for 17s a lot.
That's my interpretation at least.

Hi Guenter,

Using the Spearman's rank order correlation, the correlation coefficient is 0.903. The significance value is 0.000, suggesting that they are definately correlated with each other.

BTW, could you please tell me how do you find a 17 hints puzzle?

[dukuso]

[
BTW, could you please tell me how do you find a 17 hints puzzle?

ask Gordon !
I have 14, he 9000+ and mine were made from his.
I described my method some posts ago here

[gfroyle]

I have updated the page

http://www.csse.uwa.edu.au/~gordon/sudokumin.php

to reflect the current listing of 17-clue puzzles, and to provide a link to download the whole collection for your perusal...

Current status: 17273 distinct 17-clue puzzles...

I have stopped constructing 18-clue puzzles as I have over 5.6 million of them, and the supply seems effectively inexaustible..

Gordon

[dukuso]

wow, 17000+ . About 1000 per day, an estimated year to
find about 70% of them.
BTW. the list has been used for benchmarking in the sudoku
programming contest and in the paper by H.Simonis.
He only used the 450-list but is preparing an update...
I found 2 math-papers about sudokus so far:
http://www.icparc.ic.ac.uk/~hs/sudoku.pdf
http://arxiv.org/abs/cs.DS/0507053

Most of the 17s are easy to solve but some are very
hard for some computer-programs too.
Maybe this is also the best way to find the hardest sudokus:
take your 18-list and just run it through a solver
and filter the hard ones ? Maybe you should do this before
throwing them away ?
I think, there is not only a demand for 17-clue sudokus but
also one for the hardest sudokus. Many of the hardest known
so far are from the 17-list. But "hardness" is really hard to
measure !

Guenter.

[Dusty Chalk]

But "hardness" is really hard to measure !

"Difficulty".

And agreed -- I wouldn't mind going through that list of 18's, although I haven't even started programming my own solver yet.

[Wolfgang]

Unfortunately i dont have the time to try this myself, so i just want to post my idea, how you could determine, if a given grid contains a 16 clue sudoku:
Three numbers in the grid define a "subsudoku". You have only 27 cells and three numbers. Looking at three subsudokus (with all 9 numbers then), there must be at least two of them with maximum 7 clues for a 16 clue sudoku of the whole grid.
There are about a million possibilities for up to 7 clues for a subsudoku. It should be possible to check for all of them (in short computing time), which lead to a unique subsudoku. Save them. Do the same for the other two subsudokus.
For at least two of them you now have a list of subsudoku clues (hopefully not more than thousands). Now combine each two of two lists and verify, if they solve the 6 numbers subsudoku uniquely. If so, save the clues (and forget the rest).
With those ones now, reduce the 27 clues of the third subsudoku (with a backtracking algorithm) to a minimum. If there is a 16 clue, you should find it this way.
Of course i know, this is not a big help to find a 16 clue, but just a way to eliminate many grids.