The New Sudoku Players' Forum

[dobrichev]

2 more 39s

Code: Select all

........1..2.1345..31.452.6..3.576.2.2638.5.77.........18...7..2.7.381.436..7182.
........1.12.34.5..561.23....1...47..874.31.55.47.1.63.652.873..7.......2.83.75.6


The list of known irreducible pseudopuzzles grows. 5 41s are published here.
All five 41s have some common properties:
- 43 solutions;
- 2 "solvable" cells;
- complementary 40-clue non-minimal pseudopuzzles for all 43 solutions have 67 solutions (actually i'm not sure - lost the source code);
- share the same pattern, including the solvable cells.

The number of known 40s exceeds 1200.

MD

[eleven]

When you follow dobrichev's link above, you can see, that to my big surprise blue has published 72 new 39's (see the list at the end of the first post).

Going down from the 72 new 39's i got 31710 37's with an average weight of only 8.2. Only 2467 have a weight greater 12, which was the average of the derived 37's of the former known 39's.
From the dobbed 37's i have almost 2.9 mio puzzles with weight > 12, which i never expanded with {-2+2}. So i would not have found these new 39's for a very long time, even if i had found 37's within {-2+2} of these 31710 37's.

After all this suggests, that my 300 39's estimate is too low. On the other hand it makes my 39 conjecture (there is no minimal 40 clue) more probable, because blue must have scanned a huge set of high clues for finding the new 39's.

[dobrichev]

http://software.intel.com/sites/products/parallelmag/Parallel_Mag_Issue4.pdf, pages 20-25

[eleven]

Thanks for the link.

Poor Havard, he has done good work in 2006. And now, 4 years later they write such an awkward article.

I manually copied the 3 puzzles. What i got were 2 multisulution puzzles and an invalid one.

[m_b_metcalf]

In fact, the 'The three 39 minimal solutions' are two 38-clue puzzles with multiple solutions and a 39-clue invalid puzzle in which, if the clue at r7c9 is removed, another multiple-solution 38-clue puzzle is lurking.

Is someone going to tell them?

Regards,

Mike Metcalf

[dobrichev]

blue posted 2 lots of new 39s (101+18) here.

[dobrichev]

Recent lists with known 336 39's, 121038 38's, 2508 multi-solution 40's and 5 41's are available for downloading from https://sites.google.com/site/dobrichev/sudoku-puzzle-collections

Cheers,
MD

[eleven]

Thanks again, i missed these breaking news.
I have updated the list and added an intro to the first post, which also points to your thread on the programmers forum and your homepage.

[dobrichev]

The puzzle below is the only new 39 found within {-3+3} of the previously known 336 39's.

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.....1..2..3.2..4..5246..31..7....1..31.874.558..14.73.28.7..54.7...23..3.584..27


edit: only 1 new 39, erased non-minimal "twins". ...bugs again...

[eleven]

Congratulations on a new one !

I added it to the list, but I dont have the tool any more (unpacked) to calculate the weight .

[dobrichev]

337+3 = 340

Code: Select all

........1..2.13.4.14..56237.1..75.82.8.3..1..2.5.81374.2..3...84...687238....74..
........1.12.34....3561.247..7.8..6..2.4....8.58.6.472.731..8.4.81.437262..8...1.
........1.12.34....356.1247..7..8.6..2.4....8.58..6472.731..8.4.81.437262..8...1.


There are no new fatties within the {-4+4} vicinity.
The newcomers live on its own {-4+4} island.

[GouinJP]

software.intel.com/sites/default/files/parallel_mag_issue4.pdf,
pages 20-25

Did you see in the puzzle figure 1,
the two numbers 6 in the same column?

JPS

[Serg]

Hi, dobrichev!

337+3 = 340

Code: Select all

........1..2.13.4.14..56237.1..75.82.8.3..1..2.5.81374.2..3...84...687238....74..
........1.12.34....3561.247..7.8..6..2.4....8.58.6.472.731..8.4.81.437262..8...1.
........1.12.34....356.1247..7..8.6..2.4....8.58..6472.731..8.4.81.437262..8...1.


There are no new fatties within the {-4+4} vicinity.
The newcomers live on its own {-4+4} island.

Congratulations with new found 39-clue minimal puzzles! Well done!
What is your method of search?

Serg

[coloin]

software.intel.com/sites/default/files/parallel_mag_issue4.pdf,
pages 20-25

Did you see in the puzzle figure 1,
the two numbers 6 in the same column?
JPS

Yes it is a shame to do all that programming and balls up the presentation !
he says he has found 3 new minimal 39s .....
And i see that some have already commented ....
except
The first two are both missing a 2 in r9c9 - but they are minimal.

Code: Select all

+---+---+---+
|...|.3.|...|
|..3|6.7|..1|
|6.4|.91|3.7|
+---+---+---+
|5..|..3|.24|
|74.|.62|5.3|
|..2|..5|71.|
+---+---+---+
|2.5|716|4..|
|4.6|.29|175|
|...|...|..2|
+---+---+---+

+---+---+---+
|...|.3.|...|
|..3|6.7|..1|
|6.4|.91|3.7|
+---+---+---+
|5..|..3|.24|
|14.|.62|5.3|
|..2|..5|17.|
+---+---+---+
|2.5|176|4..|
|4.6|.29|715|
|...|...|..2|
+---+---+---+


the third effort is invalid and i cant easily see the 39
As to the question of whether they are new ...
I will check - and indeed they are not new ....one of them is an isomorph of one of havards original 39

C

[dobrichev]

Hi, dobrichev!

337+3 = 340

Code: Select all

........1..2.13.4.14..56237.1..75.82.8.3..1..2.5.81374.2..3...84...687238....74..
........1.12.34....3561.247..7.8..6..2.4....8.58.6.472.731..8.4.81.437262..8...1.
........1.12.34....356.1247..7..8.6..2.4....8.58..6472.731..8.4.81.437262..8...1.


There are no new fatties within the {-4+4} vicinity.
The newcomers live on its own {-4+4} island.

Congratulations with new found 39-clue minimal puzzles! Well done!
What is your method of search?

Serg

Thank you, Serg.

Nothing special in my method. I found that the vicinity search algorithm I used for hard puzzles more than one year ago, performs very well on high-clue puzzles. {-4+1,2,3,4} search on a single 39-clue puzzle executes for about 400 to 800 seconds on a regular PC.
I closed the existing 39s with no new discoveries but with some distant 38-clue stuff.

Code: Select all

Clues   puzzles
36      22306
37      16680
38      2626
39      337

I searched {-3+4} around the 38s and found the second and the third puzzles in the list. The first arose latter at < {-4+4} to the other two.
In the next days I'll try moving a bit farther.

Lars Petter Endresen, one of the players in Havard's team that discovered the first 39-clue puzzle, motivated me to do in this exercise. (Motivation has nothing in common with the discussed above publication)