Grid containing a 20 and no 19

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

Postby coloin » Tue Jan 31, 2006 3:05 pm

This thread should of course read "Grids which have an 19 but not an 18 ? "

No luck with an 18 in this grid [grid 3] ....despite many attempts.
Code: Select all
+---+---+---+
|146|328|975|
|785|196|342|
|329|457|861|
+---+---+---+
|493|561|728|
|218|973|654|
|657|284|139|
+---+---+---+
|564|839|217|
|832|715|496|
|971|642|583|
+---+---+---+


Ocean has found 2008 19 clue puzzles........utilizing all different clues.

No 18

Ocean - I used the 4 common clues plus the next common 8 in your stats but no 18. I think I need the next clue which occurs with 4+1 clues, and then the next which occurs most frequently with this 6.......up to 12 clues total. The 10 clue pseudopuzzle seems to have all the clues with a high frequency.

I cant explain the 5 at r1c9 occuring 105 times [its not in either pseudopuzzle][although its in one of the clue completions in the one with 19 clue completions]

We really dont have an idea which are the best 3 clues for checker to work on when it comes out revamped.!
coloin
 
Posts: 1638
Joined: 05 May 2005

Postby coloin » Wed Feb 01, 2006 2:29 pm

Ive analysed the two pseudopuzzles of grid 3 with the suexsf program

Not unexpectedly if you remove the 14 clues which are in one pseudo puzzle but not the other i.e

Code: Select all
the grid with clues from the 2/10 removed

146328.75.85196.4.3294.78614935.172821.9736..65..84139564839.17832.154.6971642583


"suexsf" comes up with 15 clues from the other pseudopuzzle 2/18. [and vice versa]

Code: Select all
suexsf ran3a.txt seed 10002
0 0 0 0 0 24 464  24.221056/ 10002

  12    3    9    6    3    6    0    5    5
   0    7    6   11   11   10    0    9    0
   7    5    9    8    0    4    7    8    5
   6    7    8    7    0    3    8   12    6
   6    8    0    7   13    5    8    0    0
   6   12    0    0   16    8    9    9    8
   7    9    8    3    8    8    0    4    5
  15    3    9    0    8    6   13    0    7
   4    5    1    8    7    7   11    9   11
step:1  best:r6c5 worst:r1c7............

best clue is r6c5...16 of the 24 22s generated had this clue. Note only some of the clues are prominent....more would be prominent if you had a higher "seed". The clues become more prominent as the best clue is fixed at each step.....

Pseudopuzzle for reference
+---+---+---+
|1..|..8|...|
|...|.9.|...|
|.2.|...|.6.|
+---+---+---+
|.9.|...|.2.|
|...|.7.|...|
|...|.8.|1..|
+---+---+---+
|.6.|...|..7|
|8..|..5|4..|
|..1|6.2|...|
+---+---+---+

step:1  best:r6c5 worst:r1c7
step:2  best:r8c1 worst:r2c1
step:3  best:r4c8 worst:r2c7
step:4  best:r8c7 worst:r2c9
step:5  best:r9c4 worst:r3c5
step:6  best:r3c8 worst:r4c5
step:7  best:r9c6 worst:r5c3
step:8  best:r2c5 worst:r5c8
step:9  best:r3c2 worst:r5c9
step:10  best:r5c5 worst:r6c3
step:11  best:r7c9 worst:r1c5
step:12  best:r1c6 worst:r6c4
step:13  best:r1c1 worst:r2c6
step:14  best:r6c7 worst:r7c4

0 0 0 5429 27235 85973 112508  21.868101/ 320064

116237   39583     7715   10013     0     116369      0       11045 13083
   0     20007     13626   2548   118557    0         0       16944   0
19801    117889    10425  10459     0      8565       6221   118634  2719
14042    42906     23859  8838      0       2043      5575   118570  7155
2024     24147       0     9800   117877    12922     4731     0      0
7477     43934       0      0     117734    12689    115724   34390  18041
39628    46117     39760    0     12635     10327      0      7733  117851
118410   16817     4421     0      8052     30053    118479     0    4245
27164    20693     32849  118469   9322    118498     11779   1698   13366
step:15  best:r7c2 worst:r7c7

Im not sure you can pay much attention to the order which the clues come out of the hat.........it depends very much on the first clue


These two pseudos - and many of the other 19 puzzles are from different "regions" of a grid.
coloin wrote:I do this by finding the 14 or 15 best clues by individually scanning the 9 text files of this grid where each file has one clue number removed - this forces the grids to be generated over one region........


It is fairly easy to visualize the region of 17 clues in the SF grid where the 17 clue puzzles originate........but in "grid 3" with many 19s and no 18s Im struggling to get a mental picture of what a "region " looks like !

A "region" perhaps is a set of identical clues eg 14 which has a high number of clue completions, which in this grid is 14 plus 5 clues.
Code: Select all
+---+---+---+
|...|...|...|
|7..|.9.|...|
|...|...|.61|
+---+---+---+
|...|...|72.|
|.1.|...|...|
|.5.|.8.|...|
+---+---+---+
|...|...|...|
|83.|...|4..|
|...|6.2|...|
+---+---+---+ 14 clues =   248   clue completions with 5 extra clues


Ocean has found over 2000 19s - and the regions are interwoven around the grid.

The large number of 19s - especially as not even one clue is consistantly in these 2008 puzzles make me think there is an 18 lurking. Our statistical methods of highlighting the best clues are lost in the high number of 19s and therefore 20s and 21s.

The only other grid which was subjected to this much scrutiny was the MC grid or mosch 1 grid which had over 190 19s but no 18. This grid was miraculous as it had a large number of small unavoidables [MCN15]. Checker program was able to show there was no 18.......
http://forum.enjoysudoku.com/viewtopic.php?t=1527&start=0
http://www.csse.uwa.edu.au/~gordon/sudokupat.php?cn=6
coloin
 
Posts: 1638
Joined: 05 May 2005

Postby Ocean » Wed Feb 01, 2006 10:10 pm

coloin wrote:.......but in "grid 3" with many 19s and no 18s Im struggling to get a mental picture of what a "region " looks like !


As a suggestion for the mental picture of the 'landscape': It seems that many of the 19s occur on 'ridges'. The dense regions around the pseudos are connected by ridges, and there are also many other ridges in various directions. (Or, in terms of search: it's a lot faster to find new 'tops' by stepping slowly along a ridge, than to make big jumps in arbitrary directions.)

After some more running time, I now have 2500+ 19s. Also found one new 18-clue pseudopuzzle for this grid (2 solutions, 6 clue completions). This new pseudo has only one clue in common with both the two first, it has four clues in common with each of those two, and 11 of its clues are not found in any of the first two pseudos. Here are the three 18-clue pseudos shown together:

10: 000008900700000302020050000000060000008000054007200000060000200000705090000000000
06: 040300000000000000009050860000000700010000004600080000000000010802705000070000003
19: 100008000000090000020000060090000020000070000000080100060000007800005400001602000

The large number of 19s - especially as not even one clue is consistantly in these 2008 puzzles make me think there is an 18 lurking. Our statistical methods of highlighting the best clues are lost in the high number of 19s and therefore 20s and 21s.


There could be an 18, but hard to tell. Interesting that the third 18-pseudo is so distant from the two others.

Ocean - I used the 4 common clues plus the next common 8 in your stats but no 18. I think I need the next clue which occurs with 4+1 clues, and then the next which occurs most frequently with this 6.......up to 12 clues total. The 10 clue pseudopuzzle seems to have all the clues with a high frequency.


I'm not sure what exactly you mean here. I have not automized this specific way of counting, and doing it manually it's easy to get things wrong. There are now 272 sudokus in this category (containing those four clues). Maybe the simplest is just to list all those?
But for a start: The four clues (#6,20,56,69) are found in 272 19s. Adding #39 gives 223 19s with all five. Adding #49 gives 215 with all six. Adding #61 gives 184 19s with all seven.

And, now it may also be interesting to take the third pseudo into consideration.
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby coloin » Thu Feb 02, 2006 1:27 am

Wow ......more 19s and another pseudo.....
Yes the purpose in thinking about regions is to find the most dense "area" with 12 clues [realistic limit of 12 + 6 clue search].

I think probably there are no 18s around the original 2 pseudo-puzzles - otherwise we would have been led to them. So the 4 clues which intersect with the 2 pseudopuzzles pretty much diverge at the 5th clue.

Code: Select all
The four clues (#6,20,56,69) are found in 272 19s. Adding #39 gives 223 19s with all five. Adding #49 gives 215 with all six. Adding #61 gives 184 19s with all seven.

Yes thats what I need [5 more !] - these clues are from the 10 pseudo - it might give us more 19s if it doesnt yield an 18 !


I will see what the 3rd pseudopuzzle brings.

Im getting more convinced now there isnt an 18.....and the reason ?

Well I dare to suggest that there just isnt 18 clues which hit all the unavoidable sets.


Code: Select all
639241785284765193517983624123857946796432851458619237342178569961524378875396412

This grid is also thought not to have an 18
http://forum.enjoysudoku.com/viewtopic.php?t=1527&start=15
It was called the gr16 and it has a very low suexsf of 24.076200 [lower than the SF] MCN of 8 ! - I cant get an 18 in it either !
coloin
 
Posts: 1638
Joined: 05 May 2005

Postby Ocean » Fri Feb 03, 2006 9:40 am

coloin wrote:
Code: Select all
The four clues (#6,20,56,69) are found in 272 19s. Adding #39 gives 223 19s with all five. Adding #49 gives 215 with all six. Adding #61 gives 184 19s with all seven.

Yes thats what I need [5 more !] - these clues are from the 10 pseudo - it might give us more 19s if it doesnt yield an 18 !

I don't have a quick way of finding those extra five, but .... this is how those four clues distribute in the set of 19s:
Code: Select all
 500 0000
 201 0005
 320 0060
  97 0065
  85 0200
  34 0205
  29 0260
   5 0265
  77 8000
  14 8005
 342 8060
 180 8065
 168 8200
  80 8205
 255 8260
 283 8265

And: The list of those 283 containing all four clues (#6,20,56,69):
000008000000000340029000060090000020010070000000080100060009000800005400000602000
000008000000090002020000060000000700008000050000200100060800000030705400900600003
000008000000090002020000060000000700008000050000200109060000000030705400900600003
000008000000090002020000060000000700008000050000280100060000000030705400900600003
000008000000090002020000060000000700010000050000280100060000000800705400900600003
000008000000090002020000060000000708008000050000200100060000000030705400900600003
000008000000090002020000060000060700008000050000200100060800000030705400900000003
000008000000090002020000060000500700008000050000200100060000000030705400900600003
000008000000090002020050060000000700008000050000200100060000000030705400900600003
000008000000090002020400061000000700008000050000200000560000010030005400900000003
000008000000096000320000000000500700018000004000200100064000000000005090070000580
000008000000096040020000000000500700008000050000200100060000000030705400900000083
000008000000096040020000000000500700008000600000200130064000000030705090000000500
000008000000096040020000000000500700018000000000200100064000000030005096000000580
000008000000096040020000000000500700018000000000200100064009000800005006000000503
000008000000096040020000000003500000008000650000200100060000207800705000000000003
000008000000096040020000000003500000008070650000200100060000207800005000000000003
000008000000096040020000000400500000008000600000200030060000207030705000900000500
000008000000096040020000001400500000008000600000200030060000200030705000000000580
000008000000096040020050000000000700008000050000200100060000000030705400900000083
000008000000096040020050000003000000008000650000200100060000207800705000000000003
000008000000096040020050000003000000008070650000200100060000207800005000000000003
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000008000005000040020000001000060000008900054007200000060030200030005000000000580
000008000700000002020050800000060700008000050000200100060030000000705490000000500
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Ocean
 
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Postby Ocean » Fri Feb 03, 2006 9:48 am

coloin wrote:
Code: Select all
639241785284765193517983624123857946796432851458619237342178569961524378875396412

This grid is also thought not to have an 18
http://forum.enjoysudoku.com/viewtopic.php?t=1527&start=15
It was called the gr16 and it has a very low suexsf of 24.076200 [lower than the SF] MCN of 8 ! - I cant get an 18 in it either !
Here is a couple of 18s:
000040700080000000017000000100800006090000000400000200002070000000000308000096010
000040700080000090017000000100800006000000000400000200002070000060000008000390010
(found 40+ 18s in this grid).
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Postby Moschopulus » Fri Feb 03, 2006 11:44 am

Well done on finding an 18. This grid is called SFB by most people, I think.

Can you find a 17?
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Postby coloin » Fri Feb 03, 2006 12:59 pm

Well done on that too......it should have an 18 by rights....and it does.

Moschopulus wrote:.......This grid is called SFB by most people, I think.
Can you find a 17?


I dont think it is the SFB.....here is one of the 3 17s in the sfb
dukoso wrote:sfb: .......1..2..5.....4.......8..1.9.........2.....3......6..7.5.23.....4..1...8....

it's the only grid with a proven 17 and no 2-unavoidables

This gf16 grid was suggested by Gordon as being a candidate for a 17 but he couldnt find an 18 !- [ its the SF with a different B789]


Getting back to the "grid 3" ......which also should have an 18.......

thanks for the data

the 3rd pseudopuzzle didnt reveal any more 19s even when I removed 5 of what I deemed the least powerful clues...

Mosch - So how is checker coming along ?
Last edited by coloin on Fri Feb 03, 2006 9:06 am, edited 1 time in total.
coloin
 
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Postby Wolfgang » Fri Feb 03, 2006 1:02 pm

Moschopulus wrote:Well done on finding an 18. This grid is called SFB by most people, I think.

Now that you say that: this grid is called ssf (similar to strange familiar) and i have found 18's in it months ago. (sfb is a known 17-clue grid)
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Postby coloin » Fri Feb 03, 2006 1:31 pm

Thanks Wolfgang, it was a long time ago - and you did

Interesting comment as well

Wolfgang wrote:Though the program is still in construction and not fully automised, my approach for searching for low clue sudokus in given grids seems to be rather effective now, but it is very slow, ie needs days for one grid (on my notebook).
I tested it with three of the known 17-clue grids (sf, one of the twin grids and now the grid without unavoidables for 2 or 3 different digits and 3 known 17-clues, which - forgive me - i call NU23 now). In all of the grids i did find (known) 17-clues. Whereas in the first 2 grids i already found one in the region of the 2nd 19-clue that i detected directly with weighted random clue sets, i needed about 20 19-clues, until i had the region of the 17-clues in NU23. With a region i mean, that 2 sudokus belong to the same region, when they have say 14 clues in common.
In ssf (similar to strangely familiar) i only found 16 18-clues in two regions. But the probability that the program does not find an 18 clue is higher than for a 17 clue, because normally there are much less 19- and 20- clues around it.
A 16 clue should be very attractive for my method with all the 17-,18- and 19-clues around. So it is unlikely for me that one of the grids would contain one.

My current impression is the following:
- there are less grids containing a 17-clue than i thought
- it is unlikely that a grid has two 17-clues in different regions (are there any in the known grids with multiple 17-clues?)
- then it does not make much sense to search in known 17-clues grids
- we cannot say if a grid is promising without making a rather deep search. Criteria like the number of unavoidables, unique pairs, random clue set results, minimum number of clues for unique 3-rookeries are not more than a hint. There are grids with poor such properties that contain 17-clues and others that look much better that dont seem to have one.


Any thoughts why we cant find an 18 in "grid 3"

Wolfgang wrote:As i posted some time ago, my idea for searching for low clues in a given grid was, first to try to find low clue sets that make all 3-rookeries unique. Now i implemented a simple method for this (starting with 12 or 18 randomly chosen cells and dropping and adding numbers then, based on how much they contribute to make 3-rookies unique) and tested it with the 2 gfroyle grids.
It was easy to find 14 and 15 clue sets. The second ("new") grid seemed to be slightly better, i also found 3 13 clue sets under about 100 less 16 clues each (none in the first). With the 13 and 2 of the 14 clue sets i tried to continue to make the (126) 4- and (84) 6-rookeries unique, but i needed at least 19 clues for the latter (ending up with 22 clues).
The obvious problem was that with the best 15 clue set i got this way, only 14 of the 84 6-rookeries were unique and no number could improve that much. (Compare: in gfroyles nr 1000 there was a 15 clue set for the 3-rookies, 41 of the 6-rookies were unique and one number made them all unique).
But maybe my method can be of some worth, when it can be improved to be faster (and is run on a faster machine than my notebook).


Please could you try this or other methods on our grid 3 !

We really dont know which clues combine the best !

Cheers[quote]
coloin
 
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Postby Wolfgang » Fri Feb 03, 2006 2:45 pm

Sorry, but i already had tried my old program for half a day, but only found 2 19's in that time, so Oceans program seems to be much faster. As you stated, the problem is that there are so much good regions in that grid, so my method converges very slow to a 19-clue (where it starts to search more intensively). The only chance i see is to run CHECKER and wait until it has finished. I dont know, how fast Moschopulus' solver is, maybe he should give gsf's solver a try.
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Postby gsf » Fri Feb 03, 2006 3:08 pm

Wolfgang wrote:I dont know, how fast Moschopulus' solver is, maybe he should give gsf's solver a try.

I have checker coded with my solver
it runs in 2 modes
the first mode is a fast(er) sweep not guaranteed to find all solutions
its based on properties exibited by most random puzzles
and basically prunes the solver before it backtracks
if the first sweep fails it goes to the second mode with full forward check backtrack enabled
both have performed better than the original code in ranges 19..25
looking for < 18 tends to be overwhelmed by the puzzle generator
and washes out any solver gains

name a grid and checker command line that I should try
if it does well I'll send the modified code to M
gsf
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Postby Wolfgang » Fri Feb 03, 2006 3:18 pm

Sounds good:) Im not familiar with the checker commands, we're looking for an 18 clue in the grid on the top of this page.
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Postby gsf » Fri Feb 03, 2006 3:24 pm

I forgot to mention another checker modification

the fast solver sudocoup builds grids via a heavyweight move() function
that amortizes FN constraint computation over each move
for most random puzzles by the time the last clue is placed by move() the puzzle is solved

I modified checker to keep a stack of grids starting with the empty grid at level 0
each level i adds one clue via move()
a move to level i+1 copies the grid state from level i and makes the move()
the grid state has no pointers so C struct assignment does an efficient copy
the state is 492 bytes, which, when combined with the amortization, compares
favorably with the 729 item init loop in Guenter's DoesPuzzleHaveUniqueSolution() solver
gsf
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Postby coloin » Fri Feb 03, 2006 5:36 pm

Great - the more on the case the better

Yes - I am awaiting the definitive "checker" on this one

Perhaps the more appropriate link for disscussing checker is
http://www.setbb.com/sudoku/viewtopic.php?p=4352&mforum=sudoku#4352

and an explanation of checker is on
http://www.maths.nuim.ie/staff/gmg/sudoku

C
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