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 dobrichev
 Joined: 18 Dec 2009  Posts: 28  :   Items 

Posted: Thu Mar 25, 2010 8:53 pm Post subject: More data 


Here is the status at the moment
New data
Data for the known 37 and 38clue solution grids are available.
The updated raw data for the following graphics are in these files:
The islands
Each Sudoku grid contains 36 2digit unavoidable sets of size 18 for each digit pair (1,2), (1,3)...(8,9).
Depending on the grid, such set may, or may not be split into unavoidable subsets of size: Code:  18
14+4
12+6
10+8
10+4+4
8+6+4
6+6+6
6+4+4+4

Respectively there are 84 3digit UA sets of size 36, up to one trivial 9digit UA of size 81.
Someone may want to calculate the probabilities for each of the combinations.
Regardless of the exact distribution, there is a trend some combinations of UA to exist in a grid more probably than others. This, at least parially, explains the existence of islands in the above graphics.
Finally, there is a difference between the trivial unavoidables for 2 and 3+ digits since latest require more than one clue to be solved.
Distribution of Solution Grids for known 17, 18, 37, 38, and 39clue puzzles
Here are some pictures representing the distrubution of the grids known to have nclue puzzles.
The smoothness of the proportion explains the flattening mentioned in the previous posts.
Grids with least UA
For the processed UA types (2digit UA of size 4 and 6, and 3digit UA of size 6) the top three grids are
Code: 
123456789456789132789213645275941368638527914941638257394175826517862493862394571 #minlex 777870326 3xU6 MCN8(70+11)
123456789456789231789231564234968175867125493915374826348617952592843617671592348 #minlex 1058269476 3xU6 MCN7(65+16)
123456789456789231789231564218593647347628195695174823531962478864317952972845316 #minlex 1057946268 1xU4+2xU6 MCN8(67+14)
123456789456789231798213645239174856574628913681395427367841592815962374942537168 #minlex 1074133462 2xU4+1xU46 MCN8(74+7)

where
minlex is the zerobased index of the grid in the minimal lexical row catalogue
MCN is the Maximum Clique Number
in the parenthesis the first number is the cells covered by the UA sets forming one of the cliques.
Cheers,
MD
Last edited by dobrichev on Tue Apr 06, 2010 11:52 pm; edited 1 time in total 

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 dobrichev
 Joined: 18 Dec 2009  Posts: 28  :   Items 

Posted: Fri Mar 26, 2010 2:05 pm Post subject: Source Code 


The source code in C++ used for grid processing is here. 

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 dobrichev
 Joined: 18 Dec 2009  Posts: 28  :   Items 

Posted: Wed Apr 07, 2010 12:46 am Post subject: Update 


With cooperation of Ano1 the data for a collection of 18clue puzzles is available. The above pictures are updated and a link to the tabular data for 18's is added. All 4 of the extreme grids published in the previous post have 18clus puzzles.
The gridsets for 17's and 39's are updated to reflect the recently discovered puzzles (49151 and 65 resp.).
There is one new picture for the proportion between the solution grids of the known extremeclue puzzles and their less extreme adjacent gridset.
A solution grid known to have 18clue puzzle is more likely to have 17clue one if it has less unavoidable sets of size 4. No similar correlation for the highclue puzzles.
Finally, the second of the extreme grids in the previous post has been scanned for 17's w/o success
Code:  ....
460799/460800 (3131176643 puzzles gen'd; 0 uniques found); ETTF 0d 00h 00m
Time spent in solver: 9.7% (30195 puzzles / second).
Finished. Total computation time was 12d 09h 00m.
A full search was done (all puzzles were enumerated).
No 17puzzle exists for this grid (all puzzles were solved).
No pseudo16puzzle exists for this grid (all puzzles were solved).
Any puzzles or pseudopuzzles found were saved to
3_217puzzles.txt respectively 3_2pseudo16puzzles.txt. 
MD. 

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