The hardest sudokus (new thread)

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

Re: The hardest sudokus (new thread)

Postby denis_berthier » Mon Feb 28, 2022 2:46 am

Hi Mith,
Great results.
Great examples also of the SER problem with morphs.

mith wrote:Speaking of correlation between SER and clues...

I can't see anything related to this correlation. 26 or 27 clues = 64.7% of all the minimal puzzles in unbiased stats.

My Macs are busy on other calculations, but I'll rate (wrt BpB) all these new 11.9 or 11.8 puzzles later.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Mon Feb 28, 2022 3:07 am

.
BTW, the new 11.9 has "only" 209 candidates after Singles and whips[1].
Any search strategy for finding the highest SER that relies on additional pre-filters may fail to find some of the highest.
The recent findings showed this has been the case with adding some criterion related to the q1 or q2 ratings.
But it'd also be the case if one keeps only puzzles with too high numbers of candidates as starting points for proximity search.
Last edited by denis_berthier on Mon Feb 28, 2022 10:44 am, edited 2 times in total.
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Re: The hardest sudokus (new thread)

Postby champagne » Mon Feb 28, 2022 7:52 am

mith wrote:Speaking of correlation between SER and clues...
.....

The new 11.9 is 26c, goes up to 29c with singles, and is pretty much obliterated by "Thor's Hammer".


Hi mith,

Great job. My last update of my own data base is now 2 years old.
From what I know of Sudoku Explainer, to produce such high ratings with more clues, you must have a highly interleaved system. This is usually linked to an exotic pattern.

With so any fresh stuff, I intend to mark a pause in what I am doing an to scan your (an others) new findings.
Do you have a summary of all 11.x up to date somewhere?

BTW, I have also to update my list of exotic patterns with the last published

And surely, we have no correlation between the number of candidates and the rating.
No need to refer to statistics, all of us know that the 17 clues and the 18 clues have no very high ratings, although they have big number of candidates.

EDIT I checked my last data base of potential hardest I can add that no 19 had been found at that time with a rating >=11.0
and as far as I know, the main criteria for fresh seeds for a vicinity search has been when I worked on this topic the SER of old grids.
Last edited by champagne on Mon Feb 28, 2022 3:29 pm, edited 2 times in total.
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Re: The hardest sudokus (new thread)

Postby denis_berthier » Mon Feb 28, 2022 9:03 am

champagne wrote:And surely, we have no correlation between the number of candidates and the rating.
No need to refer to statistics, all of us know that the 17 clues and the 18 clues have no very high ratings, although they have big number of candidates.

That's where some basic knowledge of statistics could help you avoid such false claims.
The mean number of candidates for the 17s (even after eliminating those that are solved by whips[1]) is much lower than those presented above.
Open the most elementary book of stats to learn what "mean" means.

To be more precise, one has (not taking into account the 17s that are in W1, for which nb-cands is 0)):
Code: Select all
mean-nb-cands= 118.30        sd-nb-cands= 66.30
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Re: The hardest sudokus (new thread)

Postby hendrik_monard » Mon Feb 28, 2022 1:35 pm

mith wrote:Speaking of correlation between SER and clues...

Meet 11.9 #10 (and friends):

Hi mith,

Fantastic finding. Congratulations.
So my forecast of September 30th (see http://forum.enjoysudoku.com/post310478.html#p310478 ) was not so unrealistic after all.
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Re: The hardest sudokus (new thread)

Postby hendrik_monard » Mon Feb 28, 2022 4:22 pm

mith wrote:Thanks; I think this one may be somewhat fragile in terms of morph. The three other minimals of the 30c are 11.8 after being minlexed. I'll have to try maxlex at some point.


Hi mith,
I calculated the SER of the canonical isomorph of your new 11.9, and got the following result:
........1.....2.......3..45..6.......71.8....23..67..8.827..1..6...23...7.381.6.. ED=11.9/1.2/1.2
98.76.5..7.4.5......6......5.8..7.4..79.45.6..6.98.......8.........9.3.2......4.. ED=11.8/1.2/1.2
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Re: The hardest sudokus (new thread)

Postby mith » Mon Feb 28, 2022 4:41 pm

denis_berthier wrote:.
BTW, the new 11.9 has "only" 209 candidates after Singles and whips[1].
Any search strategy for finding the highest SER that relies on additional pre-filters may fail to find some of the highest.
The recent findings showed this has been the case with adding some criterion related to the q1 or q2 ratings.
But it'd also be the case if one keeps only puzzles with too high numbers of candidates as starting points for proximity search.


Indeed, my previous q2 filters would have easily missed this one (49386 q2, 46752 q1).

(The correlation comment was just that the new 11.9 is 26c, expandable to 30c, vs. the 21c-23c previously known ones. The higher clue counts were just not well explored previously.)

champagne wrote:Great job. My last update of my own data base is now 2 years old.
From what I know of Sudoku Explainer, to produce such high ratings with more clues, you must have a highly interleaved system. This is usually linked to an exotic pattern.


Yes, the initial breakthrough on the high clue front was finding the trivalue oddagon pattern ("Thor's Hammer"), pointed out by marek previously in this thread. Essentially all of the high clue puzzles found have shown some variant of the pattern, and there have been a huge number of them from that initial seed.

In all cases I've looked at, there is a pattern of 6 digits in three boxes (after basics), one of which sees the other two, such that the empty cells span all three rows and columns, along with a fourth box (completing the rectangle of boxes) with 4 or 5 digits, such that some completions of the fourth box are impossible due to the parity of the permutations of missing digits. It shouldn't be all that hard to search for in existing puzzles, I just haven't written code to do it yet. It may also be possible to use the pattern as a starting point for generating puzzles, vs. neighborhood searching on existing puzzles.

Aside from the trivalue oddagon "exotic" pattern, there have been some other more specific non-3-colorable patterns discovered (shye's Patto Patto pattern being the one that comes to mind), so a generalized search for patterns with chromatic number 4 could be fruitful.

With so any fresh stuff, I intend to mark a pause in what I am doing an to scan your (an others) new findings.
Do you have a summary of all 11.x up to date somewhere?


I have been planning to get an update posted soon anyway. I still need to find some time to process jovi_al's two puzzle batches (a bunch of 19c puzzles, including some new 10.X, and a large collection of DJE puzzles as yet unchecked), as well as the pattern game. I think it may also be wise to let the neighborhood search iterate a bit longer with the new finds - I woke up this morning to a new batch of 139 11.8s (!), which more than doubles what was in the database. (I'll post those shortly.)

EDIT I checked my last data base of potential hardest I can add that no 19 had been found at that time with a rating >=11.0
and as far as I know, the main criteria for fresh seeds for a vicinity search has been when I worked on this topic the SER of old grids.


The high for 19c remains at 10.5 (three puzzles using gsf minlex, though I am aware of at least one coloin puzzle which is a 10.5 with the right morph). When I publish an update, I will include any 10.2+ from 19c and 35c-36c, since no 11s have been found there. (Edit while typing - I hadn't checked in a while, but I did finally generate some minimal 37c, two of which are skfr 10+. I'll have to rate those as well.)
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Re: The hardest sudokus (new thread)

Postby mith » Mon Feb 28, 2022 4:43 pm

hendrik_monard wrote:
mith wrote:Thanks; I think this one may be somewhat fragile in terms of morph. The three other minimals of the 30c are 11.8 after being minlexed. I'll have to try maxlex at some point.


Hi mith,
I calculated the SER of the canonical isomorph of your new 11.9, and got the following result:
........1.....2.......3..45..6.......71.8....23..67..8.827..1..6...23...7.381.6.. ED=11.9/1.2/1.2
98.76.5..7.4.5......6......5.8..7.4..79.45.6..6.98.......8.........9.3.2......4.. ED=11.8/1.2/1.2


This doesn't surprise me; I ran a few more morphs, and it was essentially 50-50 on whether it rated 11.9 or 11.8. I'm going to take a close look at these puzzles to see what exactly is going on with the rating.
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Re: The hardest sudokus (new thread)

Postby mith » Mon Feb 28, 2022 4:46 pm

Both 37c puzzles rate at 10.2 SER:

Code: Select all
...........1.23.45.24.5.6.3....75.8....38.7.6.8.6.435...6.47.38.7853.46.4..8..5.7  ED=10.2/1.2/1.2
...........1..2.34..5.3162.....2786..6.3.8..77.864.2.3..6.7438..4.8...728.72.34..  ED=10.2/1.2/1.2
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Re: The hardest sudokus (new thread)

Postby mith » Mon Feb 28, 2022 4:49 pm

This is the state of the max SER by clue count (for minimals), with the new 11.8s filling in at 25c and 28c:
Code: Select all
19c - 10.5
20c - 11.8
21c-23c - 11.9
24c-25c - 11.8
26c - 11.9 (morph dependent)
27c-30c - 11.8
31c - 11.6
32c - 11.5
33c - 11.3
34c - 11.1
35c-36c - 10.6
37c - 10.2
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Re: The hardest sudokus (new thread)

Postby mith » Mon Feb 28, 2022 6:27 pm

I've verified in the GUI that when all 11.8 steps are applied just before the 30th digit is placed, the 11.9s aren't needed.

At this point in the solve, there are four 11.8 steps; I'm assuming they are sorted by complexity, as the command line path seems to take the top step in each case.

Command line: -3r1c8, -3r2c1, single 3r1c1 and next steps are 11.9
Other 11.8s:
-3r1c7 (together with -3r1c8, this would just give the single again, so this is not responsible for the difference)
-2r1c8 (this gives a pointing pair which eliminates the next 11.8 candidate; after the single from the other elims, tops out at 11.8)
-2r5c7 (likewise, gives claiming which eliminates the previous 11.8)

When starting with the single, these two steps are present in the GUI, but now at 11.9. Presumably the 11.8 version is being pruned here, but that would have to be verified by disabling the pruning.

I have already verified this for one of the other minimals, but there must definitely be 11.9 morphs of all four. So either we still have 9 11.9s, or we have 13 (at least - the other 11.8s generated in this neighborhood should also be checked).

Pencilmark grid of the 30c, if anyone wants to investigate further:

Code: Select all
+-------------------+-------------------+-------------------+
| 3     256   4789  | 4569  4579  4589  | 2789  26789 1     |
| 1459  4569  45789 | 156   479   2     | 3789  36789 3679  |
| 19    269   789   | 169   3     189   | 2789  4     5     |
+-------------------+-------------------+-------------------+
| 8     459   6     | 23    459   14    | 34579 12379 2379  |
| 459   7     1     | 23    8     459   | 23459 23569 2369  |
| 2     3     459   | 1459  6     7     | 459   19    8     |
+-------------------+-------------------+-------------------+
| 459   8     2     | 7     459   6     | 1     359   349   |
| 6     1     459   | 459   2     3     | 5789  5789  479   |
| 7     459   3     | 8     1     459   | 6     259   249   |
+-------------------+-------------------+-------------------+
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Re: The hardest sudokus (new thread)

Postby mith » Tue Mar 01, 2022 12:56 am

Here are the 11.8s so far, 146 of them (25c-28c); expecting more, my scripts are going to have to play catch up again.
Code: Select all
........1.......2......34.5..2.......3..67..886.24.7...2648....3.87.6.4.47..3..8.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2.7.7624.8...8........48.3..7.6.247....73.8.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6...7.7624.8..28........48.3..7.6.247....73.8.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..2.....4.3..67..886.24.7...2648....3.87.6...47..3..8.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2.7.7624.8...8......4.48.3..7.6.247....73.8.6...  ED=11.8/1.2/1.2
........1.......2......34.5..3.6...7.7624.8..28......4.48.3..7.6.247....73.8.6...  ED=11.8/1.2/1.2
........1.......2......34.5..2..6....3..782..67.24.8...274.....3.68.7.4.48..3..6.  ED=11.8/1.2/1.2
........1.......2......34.5..2..6..4.3..782..67.24.8...274.....3.68.7...48..3..6.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2.7.7624.8...8.3......48....7.6.247....73.8.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6...7.7624.8..28.3......48....7.6.247....73.8.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2.7.7624.8...8.3....4.48....7.6.247....73.8.6...  ED=11.8/1.2/1.2
........1.......2......34.5..3.6...7.7624.8..28.3....4.48....7.6.247....73.8.6...  ED=11.8/1.2/1.2
........1.......2......34.5..2.......34.67..886.24.7...2648.....7..3..8.3.87.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..6.......7824.6..43..7.2.8.6..3..8.72.48....8.36.7.4.  ED=11.8/1.2/1.2
........1.......2......34.5..6.3..7..8247....37.6.8.4..43.8...762.......7.824.6..  ED=11.8/1.2/1.2
........1.......2......34.5..2.....4.34.67..886.24.7...2648.....7..3..8.3.87.6...  ED=11.8/1.2/1.2
........1.......2......34.5..6.....4.7824.6..43..7.2.8.6..3..8.72.48....8.36.7...  ED=11.8/1.2/1.2
........1.......2......34.5..6.3..7..8247....37.6.8....43.8...762......47.824.6..  ED=11.8/1.2/1.2
........1.......2......34.5..2..6....34.782..67.24.8...274......8..3..6.3.68.7.4.  ED=11.8/1.2/1.2
........1.......2......34.5..2..6..4.34.782..67.24.8...274......8..3..6.3.68.7...  ED=11.8/1.2/1.2
........1.......2......34.5..2.3.....346.7..886.42.7...2684.....7.....8.3.8.76.4.  ED=11.8/1.2/1.2
........1.......2......34.5..6....7..8247....37.6.8.4..43.8.2.76..3.....7.824.6..  ED=11.8/1.2/1.2
........1.......2......34.5..6....7..8247....37.6.8.4..43.8...762.3.....7.824.6..  ED=11.8/1.2/1.2
........1.......2......34.5..2.3...4.346.7..886.42.7...2684.....7.....8.3.8.76...  ED=11.8/1.2/1.2
........1.......2......34.5..6....7..8247....37.6.8....43.8.2.76..3....47.824.6..  ED=11.8/1.2/1.2
........1.......2......34.5..6....7..8247....37.6.8....43.8...762.3....47.824.6..  ED=11.8/1.2/1.2
........1.......2......34.5..2.36....347.82..67.42.8...27.4.....8.....6.3.6.87.4.  ED=11.8/1.2/1.2
........1.......2......34.5..2.36..4.347.82..67.42.8...27.4.....8.....6.3.6.87...  ED=11.8/1.2/1.2
........1.......2......34.5..2.3.....3.6.7..886.42.7...2684....3.8.76.4.47.....8.  ED=11.8/1.2/1.2
........1.......2......34.5..2.3...4.3.6.7..886.42.7...2684....3.8.76...47.....8.  ED=11.8/1.2/1.2
........1.......2......34.5..2.36....3.7.82..67.42.8...27.4....3.6.87.4.48.....6.  ED=11.8/1.2/1.2
........1.......2......34.5..2.36..4.3.7.82..67.42.8...27.4....3.6.87...48.....6.  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.275.3.5...82.6.67.8....2.563....38.7.2...  ED=11.8/1.2/1.2
........1.......2......3..4..5..6..7.6..285.323.57.8...5.73....3.68.2...78..6...2  ED=11.8/1.2/1.2
........1.......2......3..4..5..6..7.6..285.323.57.8...5273....3.68.2...78..6....  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.275.3.5...82.6.2563....38.7.2...6.7.8....  ED=11.8/1.2/1.2
........1.....2.34..2.3156.....5......4...6...78..6.......65.4.1..2.43..4..31..25  ED=11.8/1.2/1.2
........1.......2......3..4..2.356...5.72.8..73.6.82...8.5.....3.5.86.7.62..7....  ED=11.8/1.2/1.2
........1.......2......3..4..2.356...3.72.8...576.82...26.7.....8.5.....3.5.86.7.  ED=11.8/1.2/1.2
........1.......2......3..4..2.356.7.3.72.8...5.6.82...26.7....3.5.86...78.5.....  ED=11.8/1.2/1.2
........1.......2......3..4..2.356.7.3.6.82...5.72.8...875.....3.5.86...62..7....  ED=11.8/1.2/1.2
........1.......2......3..4..2.356...5.72.8..73.6.82...875.....3.5.86...62..7....  ED=11.8/1.2/1.2
........1.......2......3..4..2..56.7.3..682...5.27.8...87.5....3.58.6...62.73....  ED=11.8/1.2/1.2
........1.......2......3..4..2..56...5.27.8..73..682...87.5....3.58.6...62.73....  ED=11.8/1.2/1.2
........1.......2......3..4..2..56...5.27.8..73..682...8..5....3.58.6.7.62.73....  ED=11.8/1.2/1.2
........1.......2......3..4..2.356...3.72.8...576.82...26.7....3.5.86...78.5.....  ED=11.8/1.2/1.2
........1.......2......3..4..5.267...2378.6..7..3.5..8..78......86.5...253.6.2...  ED=11.8/1.2/1.2
........1.......2......3..4..5.267...2378.6..7..3.5..8.86.5....2.78.....53.6.2...  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.275...5.3.82.6.256.....38.7.2...6.7.8....  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2...7...8....8624.7...47.3..8.6.24.....83.7.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..2..6....3..78..6.7.24.8...274.....3.68.7.4.48..3..6.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2.7..624.8...8...7....48.3..7.6.24.....73.8.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6...7..624.8..28...7....48.3..7.6.24.....73.8.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2...7...8..4.8624.7...47.3..8.6.24.....83.7.6...  ED=11.8/1.2/1.2
........1.......2......34.5..2..6..4.3..78..6.7.24.8...274.....3.68.7...48..3..6.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2.7..624.8...8...7..4.48.3..7.6.24.....73.8.6...  ED=11.8/1.2/1.2
........1.......2......34.5..3.6...7..624.8..28...7..4.48.3..7.6.24.....73.8.6...  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2...7.3.8....8624.7...47....8.6.24.....83.7.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2.7..624.8...8.3.7....48....7.6.24.....73.8.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6...7..624.8..28.3.7....48....7.6.24.....73.8.6.4.  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2...7.3.8..4.8624.7...47....8.6.24.....83.7.6...  ED=11.8/1.2/1.2
........1.......2......34.5..3.6.2.7..624.8...8.3.7..4.48....7.6.24.....73.8.6...  ED=11.8/1.2/1.2
........1.......2......34.5..3.6...7..624.8..28.3.7..4.48....7.6.24.....73.8.6...  ED=11.8/1.2/1.2
........1.......2......34.5..6..7....8724.6..43..8.2...6..3..7.7.36.8.4.82.4.....  ED=11.8/1.2/1.2
........1.......2......34.5..2..6....34.78..6.7.24.8...274......8..3..6.3.68.7.4.  ED=11.8/1.2/1.2
........1.......2......34.5..6..7....8.24.6..43..8.2.7.6..3..7.7.36.8.4.82.4.....  ED=11.8/1.2/1.2
........1.......2......34.5..6.3..7..824.....37.6.8.4...824.6...43.8...762...7...  ED=11.8/1.2/1.2
........1.......2......34.5..6..7..4.8724.6..43..8.2...6..3..7.7.36.8...82.4.....  ED=11.8/1.2/1.2
........1.......2......34.5..2..6..4.34.78..6.7.24.8...274......8..3..6.3.68.7...  ED=11.8/1.2/1.2
........1.......2......34.5..6..7..4.8.24.6..43..8.2.7.6..3..7.7.36.8...82.4.....  ED=11.8/1.2/1.2
........1.......2......34.5..6.3..7..824.....37.6.8.....824.6...43.8...762...7..4  ED=11.8/1.2/1.2
........1.......2......34.5..2.36....347.8..6.7.42.8...27.4.....8.....6.3.6.87.4.  ED=11.8/1.2/1.2
........1.......2......34.5..2.36..4.347.8..6.7.42.8...27.4.....8.....6.3.6.87...  ED=11.8/1.2/1.2
........1.......2......34.5..2.36....3.7.8..6.7.42.8...27.4....3.6.87.4.48.....6.  ED=11.8/1.2/1.2
........1.......2......34.5..2.36..4.3.7.8..6.7.42.8...27.4....3.6.87...48.....6.  ED=11.8/1.2/1.2
........1.......2......34.5..6....7..82.4....37..68.4..438..2..6...37...7.842.6..  ED=11.8/1.2/1.2
........1.......2......34.5..6....7..82.4....37..68.4...842.6...438..2.76...37...  ED=11.8/1.2/1.2
........1.......2......34.5..6....7..82.4....37..68....438..2..6...37..47.842.6..  ED=11.8/1.2/1.2
........1.......2......34.5..6....7..82.4....37..68.....842.6...438..2.76...37..4  ED=11.8/1.2/1.2
........1.......2......34.5..6....7..82.4....37..68.....842.6...438....762..37..4  ED=11.8/1.2/1.2
........1.......2......34.5..6....7..82.4....37..68.4...842.6...438....762..37...  ED=11.8/1.2/1.2
........1.......2......3..4..5.267...2378.6...7.3.5..8.86.5....2.78.....35.6.2...  ED=11.8/1.2/1.2
........1.......2......3..4..5.267...2378.6...7.3.5..8..78......86.5...235.6.2...  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.275...5.3.82.6.67.8....2.56.....38.7.2...  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.2.5.3.7...82.6.2563....6.7.8....83.7.2...  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.275.3.5...8..6.67.8...22.563....38.7.....  ED=11.8/1.2/1.2
........1.......2......3..4..256.7....53.8..6.8..275.3.5.6......76.8...23.87.2...  ED=11.8/1.2/1.2
........1.......2......3..4..256.7....53.8..6.8..275.3.76.8...225.6.....3.87.....  ED=11.8/1.2/1.2
........1.......2......3..4..256.7....5..8..6.8..275.3.5.63.....76.8...23.87.2...  ED=11.8/1.2/1.2
........1.......2......3..4..256.7....5..8..6.8..275.3.76.8...225.63....3.87.....  ED=11.8/1.2/1.2
........1.......2......3..4..256.7....53.8..6.8..275.3.76.8....25.6.....3.87.2...  ED=11.8/1.2/1.2
........1.......2......3..4..256.7....5..8..6.8..275.3.76.8....25.63....3.87.2...  ED=11.8/1.2/1.2
........1.......2......3..4..2.356...3.72.8..75.6.82...875.....3.5.86...62..7....  ED=11.8/1.2/1.2
........1.......2......3..4..2.356.7.3.72.8...5.6.82...875.....3.5.86...62..7....  ED=11.8/1.2/1.2
........1.......2......3..4..5..6..7.3278.5...6.2..8.3.576....2.8.37....6.3.52...  ED=11.8/1.2/1.2
........1.......2......3..4..5..6..7.3278.5...6.2..8.3.576.....28.37....6.3.52...  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.275.3.5...8..6.2563....38.7.....6.7.8...2  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.2.5.3.7...82.6.67.8....2.563....83.7.2...  ED=11.8/1.2/1.2
........1.......2......3..4..3.56.7..5.3...8.62.87......5.......8672.5..73.6..2.8  ED=11.8/1.2/1.2
........1.......2......3..4..3.56.7..5.3...8.62.87......5..8....8672.5..73.6..2..  ED=11.8/1.2/1.2
........1.......2......3..4..3.56.7..5.3...8.62.87.....8672.5..2.5......73.6....8  ED=11.8/1.2/1.2
........1.......2......3..4..5.3..6..728.....36.5.7.8..83.7...652...6...7..28.5..  ED=11.8/1.2/1.2
........1.......2......3..4..3.56.7..5.....8.62.87......5.3.....8672.5..73.6..2.8  ED=11.8/1.2/1.2
........1.......2......3..4..3.56.7..5.....8.62.87......5.38....8672.5..73.6..2..  ED=11.8/1.2/1.2
........1.......2......3..4..3.56.7..5.....8.62.87.....8672.5..2.5.3....73.6....8  ED=11.8/1.2/1.2
........1.......2......3..4..5....6..72.8....36..57.8..837..2.65...36...7..82.5..  ED=11.8/1.2/1.2
........1.......2......3..4..5....6..72.8....36..57.8..837....652..36...7..82.5..  ED=11.8/1.2/1.2
........1.......2......3..4..5....6..72.8....36..57.8..837..2..5...36...7.682.5..  ED=11.8/1.2/1.2
........1.....2.34..2.3156.....5......4...6...78..6.......651..1..2.43..4..3...25  ED=11.8/1.2/1.2
........1.......2......3..4..5.367...387..2...6.82.5...27.8.....5.6.....6.3.57.8.  ED=11.8/1.2/1.2
........1.......2......3..4..325.6...57.8.2..6..3.78....6.7.....825.....37.6.8.5.  ED=11.8/1.2/1.2
........1.......2......3..4..325.6....7.8.2...6.3.78.5.56.7....73.6.8...8.25.....  ED=11.8/1.2/1.2
........1.......2......3..4..3.5.2....627.8...8.3.65.7.527.....63.8.5...7.8.6....  ED=11.8/1.2/1.2
........1.......2......3..4..5.367...387..2...6.82.5...27.8....6.3.57...85.6.....  ED=11.8/1.2/1.2
........1.......2......3..4..3.5.2....627.8...8...65.7.5273....63.8.5...7.8.6....  ED=11.8/1.2/1.2
........1.......2......3..4..5..67...38.7.2...6.28.5...2783....6.35.7...85..6....  ED=11.8/1.2/1.2
........1.......2......3..4..5..67...38.7.2...6.28.5...2783.....5..6....6.35.7.8.  ED=11.8/1.2/1.2
........1.......2......3..4..325.6...57.8.2..6..3.78...825.....37.6.8...5.6.7....  ED=11.8/1.2/1.2
........1.....234.....56.7...65.87...25.17...8..62.....68.....72.7......51.8.....  ED=11.8/1.2/1.2
........1.......23.....24....567.....62.48...87...5....46.2..7.52.....867.8.5....  ED=11.8/1.2/1.2
........1.......23.....24....567.....62.48...87.2.5....46....7.52.....867.8.5....  ED=11.8/1.2/1.2
........1......23......2.4.....2567...271.8....56.8....61.7....25..86...7.85.....  ED=11.8/1.2/1.2
........1.......2......3..4..5.2.6...2367.8...8.3.5..7..67......78.5...253.8.2...  ED=11.8/1.2/1.2
........1.......2......3..4..5.2.6...2367.8...8.3.5..7.78.5....2.67.....53.8.2...  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.275...5.3.8..6.256.....38.7.....6.7.8...2  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.2.5...7.3.82.6.67.8....2.56.....83.7.2...  ED=11.8/1.2/1.2
........1.......2......3..4..5.2.6...2367.8..8..3.5..7.78.5....2.67.....35.8.2...  ED=11.8/1.2/1.2
........1.......2......3..4..5.2.6...2367.8..8..3.5..7..67......78.5...235.8.2...  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.275...5.3.8..6.67.8...22.56.....38.7.....  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.2.5...7.3.82.6.256.....6.7.8....83.7.2...  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.2.5.3.7...8..6.2563....6.7.8...283.7.....  ED=11.8/1.2/1.2
........1.......2......3..4..256.7...7..38..58..2..6.3.38.72...6...5....7.58....2  ED=11.8/1.2/1.2
........1.......2......3..4..256.7...7..38..58..2..6.3.38.7....62..5....7.58....2  ED=11.8/1.2/1.2
........1.......2......3..4..256.7...7...8..58..2..6.3.38.72...6..35....7.58....2  ED=11.8/1.2/1.2
........1.......2......3..4..256.7...7...8..58..2..6.3.38.7....62.35....7.58....2  ED=11.8/1.2/1.2
........1.......2......3..4..256.7...7..38..58..2..6.3.38.72...62..5....7.58.....  ED=11.8/1.2/1.2
........1.......2......3..4..256.7...7...8..58..2..6.3.38.72...62.35....7.58.....  ED=11.8/1.2/1.2
........1.......2......3..4..325.6...57.8.2...6.3.78...825.....5.6.7....73.6.8...  ED=11.8/1.2/1.2
........1.......2......3..4..325.6....7.8.2...6.3.78.5.825.....5.6.7....73.6.8...  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.2.5.3.7...8..6.67.8...22.563....83.7.....  ED=11.8/1.2/1.2
........1.....234.....56.7...18......86..5..727........52.17....6...87..8..62....  ED=11.8/1.2/1.2
........1.......23.....24....5.6.....47.2..8.62...8.57..67......72.45...58...6...  ED=11.8/1.2/1.2
........1.......23.....24....5.6.....47....8.62...8.57..67......72.45...58.2.6...  ED=11.8/1.2/1.2
........1......23......2.4...215.6....7.8.....6.2.785..815.....27.6.8...5...7....  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.2.5...7.3.8..6.67.8...22.56.....83.7.....  ED=11.8/1.2/1.2
........1.......2......3..4..356.7....8.2.5...7.3.8..6.256.....6.7.8...283.7.....  ED=11.8/1.2/1.2
mith
 
Posts: 889
Joined: 14 July 2020

Re: The hardest sudokus (new thread)

Postby mith » Tue Mar 01, 2022 12:58 am

And 11.7 (25c-30c):
Hidden Text: Show
Code: Select all
........1......234.....2.56..217.....875.9...91..285...592.1...72.98....8.1..7...  ED=11.7/1.2/1.2
.......12......345.....1..6..7.86....6913....83.9.7....167.3...39.8.....7.8..96..  ED=11.7/1.2/1.2
........1....23......145.....6...78..79.....281..7.6.9.27...1.61.87..9..69.2....8  ED=11.7/1.2/1.2
........1....12......345.....6....78.89...13.73..8.9.6.18...6.339....7..6.78....9  ED=11.7/1.2/1.2
........1....23......145.....2....16.172..8.986.9...7..91.8..676.....98.7.8.....2  ED=11.7/1.2/1.2
........1....23......145.....2.....6.172...8986.9..7...91.8.6.76.....89.7.8....12  ED=11.7/1.2/1.2
........1....23.....1.45.....6...78..79....1481..7.6.9.4......619.4...786.78..9..  ED=11.7/1.2/1.2
...............123.....1.45..6.789...714.....89.6..4...6719..8.14.8.6...9.8..7...  ED=11.7/1.2/1.2
........1....23.45..214.63.....513.4...36.52....4.2.1..2.6.....67.....5.895......  ED=11.7/1.2/1.2
........1....23.45..214.63.....513.4...36.52....4.2.1..2.6.5...67.......895......  ED=11.7/1.2/1.2
........1......234.....2.56..7..8....8.79.5...925.1....7928..1.25.1.7...8.1..9...  ED=11.7/1.2/1.2
........1......234.....2.56..7..81...8.79.5...925.1....7928....25.1.7...8.1..9...  ED=11.7/1.2/1.2
...............123.....1.45..6..78...7.69.4...914.8....6917..8.14.8.6...7.8..9...  ED=11.7/1.2/1.2
........1....23.....1.45.....6...78..79.....481..7.6.9.4....1.6.9.4...786.78..9..  ED=11.7/1.2/1.2
........1....23.....1.45.....6...78..79.....481..7.6.9..87..9...47...1.669.4....8  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....67.285.323.57.8...5.73....3.68.2...78..6...2  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...5...82...68.275.3.2563....38.7.2...6.7.8....  ED=11.7/1.2/1.2
........1....23.45..214.63....36.52....4...1..2..513.4...6.....76.....5.895......  ED=11.7/1.2/1.2
........1....23.45..214.63....36.52....4...1..2..513.4...6.5...76.......895......  ED=11.7/1.2/1.2
........1.......23....456....4..7..8.85.6....79.4......6795.8..54..789..8..6.4...  ED=11.7/1.2/1.2
........1.......23....456....4..7..8.85.6....79.4.......96.4....6795.8..54..789..  ED=11.7/1.2/1.2
........1.......23....456....4..6.....5.7...879.5.8....679.48..45..879..8..65....  ED=11.7/1.2/1.2
........1....23.....4.56.....78...19.41...85..9.5..4.7.79......1.8.9..7445.....8.  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...5...82..6.8.275.3.67.8....2.563....38.7.2...  ED=11.7/1.2/1.2
........1.......2......3..4..256.7....53.82..68..275.3.76.8....25.6.....3.87.2...  ED=11.7/1.2/1.2
........1.......2......3..4..256.7....5..82..68..275.3.76.8....25.63....3.87.2...  ED=11.7/1.2/1.2
........1....23......145.....2....6..172...8996.8..2.7.29...7.66.....89.78.....1.  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....3..672..65.28.7...2685....3..7.6.8.87..3..5.  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....3..672..65.28.7...268.....3.57.6.8.87..3..5.  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....3.6.72..65.82.7...2658....3...76.8.87.....5.  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....3.6.72..65.82.7...26.8....3.5.76.8.87.....5.  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....36.782..75.26.8...2765.....8..3..5.3..8.7.6.  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....36.782..75.26.8...276......8..3..5.3.58.7.6.  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....367.82..75.62.8...2756.....8.....5.3...87.6.  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....367.82..75.62.8...27.6.....8.....5.3.5.87.6.  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....372.85..26.75.8...5..7....3.6.82...78.6....2  ED=11.7/1.2/1.2
........1.......2......3..4..5..62...37.285...6.57.8...5273....3.68.2...78..6....  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....37.285..26.57.8...5.73....3.68.2...78..6...2  ED=11.7/1.2/1.2
........1.......2......3..4..5.362...372.85...6.75.8...52.7....3.6.82...78.6.....  ED=11.7/1.2/1.2
........1.....2.......3456...2....16.172..8..86.5..72..28....7..5.......1.6..7.58  ED=11.7/1.2/1.2
........1.....2.......3456...5.......72....8.16...8..7.812..7.55......167.65..82.  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5...6.3.72.8.268.....37.5.2...8.5.7....  ED=11.7/1.2/1.2
........1.......2......3..4..3.256...2768.5..6..3.7..8.85.7....2.68.....73.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256...2768.5..6..3.7..8..68......85.7...273.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5...6...72.8.2683....37.5.2...8.5.7....  ED=11.7/1.2/1.2
........1.......2......3..4..3.256...2768.5..6....7..8.85.7....2.683....73.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256...2768.5..6....7..8..683.....85.7...273.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..2.356....76.82...5.72.8.3.26.7....3.5.86...78.5.....  ED=11.7/1.2/1.2
........1.......2......3..4..2.356....76.82...5.72.8.3.26.7.....8.5.....3.5.86.7.  ED=11.7/1.2/1.2
........1.......2......3..4..5.267....73.8...28.75.6.3.7.5.....3.86.2...56..8...2  ED=11.7/1.2/1.2
........1.......2......3..4..5.267....73.82...8.75.6.3.725.....3.86.2...56..8....  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....672.85..23.75.8...5..7....3.6.82...78.6....2  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...5.3.82...68.275...256.....38.7.2...6.7.8....  ED=11.7/1.2/1.2
........1.......2......3..4..2.35..6.3.7.82..75.62.8...27.6....3.5.87...68.....5.  ED=11.7/1.2/1.2
........1.......2......3..4..5.267....73.8..5.8.75.6.3.725.....3.86.2...56..8....  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5.3.6...7..8.2683....37.5.2...8.5.7....  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5.3.6.3.7..8.268.....37.5.2...8.5.7....  ED=11.7/1.2/1.2
........1.....2.......3456...2....16.172..8.586.5..72..28....7..5.......1.6..7..8  ED=11.7/1.2/1.2
........1.......2......3..4..325.6...57.8...362.3.78...825.....37.6.8...5.6.7....  ED=11.7/1.2/1.2
........1.......2......3..4..325.6...57.8...362...78...8253....37.6.8...5.6.7....  ED=11.7/1.2/1.2
........1.......2......3..4..325.6...57.8.2.36....78...8253....37.6.8...5.6.7....  ED=11.7/1.2/1.2
........1.......2......3..4..2.356...3.72.8...576.8..3.26.7....3.5.86...78.5.....  ED=11.7/1.2/1.2
........1.......2......3..4..2..56...3.27.8...57.68..3.2673....3.58.6...78..5....  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....3278.5..76.2..8.3.576....2.8.37....6.3.52...  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...5...8....68.275.3.2563....38.7.....6.7.8...2  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...582..6.37....82...2635....38..72...5.78.....  ED=11.7/1.2/1.2
........1.......2......3..4..2.35..6.3.7.82..75.62.8...2756....3...87...68.....5.  ED=11.7/1.2/1.2
........1.......2......3..4..2..5..6.3..782..75.26.8...2765....3..8.7...68..3..5.  ED=11.7/1.2/1.2
........1.......2......3..4..2..5..6.3..782..75.26.8...276.....3.58.7...68..3..5.  ED=11.7/1.2/1.2
........1.......2......3..4..2.356.7.3.72.8...5.6.8..3.26.7....3.5.86...78.5.....  ED=11.7/1.2/1.2
........1.......2......3..4..2..56.7.3.27.8...5..68..3.2673....3.58.6...78..5....  ED=11.7/1.2/1.2
........1.....2.34..2.3156.....5......4...6...781.6.......65.4.1..2.43..4..3...25  ED=11.7/1.2/1.2
........1.......2......3..4..2.356...3.72.8...576.8..3.26.7.....8.5.....3.5.86.7.  ED=11.7/1.2/1.2
........1.......2......3..4..2..56...3.27.8...57.68..3.2673.....8..5....3.58.6.7.  ED=11.7/1.2/1.2
........1.......2......3..4..2.356...3.72.8...5.6.8..3.26.7....3.5.86.7.78.5.....  ED=11.7/1.2/1.2
........1.......2......3..4..2..56...3.27.8...5..68..3.2673....3.58.6.7.78..5....  ED=11.7/1.2/1.2
........1.......2......3..4..325.6....7.8.2.3.6.3.78...56.7....73.6.8.5.8.25.....  ED=11.7/1.2/1.2
........1.......2......3..4..325.6....7.8.2.3.6...78...56.7....73.6.8.5.8.253....  ED=11.7/1.2/1.2
........1.......2......3..4..325.6....7.8...326.3.78...56.7....73.6.8.5.8.25.....  ED=11.7/1.2/1.2
........1.......2......3..4..325.6....7.8...326...78...56.7....73.6.8.5.8.253....  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....567.82..73.62.8...27.6.....8.....5.3.5.87.6.  ED=11.7/1.2/1.2
........1.....2.34..2.3.56.....5......4...6...781.6.......651..1..2.43..4..31..25  ED=11.7/1.2/1.2
........1.....2.34..2.3.56.....5......4...6...781.6.......65.4.1..2.43..4..31..25  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....5672.8..73.6.82...8.....5.3...86.7.62.57....  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....567.82..73.62.8...2756.....8.....5.3...87.6.  ED=11.7/1.2/1.2
........1......23......2.4.....56..7..52....8.6187.....1...8....726.51..6.871.5..  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5627.8..82...6....78.3..6.36.8.5.7.5.27.....  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....3..672...5628.7...78.3..5.3.57.6.8.62.8.....  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....3..67..5.5628.7...78.3..5.3.57.6.8.62.8.....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5627.8..82.3.6....78....6.36.8.5.7.5.27.....  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....3.6.72...5682.7...78....5.3.5.76.8.62..8....  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....3.6.7..5.5682.7...78....5.3.5.76.8.62..8....  ED=11.7/1.2/1.2
........1.......2......3..4..5.3..6..728.....63.5.7.8..83.7...625...6...7.628.5..  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....5627.8..73..682...8..3..5.3.58.6.7.62.7.....  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....5627.8..73..68..5.8..3..5.3.58.6.7.62.7.....  ED=11.7/1.2/1.2
........1.......2......3..4..5....6..72.8....63..57.8..837....625..36...7.682.5..  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....5672.8..73.6.82...8.....5.3.5.86.7.62..7....  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....5672.8..73.6.8..5.8.....5.3.5.86.7.62..7....  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....3..672...5628.7...78.3..5.3..7.6.8.62.85....  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....3.6.72...5682.7...78....5.3...76.8.62.58....  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....5627.8..73..682...8..3..5.3..8.6.7.62.75....  ED=11.7/1.2/1.2
........1......23......2.4.....56..7.1687....75.2....8..1..8....2.6.51..68.71.5..  ED=11.7/1.2/1.2
........1.......2......3..4..2.3.....567.82..73.62.8.5.2756.....8.....5.3...87.6.  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....6275.8..73.2.85...5..7.....876....23.6.82...  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....6257.8..73..285...5.73.....87.6...23.68.2...  ED=11.7/1.2/1.2
........1.......2......3..4..5.362...6.75.8..73.2.85...876.....25..7....3.6.82...  ED=11.7/1.2/1.2
........1.......2......3..4..5..62...6.57.8..73..285...87.6....25.73....3.68.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256...2768.5...6.3.7..8.85.7....2.68.....37.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256...2768.5...6.3.7..8..68......85.7...237.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256...2768.5...6...7..8.85.7....2.683....37.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256...2768.5...6...7..8..683.....85.7...237.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5...6.3.72.8.85.7....2.68.....37.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5...6...72.8.85.7....2.683....37.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....3275.8..76.2.85...5..7.....876....23.6.82...  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...5.3.82..6.8.275...67.8....2.56.....38.7.2...  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...582..6.3.7...82...2635....5.78.....83..72...  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...5...8...6.8.275.3.67.8...22.563....38.7.....  ED=11.7/1.2/1.2
........1.......2......3..4..256.7...7..382..85.2..6.3.38.72...62..5....7.58.....  ED=11.7/1.2/1.2
........1.......2......3..4..256.7...7...82..85.2..6.3.38.72...62.35....7.58.....  ED=11.7/1.2/1.2
........1.......2......3..4..256.7....53.8...68..275.3.5.6......76.8...23.87.2...  ED=11.7/1.2/1.2
........1.......2......3..4..256.7....53.8...68..275.3.76.8...225.6.....3.87.....  ED=11.7/1.2/1.2
........1.......2......3..4..256.7....5..8...68..275.3.5.63.....76.8...23.87.2...  ED=11.7/1.2/1.2
........1.......2......3..4..256.7....5..8...68..275.3.76.8...225.63....3.87.....  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5.3.6.3.7..8.85.7....2.68.....37.5.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5.3.6...7..8.85.7....2.683....37.5.2...  ED=11.7/1.2/1.2
........1....23.....4.56.....1....75..87..49..9....1.8.57......41..8.7.98.9....54  ED=11.7/1.2/1.2
........1....23.....4.56.....1.....7.789..45.95.....18.47......18..7..945.9...8..  ED=11.7/1.2/1.2
........1....23.....4.56.....1.....5..78..49.89....1.7.58......41..7.8.97.9....54  ED=11.7/1.2/1.2
........1....23.....4.56.....1.....5..78..49.89......7.58....1.41..7.8.97.9....54  ED=11.7/1.2/1.2
........1.......2......3..4..2.......3..56..757.28.6...2587....3..6.5.8.86..3..7.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6.5627.8...8........3.8.5.7..78.3..6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8...8...6....3.8.5.7..78.3..6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5627.8..28........3.8.5.7..78.3..6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....3..67..56..28.7...268.....3.57.6.8.87..3..5.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6.5.27.8...8...6....78.3..6.5.27.....63.8.5.7.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8...8...6....78.3..6.5.27.....63.8.5.7.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5.27.8..28...6....78.3..6.5.27.....63.8.5.7.  ED=11.7/1.2/1.2
........1.......2......3..4..2.3.....3.5.6..757.82.6...2578....3...65.8.86.....7.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6.5627.8...8.3......3.8.5.7..78....6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8...8.3.6....3.8.5.7..78....6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5627.8..28.3......3.8.5.7..78....6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....3.6.7..56..82.7...26.8....3.5.76.8.87.....5.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6.5.27.8...8.3.6....78....6.5.27.....63.8.5.7.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8...8.3.6....78....6.5.27.....63.8.5.7.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5.27.8..28.3.6....78....6.5.27.....63.8.5.7.  ED=11.7/1.2/1.2
........1.......2......3..4..2.......35.67..868.25.7...2658.....7..3..8.3..7.6.5.  ED=11.7/1.2/1.2
........1.......2......3..4..2..5....36.78..57..26.8...276......8..3..5.3.58.7.6.  ED=11.7/1.2/1.2
........1.......2......3..4..5..6.....728.5..38..7.2.6.635.7.8.27.8.....5...3..6.  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....6728.5..83..7.2...5..3..6.6.35.7.8.72.8.....  ED=11.7/1.2/1.2
........1.......2......3..4..2.3.....356.7..868.52.7...2685.....7.....8.3...76.5.  ED=11.7/1.2/1.2
........1.......2......3..4..2.35....367.8..57..62.8...27.6.....8.....5.3.5.87.6.  ED=11.7/1.2/1.2
........1.......2......3..4..5.362...6.78.5..73.2..8...576.....28..7....6.3.52...  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....6278.5..73.2..8...576....2.8..7....6.3.52...  ED=11.7/1.2/1.2
........1.......2......3..4..5..62...6.78.5..73.2..8...576.....28.37....6.3.52...  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....6278.5..73.2..8...576....2.8.37....6.3.52...  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....372.85...6.75.8...52.7....3.6.8....78.6....2  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....37.285...6.57.8...5273....3.68.....78..6...2  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8...8.3.62.7.78.6....2.57.....63.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5...2657.8...8.3.6..7.78.6....2.57.....63.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5...2657.8...8.3.6..7..57......78.6...263.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8...8...62.7.78.6....2.573....63.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5...2657.8...8...6..7.78.6....2.573....63.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5...2657.8...8...6..7..573.....78.6...263.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5...6.3.7..8.268.....37.5.....8.5.7...2  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5...6...7..8.2683....37.5.....8.5.7...2  ED=11.7/1.2/1.2
........1.......2......3..4..5.367...6.82.5.38..7..2...586.....6.3.57...72..8....  ED=11.7/1.2/1.2
........1.......2......3..4..5.367...6.82.5.38..7..2...5.6.....6.3.57.8.72..8....  ED=11.7/1.2/1.2
........1.......2......3..4..2.3.5...6.72.8..73.5.8..6.8.6.....3.6.85.7.52..7....  ED=11.7/1.2/1.2
........1.......2......3..4..5.2.6...7.3.8...82.65.7.3.387.2...6..5.....75..8...2  ED=11.7/1.2/1.2
........1.......2......3..4..5.267....73.8....8.75.6.3.725.....3.86.....56..8...2  ED=11.7/1.2/1.2
........1.......2......3..4..5.2.6...7.3.82..8..65.7.3.387.2...6.25.....75..8....  ED=11.7/1.2/1.2
........1.......2......3..4..2...5...6.27.8..73..58..6.8..6....3.68.5.7.52.73....  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....3278.5..76.2..8...576....2.8..7....6.3.52...  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...5.3.8....68.275...256.....38.7.....6.7.8...2  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...582..6..7...382...26.5....38..72...5.78.....  ED=11.7/1.2/1.2
........1.......2......3..4..2.35..6.3.7.8..57..62.8...27.6....3.5.87...68.....5.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8...8.3.6..7.78....6.5.27.....63.8.5...  ED=11.7/1.2/1.2
........1.......2......3..4..5.2.6...7.3.8..58..65.7.3.387.2...6.25.....75..8....  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8.3.8.3.6..7.78.6....2.57.....63.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8.3.8...6..7.78.6....2.573....63.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...582..6.37....8....2635....38..7....5.78....2  ED=11.7/1.2/1.2
........1.......2......3..4..325.6...57.8...36..3.78....6.7.....825.....37.6.8.5.  ED=11.7/1.2/1.2
........1.......2......3..4..325.6....7.8...3.6.3.78.5.56.7....73.6.8...8.25.....  ED=11.7/1.2/1.2
........1.......2......3..4..325.6...57.8...36....78....6.7.....8253....37.6.8.5.  ED=11.7/1.2/1.2
........1.......2......3..4..325.6....7.8...3.6...78.5.56.7....73.6.8...8.253....  ED=11.7/1.2/1.2
........1.......2......3..4..2.3...5.3.6.7..868.52.7...2685....3...76...57.....8.  ED=11.7/1.2/1.2
........1.......2......3..4..2.....5.3..67..868.25.7...2658....3..7.6...57..3..8.  ED=11.7/1.2/1.2
........1.......2......3..4..2..5..6.3..78..57..26.8...276.....3.58.7...68..3..5.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6.5627.8...8.3....7.3.8.5....78....6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6.5627.8...8......7.3.8.5....78.3..6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6.5.27.8...8.3.6..7.78....6.5.27.....63.8.5...  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6.5.27.8...8...6..7.78.3..6.5.27.....63.8.5...  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8...8.3.6..7.3.8.5....78....6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8...8...6..7.3.8.5....78.3..6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8...8...6..7.78.3..6.5.27.....63.8.5...  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5627.8..28.3....7.3.8.5....78....6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5627.8..28......7.3.8.5....78.3..6.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5.27.8..28.3.6..7.78....6.5.27.....63.8.5...  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5.27.8..28...6..7.78.3..6.5.27.....63.8.5...  ED=11.7/1.2/1.2
........1.......2......3..4..5....6..72.8....36..57.8..867..2..5...36...7.382.5..  ED=11.7/1.2/1.2
........1.......2......3..4..2.3.....5672.8..73.6.8..5.8.....5.3...86.7.62.57....  ED=11.7/1.2/1.2
........1.......2......3..4..3.56.7..2687.....5.....8...5.38....376..2..68.72.5..  ED=11.7/1.2/1.2
........1.......2......3..4..3.56.7..5.....8.62.87......5.38....3672.5..78.6..2..  ED=11.7/1.2/1.2
........1......23......2.4.....56..7..52....8.6187.....1........726.5.8.6.871.5..  ED=11.7/1.2/1.2
........1......23......2.4.....56..7..52....8.6187.....726.51..5....8...6.871....  ED=11.7/1.2/1.2
........1......23......2.4.....56..7..52....8.6187.....726..1..5....8...6.871.5..  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8..8....6....78.3..6.36.8.5.7.5.27.....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8..8..3.6....78....6.36.8.5.7.5.27.....  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....37.8.2..86.27.5...287......5..3..6.6.35.8.7.  ED=11.7/1.2/1.2
........1.......2......3..4..5....6..72.8....63..57.8..5..36....837..2..7.682.5..  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5627.8..82........78.3..6.3..8.5.7.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..2.......3..56..7.7528.6...68.3..7.3..6.5.8.52.87....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8..8....6....78.3..6.3..8.5.7.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6.5627.8..8.........78.3..6.3..8.5.7.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6.5627.8..82.3......78....6.3..8.5.7.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..2.3.....3.5.6..7.7582.6...68....7.3...65.8.52.78....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2...5627.8..8..3.6....78....6.3..8.5.7.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6.5627.8..8..3......78....6.3..8.5.7.5.276....  ED=11.7/1.2/1.2
........1.......2......3..4..3.56.7..2687.....5.3...8..376....82.5......68.72.5..  ED=11.7/1.2/1.2
........1.......2......3..4..2.......5627.8..73..68..5.8..3..5.3..8.6.7.62.75....  ED=11.7/1.2/1.2
........1.......2......3..4..3.56.7..2687.....5.3...8...5..8....376..2..68.72.5..  ED=11.7/1.2/1.2
........1.......2......3..4..3.56.7..2687.....5.3...8...5.......376..2.868.72.5..  ED=11.7/1.2/1.2
........1.......2......3..4..3.56.7..2687.....5.....8..376....82.5.3....68.72.5..  ED=11.7/1.2/1.2
........1.......2......3..4..3.56.7..2687.....5.....8...5.3.....376..2.868.72.5..  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8...8...62.7.2573....63.8.2...7.8.6....  ED=11.7/1.2/1.2
........1......23......2.4.....56..7.1687....75.2....8.2.6.518.5........68.71....  ED=11.7/1.2/1.2
........1......23......2.4.....56..7.1687....75.2....8.2.6.51..5....8...68.71....  ED=11.7/1.2/1.2
........1......23......2.4.....56..7.1687....75.2....8.2.6.5.8.5.1......68.71....  ED=11.7/1.2/1.2
........1......23......2.4.....56..7.1687....75.2....8..1.......2.6.5.8.68.71.5..  ED=11.7/1.2/1.2
........1......23......2.4.....56..7.1687....75.2....8.2.6..18.5........68.71.5..  ED=11.7/1.2/1.2
........1......23......2.4.....56..7.1687....75.2....8.2.6..1..5....8...68.71.5..  ED=11.7/1.2/1.2
........1......23......2.4.....56..7.1687....75.2....8.2.6...8.5.1......68.71.5..  ED=11.7/1.2/1.2
........1......23......2.4.....56..7..52....8.6187.....726.518.5........6.871....  ED=11.7/1.2/1.2
........1......23......2.4.....56..7..52....8.6187.....726.5.8.51.......6.871....  ED=11.7/1.2/1.2
........1......23......2.4.....56..7..52....8.6187.....726..18.5........6.871.5..  ED=11.7/1.2/1.2
........1......23......2.4.....56..7..52....8.6187.....726...8.51.......6.871.5..  ED=11.7/1.2/1.2
........1.......2......3..4..3.56.7..5.....8.62.87......5.3.....3672.5.878.6..2..  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....6.75.8..73.2.85...876....225..7....3.6.8....  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....6.57.8..73..285...87.6...225.73....3.68.....  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....372..8..26.78.5...8..7....6.3.52...75.6....2  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....37.2.8..26.87.5...8.73....6.35.2...75..6...2  ED=11.7/1.2/1.2
........1.......2......3..4..5.362...372..8...6.78.5...82.7....6.3.52...75.6.....  ED=11.7/1.2/1.2
........1.......2......3..4..5..62...37.2.8...6.87.5...8273....6.35.2...75..6....  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5...6.3.7..8.85.7...22.68.....37.5.....  ED=11.7/1.2/1.2
........1.......2......3..4..3.256....768.5...6...7..8.85.7...22.683....37.5.....  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5...2657.8..8..3.6..7.78.6....2.57.....36.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5...2657.8..8..3.6..7..57......78.6...236.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5...2657.8..8....6..7.78.6....2.573....36.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5...2657.8..8....6..7..573.....78.6...236.8.2...  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8...8.3.62.7.257.....63.8.2...7.8.6....  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....672..8..23.78.5...8..7....6.3.52...75.6....2  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...5.3.8...6.8.275...67.8...22.56.....38.7.....  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...582..6...7..382...26.5....5.78.....83..72...  ED=11.7/1.2/1.2
........1.......2......3..4..256.7...7..38...85.2..6.3.38.72...6...5....7.58....2  ED=11.7/1.2/1.2
........1.......2......3..4..256.7...7...8...85.2..6.3.38.72...6..35....7.58....2  ED=11.7/1.2/1.2
........1.......2......3..4..256.7...7...8...85.2..6.3.38.7....62.35....7.58....2  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...582..6.3.7...8....2635....5.78....283..7....  ED=11.7/1.2/1.2
........1.......2......3..4..256.7...7..38...85.2..6.3.38.7....62..5....7.58....2  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8.3.8...6..7.2573....63.8.2...7.8.6....  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8.3.8.3.6..7.257.....63.8.2...7.8.6....  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....6.78.5..73.2..8...576....228..7....6.3.5....  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....6.78.5..73.2..8...576....228.37....6.3.5....  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8...8.3.6..7.78.6...22.57.....63.8.....  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8...8...6..7.78.6...22.573....63.8.....  ED=11.7/1.2/1.2
........1.......2......3..4..5.3.6...376....8.8.72.5...26.7.....5.8.....8.3.56.7.  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...582..6..7...38....26.5....38..7....5.78....2  ED=11.7/1.2/1.2
........1.......2......3..4..5.2.6...7.3.8...8..65.7.3.387.....6.25.....75..8...2  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6..627.8..28.3..5...527.....63.8.5...7.8.6....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6..627.8..28....5...5273....63.8.5...7.8.6....  ED=11.7/1.2/1.2
........1.......2......3..4..2...5...3..56..7.7.28.6...68.7....3.76.5...52.83....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6..627.8...8.3..5.7.527.....63.8.5...7.8.6....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6..627.8...8.3..5...527.....63.8.5...7.8.6....  ED=11.7/1.2/1.2
........1.......2......3..4..3.5...6..627.8...8....5.7.5273....63.8.5...7.8.6....  ED=11.7/1.2/1.2
........1.......2......3..4..5...6...37.6...8.8.27.5...2673.....5..8....8.35.6.7.  ED=11.7/1.2/1.2
........1.......2......3..4..3.5.2.6..627.8...8....5...5273....63.8.5...7.8.6....  ED=11.7/1.2/1.2
........1.......2......3..4..2.3.5...3.5.6..7.7.82.6...687.....3.7.65...52..8....  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8...8...6..7.2573....63.8.....7.8.6...2  ED=11.7/1.2/1.2
........1.......2......3..4..5.36....372..8...6.78.5...82.7....6.3.5....75.6....2  ED=11.7/1.2/1.2
........1.......2......3..4..5..6....37.2.8...6.87.5...8273....6.35.....75..6...2  ED=11.7/1.2/1.2
........1.......2......3..4..3.2.5....657.8...8.3.6..7.257.....63.8.....7.8.6...2  ED=11.7/1.2/1.2
........1.......2......3..4..356.7...582..6...7..38....26.5....5.78....283..7....  ED=11.7/1.2/1.2

And 11.6 (26c-29c):
Hidden Text: Show
Code: Select all
........1...234.....2.15.....6...27..786..1.992......8..7.9168..6......281....9.7  ED=11.6/1.2/1.2
........1....23.45.2541.36......4.26...36.1..1...524.3...6.5....57......689......  ED=11.6/1.2/1.2
........1.....2.3...4.15....16.7.8.4.3....67.8.7....13.4..37..86.3......78.6.1.4.  ED=11.6/1.2/1.2
........1.....2.3...4..5....16.7.8.4.3.1..67.8.7....13.4..37..86.3......78.6.1.4.  ED=11.6/1.2/1.2
.......12......345....13.....6.7.....7.6.8.918.193.....6.3.7....8319.6..9.7.8....  ED=11.6/1.2/1.2
.......12......345....13.....6.7.....819.....73.6.8.91.97.8....6..3.7...8.319.6..  ED=11.6/1.2/1.2
........1..2.34.....3.56.....7.8..19.9....2..13....7.8..98...7..21....8378.3..9.2  ED=11.6/1.2/1.2
........1...234.....2.15.....6...27..286..1.997......8..7.9168..6......781....9.2  ED=11.6/1.2/1.2
........1.......2......34.5..2.367...347.82..6..42.8...27.4.....8.6.....3.6.87.4.  ED=11.6/1.2/1.2
........1......23......2.4...1.25....267.81..75.61.8...17.6.....8.5.....2.5.87..6  ED=11.6/1.2/1.2
........1.......2......34.5..2.367.4.3.7.82..6..42.8...27.4....3.6.87...48.6.....  ED=11.6/1.2/1.2
........1.......2......34.5..2..67.4.3..782..6..24.8...2743....3.68.7...48..6....  ED=11.6/1.2/1.2
........1.......2......34.5..2..67...34.782..6..24.8...2743.....8..6....3.68.7.4.  ED=11.6/1.2/1.2
........1.......2......34.5..2..67...34.782..6..24.8...2743....3.68.7...48..6....  ED=11.6/1.2/1.2
.......12.....1..3..1...4....4.15.....67.8.4.57.64..8..15.876..4.7.6....8..5.....  ED=11.6/1.2/1.2
........1....23.45..45.136.....54.16...2.6..3.4.1..52...36.....4......3278.......  ED=11.6/1.2/1.2
........1......23......2.4...1..5....26.781..75.16.8...1762.....8..5....2.58.7..6  ED=11.6/1.2/1.2
........1.......2......34.5..2.367...347.82..6..42.8...27.4....3.6.87...48.6.....  ED=11.6/1.2/1.2
........1.......23.....24....5.6.....72.48...86...57...4785..6.52...4...6.8.27.4.  ED=11.6/1.2/1.2
........1.......23.....24....5.6.....72.48...86.2.57...4785..6.52...4...6.8..7.4.  ED=11.6/1.2/1.2
.......12......345....13.....6..7....7819.6..93..8......76.8.91.6..3....81.97....  ED=11.6/1.2/1.2
........1..2.34.....3.56.....7.8..19.9....2..13....8.7..98...7..21.....387.3..9.2  ED=11.6/1.2/1.2
........1....23.45.2541.36......4.2....36.1..1...524.3.....5....57...6..689......  ED=11.6/1.2/1.2
........1....23.45.2541.36......4.2....36.1..1...524.3...6.5....57...6...89......  ED=11.6/1.2/1.2
........1.......23....456.7..458.7...65..9...78.4.69...4.69....59.7.8...6.8......  ED=11.6/1.2/1.2
........1.......23....456.7..458.7...65..9...78.4.69...4.6.....59.7.8...6.8.....9  ED=11.6/1.2/1.2
........1.......23....456.7..4.8.7...65..9...78.4.69...4.69....59.7.8...6.8.5....  ED=11.6/1.2/1.2
........1.......23....456.7..4.8.7...65..9...78.4.69...4.6.....59.7.8...6.8.5...9  ED=11.6/1.2/1.2
........1.....2.3...4..5....16.7.8.4.3.1..67.8.7....1..4..37..86........78.6.134.  ED=11.6/1.2/1.2
........1.....2.3...4.15....16.7.8.4.3....67.8.7....1..4..37..86........78.6.134.  ED=11.6/1.2/1.2
........1.....2.3...4.15....16.7.8.4.3....67.8.7.....3.4..37..86.....1..78.6.1.4.  ED=11.6/1.2/1.2
........1.....2.3...4.15....16.7.8.4.3....67.8.7.......4..37..86.....1..78.6.134.  ED=11.6/1.2/1.2
........1..2.34.....3.56.....7.8..19.98...2..13....7....98...7..21....837..3..9.2  ED=11.6/1.2/1.2
........1...234.....2.15.....6...27...86..1.979......8.27.9168.18....9..6.......7  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....53.....4.......781.6.......65...1..2.43.64..3...25  ED=11.6/1.2/1.2
........1.....2.34..2.3.56.....53.....4.......781.6.......65...1..2.43.64..31..25  ED=11.6/1.2/1.2
........1.......2......34.5..3.6.2...7.24.8...8.3.76.4.48.7....6.24.....73.8.6...  ED=11.6/1.2/1.2
........1.......2......34.5..6.378....742.6..34.8..2...73.68...28..4....6.47.....  ED=11.6/1.2/1.2
........1.......2......34.5..3.6.2...7...86.4.8.24.7...47.8....6.243....83.7.6...  ED=11.6/1.2/1.2
........1.......2......34.5..6..78....724.6..34..8.2...736.8.4.28.43....6...7....  ED=11.6/1.2/1.2
........1.......2......34.5..6..78....724.6..34..8.2...736.8...28.43....6.4.7....  ED=11.6/1.2/1.2
.......12.....1..3..1...4....5.6..4..7.1.8...86.45..7..187.65..4.65.....7...8....  ED=11.6/1.2/1.2
.......12.....1..3..1...4....5.678...4718.....6.5......187...4.6....5...75.84..6.  ED=11.6/1.2/1.2
........1......23......2.4...5..6....6718.5..82..7.1...5..6....6.25.7..871.82....  ED=11.6/1.2/1.2
........1.......2......34.5..6.378....742.6..34.8..2...73.68.4.28..4....6..7.....  ED=11.6/1.2/1.2
........1......23......2.4...5.26....6781.5..82.7..1...5.6.....6.2.57..871..8....  ED=11.6/1.2/1.2
........1.......23.....24....5.26.4..4657..8.72.8.......7.8.....62.45...58...76..  ED=11.6/1.2/1.2
........1.......23.....24....5..6.4..4657..8.72.8.......7.8.....62.45...58.2.76..  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....53.....4...6...78..6.......65...1..2.43..4..31..25  ED=11.6/1.2/1.2
........1....23......145.....6....7..786..2.991.2....8..7...68..69....1.82....9.7  ED=11.6/1.2/1.2
........1.....2.3...4..5....16.7.8.4.3.1..67.8.7.....3.4..37..86.....1..78.6...4.  ED=11.6/1.2/1.2
........1.....2.3...4..5....16.7.8.4.3.1..67.8.7.......4..37..86.....1..78.6..34.  ED=11.6/1.2/1.2
........1.....2.3...4..5....16.7.8.4.3.1..6..8.7....13.4..3...8.8.6.1.4.6.3.....7  ED=11.6/1.2/1.2
........1.....2.3...4.15....16.7.8.4.3....6..8.7....13.4..3...8.8.6.1.4.6.3.....7  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....5......4...6...781....3....65.4.1..2.4...4..3...25  ED=11.6/1.2/1.2
........1.....2.34..2.3156.....5......4...6...781....3....651..1..2.4...4..3...25  ED=11.6/1.2/1.2
........1.....2.34..2.3.56.....5......4...6...781....3....651..1..2.4...4..31..25  ED=11.6/1.2/1.2
........1.....2.34..2.3.56.....5......4...6...781....3....65.4.1..2.4...4..31..25  ED=11.6/1.2/1.2
........1.....2.3...4.15....16.7.8.4.3....6..8.7....1..4..3...8.8.6.134.6.......7  ED=11.6/1.2/1.2
........1.....2.3...4.15....16.7.8.4.3....6..8.7.....3.4..3...8.8.6.1.4.6.....1.7  ED=11.6/1.2/1.2
........1.....2.3...4.15....16.7.8.4.3....6..8.7.......4..3...8.8.6.134.6.....1.7  ED=11.6/1.2/1.2
........1.....2.3...4..5....16.7.8.4.3.1..6..8.7....1..4..3...8.8.6.134.6.......7  ED=11.6/1.2/1.2
........1.....2.3...4..5....16.7.8.4.3.1..6..8.7.....3.4..37..8.8.6...4.6.....1.7  ED=11.6/1.2/1.2
........1.....2.3...4..5....16.7.8.4.3.1..6..8.7.....3.4..3...8.8.6.1.4.6.....1.7  ED=11.6/1.2/1.2
........1.....2.3...4..5....16.7.8.4.3.1..6..8.7.......4..37..8.8.6..34.6.....1.7  ED=11.6/1.2/1.2
........1.....2.3...4..5....16.7.8.4.3.1..6..8.7.......4..3...8.8.6.134.6.....1.7  ED=11.6/1.2/1.2
mith
 
Posts: 889
Joined: 14 July 2020

Re: The hardest sudokus (new thread)

Postby denis_berthier » Tue Mar 01, 2022 7:31 am

.
Here is probably the breakthrough of the year in Sudoku.
THE FOLLOWING TWO PUZZLES FOUND BY MITH ARE NOT IN T&E(2):

Code: Select all
........1.....2.......3..45..6.......71.8....23..67..8.827..1..6...23...7.381.6.. ED=11.9/1.2/1.2
........1.....2.......3..45..1.23....267.81..73.61.8...17.6.....8.......2.3.87..6 ED=11.8/1.2/1.2


Mith, all my congratulations for this exceptional finding.

First consequence: my very old T&E(2) conjecture (~2008) no longer holds. Notice that exceptions to it can only be extremely rare, knowing that puzzles not in T&E(1) are already extremely rare - of the order of 1 in 30M.

Second consequence: this opens a totally new approach to the search for the really hardest puzzles.
Instead of searching for high SER, search for puzzles not in T&E(2). This implies trying billions or trillions of puzzles but very fast generators already exist and a very fast T&E(2) procedure can be written (contrary to the SER test).
The only disadvantage of this approach would be it can't produce any of the already known 'hardest" (except the above two).
One clear advantage is, my T&E(n) classification is intrinsic and stable under Sudoku isomorphisms.


Note1: the existence of Sukakus not in T&E(2) and not derived from sudokus was already known.
Note2: the other 11.8s in the last batch (28 Feb.) are in T&E(2).
Last edited by denis_berthier on Tue Mar 01, 2022 9:56 am, edited 1 time in total.
denis_berthier
2010 Supporter
 
Posts: 3535
Joined: 19 June 2007
Location: Paris

Re: The hardest sudokus (new thread)

Postby denis_berthier » Tue Mar 01, 2022 9:52 am

.
One may be interested in the resolution states after T&E(2) has been applied to these two puzzles:

For ........1.....2.......3..45..6.......71.8....23..67..8.827..1..6...23...7.381.6.. ED=11.9/1.2/1.2
Code: Select all
Resolution state after T&E(2):
   +----------------+----------------+----------------+
   ! 3    256  478  ! 459  4579 4589 ! 27   68   1    !
   ! 145  456  458  ! 156  47   2    ! 39   678  39   !
   ! 19   269  79   ! 16   3    18   ! 278  4    5    !
   +----------------+----------------+----------------+
   ! 8    459  6    ! 23   459  14   ! 4579 1237 237  !
   ! 459  7    1    ! 23   8    459  ! 3459 235  6    !
   ! 2    3    459  ! 1459 6    7    ! 459  19   8    !
   +----------------+----------------+----------------+
   ! 459  8    2    ! 7    459  6    ! 1    359  34   !
   ! 6    1    459  ! 459  2    3    ! 58   5789 47   !
   ! 7    459  3    ! 8    1    459  ! 6    259  249  !
   +----------------+----------------+----------------+
141 candidates


For ........1.....2.......3..45..1.23....267.81..73.61.8...17.6.....8.......2.3.87..6 ED=11.8/1.2/1.2
Code: Select all
Resolution state after T&E(2):
   +----------------+----------------+----------------+
   ! 3    467  258  ! 459  4579 4569 ! 27   68   1    !
   ! 145  456  458  ! 158  47   2    ! 39   678  39   !
   ! 19   79   289  ! 18   3    16   ! 267  4    5    !
   +----------------+----------------+----------------+
   ! 8    459  1    ! 459  2    3    ! 56   5679 47   !
   ! 459  2    6    ! 7    459  8    ! 1    359  34   !
   ! 7    3    459  ! 6    1    459  ! 8    259  249  !
   +----------------+----------------+----------------+
   ! 459  1    7    ! 23   6    459  ! 3459 235  8    !
   ! 6    8    459  ! 23   459  14   ! 4579 1237 237  !
   ! 2    459  3    ! 1459 8    7    ! 459  19   6    !
   +----------------+----------------+----------------+
141 candidates
denis_berthier
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Joined: 19 June 2007
Location: Paris

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