Max number of clues 2

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

Postby ravel » Thu Aug 02, 2007 11:43 am

Then your 2off/2on must be about that fast as my 1off/1on:)

The steady 37 rate looks very promising. For me it seems only to be a matter of a few weeks, that it should move to an area with higher 38 density - high enough for a 39 (if there are such areas). Exciting.
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Postby Havard » Thu Aug 02, 2007 12:20 pm

ravel wrote:Then your 2off/2on must be about that fast as my 1off/1on:)

The steady 37 rate looks very promising. For me it seems only to be a matter of a few weeks, that it should move to an area with higher 38 density - high enough for a 39 (if there are such areas). Exciting.


Well, lets just say I have been accessing som pretty kick-ass resources... Problem is that I might lose that very soon, and then the progress will slow down intolerably...

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Belated congratulations

Postby Ocean » Fri Aug 03, 2007 10:11 pm

ravel wrote:Hey, another look and here it is:
Code: Select all
 +-------+-------+-------+
 | 3 1 2 | 6 7 . | . 5 4 |
 | 7 . . | 4 . . | . 3 6 |
 | . 4 6 | 5 . . | . . 2 |
 +-------+-------+-------+
 | . 7 1 | 3 . . | . 6 8 |
 | . 6 . | 2 . 7 | . . 3 |
 | . . 3 | . 6 . | . . . |
 +-------+-------+-------+
 | . . . | . 2 . | . 4 . |
 | 1 . 7 | 8 . . | . . 5 |
 | . 2 4 | 7 . 5 | . 8 1 |
 +-------+-------+-------+


Congratulations, ravel, on finding the (first) minimal 38! Nice job, Great find!
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Postby Ocean » Fri Aug 03, 2007 10:58 pm

Nice work on the max number of clues lately!
Havard wrote:
ravel wrote:Ah, i had this feeling at the end (with some 1000's 36's) too, that 1off/1on would never end for the 36's. But at the beginning the closure was reached for several times and i had to use 2off/2on to continue.
Now have you tried for the 38's, what i described for 37's above ?


About the 36, it seems to me that the collection needs a certain size before it will start expanding like that. Critical mass of sudoku if you like...:)

Interesting observations about closure and 'critical mass', when doing the 1-off-1-on search. However, I think that ONE starter is enough, if it is a right one, that is if it belongs to a huge-sized class. If it does, it will generate the whole class, when the 1off/1on is applied recursively (if computatonally possible, that is if the class is not too large). And it will find nothing outside its class. Of course, starting with a big set increases the chances that some of the starters belong to a huge class. And, such large classes might also be promising, with regard to finding even higher minimals being neighbours to some of the class members (this is guessing only).

Havard wrote:And I did try to go 2off/1on on the 38 (have 240 of them now), but this made no new 37.
Did anybody analyze ravel's minimal 38: How big is the class size (1off/1on) of the 37s that lead to (are neighbours to) this 38?

Havard wrote:While the 1off/1on on 36 can be exponential, the 2off/2on on the 37 delivers a steady 2000 new 37 every 4 hours.
Thanks for providing interesting statistics about distributions of these puzzles (and in effect their neigbourhoods)!
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Postby ravel » Sat Aug 04, 2007 4:26 pm

Ocean wrote:However, I think that ONE starter is enough, if it is a right one, that is if it belongs to a huge-sized class.
Of course, yes. But with my search method (always operating on sets of puzzles which i had derived with different methods) i could not see directly, which puzzles belong to the same 1/1 cluster.
Did anybody analyze ravel's minimal 38: How big is the class size (1off/1on) of the 37s that lead to (are neighbours to) this 38?!
I am off my computer for some time, but i think, a 2off/1on from this 38 only gives 2 37's (and 1/1 clusters of 37's are usually very small).
When Havard will publish his results, we will know a lot more. Possibly he also has 38's in his list, which dont have a single 37 in 2off/1on.
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Postby Havard » Sat Aug 04, 2007 9:14 pm

ravel wrote:When Havard will publish his results, we will know a lot more. Possibly he also has 38's in his list, which dont have a single 37 in 2off/1on.


I am getting a steady 10 37 per minute at the moment, so sometime next week I will have reached 100.000 and then we will see how many 38 turn out. (I expect around a thousand). The elusive 39 might then decide to pop up, or it might not... Either way I'll publish the 38's.:)

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Postby Mauricio » Sat Aug 04, 2007 9:34 pm

Havard wrote:I am getting a steady 10 37 per minute at the moment

Are you using a general 2off/2on? It seems that sudokus with high number of clues have at least one row or column without clues. Could this optimize the rate finding new 37's?
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Postby Havard » Sat Aug 04, 2007 9:36 pm

Mauricio wrote:
Havard wrote:I am getting a steady 10 37 per minute at the moment

Are you using a general 2off/2on? It seems that sudokus with high number of clues have at least one row or column without clues. Could this optimize the rate finding new 37's?


Yes, I have noticed that too, but I would not risk adding that restriction, since I guess noone knows if this applies to all 37, so yes, a very general 2off/2on.:)

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Postby Havard » Tue Aug 07, 2007 9:43 am

Mauricio wrote:Are you using a general 2off/2on? It seems that sudokus with high number of clues have at least one row or column without clues. Could this optimize the rate finding new 37's?


A little look through the list of 38 revealed that not all had one empty row or column:

Code: Select all
. . 7|1 . 4|9 . 6
. . .|. 6 7|. 8 4
4 . 6|. 8 9|1 7 .
-----+-----+-----
. . .|. . .|. 9 .
2 . 5|. 9 8|. 1 .
. . 9|. . .|. . 8
-----+-----+-----
5 . 2|. 7 6|8 4 1
6 . 4|8 1 2|7 5 .
. 7 .|. . .|. . .


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Postby Havard » Thu Aug 09, 2007 7:40 pm

The results are out:

http://sudokuarchitect.com/forum/viewtopic.php?p=6677#p6677

No new 39. I even did a 2off/3on on that list. Nothing.

Not giving up, but it sure is proving hard to find...:)

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Postby ravel » Thu Aug 09, 2007 8:13 pm

Congratulations Havard,

on finding 1000 times more 38's than i in such an amazing short time:)
I hope, the next run will reveal a 39 also. For the time you provided a lot of stuff to study for all who are interested in properties of high clue puzzles.

After looking at the ER for the first 100 the average seems to be around 7.5, so your collection also should be interesting for new advanced solving techniques.
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Postby RW » Thu Aug 09, 2007 9:16 pm

Superb work Håvard!

Seems that (unlike low clue puzzles) these high clue puzzles are completely independent from the amount off 2-digit unavoidables in the solution grid. The 952 known 38s come from 599 different solution grids with an average amount of 2d-unavs of 55.3 (55.5 for randomly generated grids). Makes me wonder how many of all solution grids have 38s in them. It's a shame we don't have any realistic methods for full searches on grids...

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Postby Havard » Thu Aug 09, 2007 11:09 pm

thanks!

ravel wrote:After looking at the ER for the first 100 the average seems to be around 7.5, so your collection also should be interesting for new advanced solving techniques.


cool, let me know if you find any worthy of your great list!:)

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Postby daj95376 » Fri Aug 10, 2007 12:29 am

Havard, This is probably old news, but I find it interesting.

Of the 951 puzzles listed in the SA forum, 944 of them have only eight distinct values among the givens. Now, this may just be an offshoot of the way they were generated, but maybe not.

BTW, With one value missing among the givens, your puzzles have some interesting Templates and Fish present.
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Postby ravel » Fri Aug 10, 2007 12:59 pm

As i expected, there are some puzzles in Havard's list, that dont have a minimal 37 within 2off/1on. The first one is #324:
Code: Select all
.7.6.....9...786..4.69..8.7...5.9..114..865..5...1...82.5..7...6148.27.578.1.52.6
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