Easter Monster Derivatives

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

Easter Monster Derivatives

Postby FLOCKMAN » Sat Dec 16, 2017 11:46 am

The HardestSudokusThread shows JPF’s 0091; 23 clue Easter Monster, SE = 11.8
12.3.....4...5......6..17..5..2......3..1..4...1..68....9....7....1..9.......9.68,

After time consuming, trial and error (no computers), I reduced this to 22 clues to produce the 43 valid sudokus below. One of our members was kind enough to evaluate them and there is an original 10.6 SE Sudoku among them, which is on the Sudokuwiki website today as #276. There are several morphs of which #275 on that website scored 11.7 SE and was identified by jkl as a morph of eleven’s MIT open source 120. Can any members identify the others?


.273.....4...5......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.36....4...5......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.39....4...5......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.34....4...5......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3..5..4...5......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3...9.4...5......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3....94...5......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....49..5......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4..95......6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...57.....6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5.6....6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5.1....6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5.....56..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5......69.17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5......6..17.35..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5......6..17.45..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5......6..17..58.2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5......6..17..5.72......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5......6..17..5..29.....3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5......6..17..5..2......3..9..4...1..68....9....7....1..9.......9.68
.2.3.....4...5......6..17..5..2......3..8..4...1..68....9....7....1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....49..1..68....9....7....1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68..3.9....7....1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....96...7....1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....95...7....1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9.6..7....1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9.2..7....1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9..2.7....1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....72...1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....73...1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7.7..1..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7...71..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7...41..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7...31..9.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7....1.39.......9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7....1..9..2....9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7....1..9....5..9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7....1..9....2..9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7....1..9.....4.9.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7....1..9......39.68
.2.3.....4...5......6..17..5..2......3.....4...1..68....9....7....1..9.......9368
.2.3.....4...5.2....6..17..5..2......3.....4...1..68....9....7....1..9.......9.68
.2.3.....4...5......6..17..5..2....3.3.....4...1..68....9....7....1..9.......9.68
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Re: Easter Monster Derivatives

Postby m_b_metcalf » Sat Dec 16, 2017 1:54 pm

This is not what you asked for, but please note that no. 31 is an SE 10.8 diamond, but is not minimal. Removing r7c8 makes it 'simpler':
Code: Select all
 . 2 . 3 . . . . .
 4 . . . 5 . . . .
 . . 6 . . 1 7 . .
 5 . . 2 . . . . .
 . 3 . . . . . 4 .
 . . 1 . . 6 8 . .
 . . 9 . . . . . .
 7 . . 1 . . 9 . .
 . . . . . 9 . 6 8   ED=10.8/10.8/2.6

All the others are minimal.

Regards,

Mike Metcalf
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Re: Easter Monster Derivatives

Postby FLOCKMAN » Sat Dec 16, 2017 3:23 pm

Hi Mike,
Thank you for your valuable comment that no. 31 was not minimal. Do you have a program that did this for you? If so, could you e-mail it to me at david [at] flockman [dot] com? When you deleted r7c8, did the minimal puzzle have a different ED score than the original? Perhaps someone else will let me know if they are morphs of specific existing sudokus in the Hardest Sudoku database?
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Re: Easter Monster Derivatives

Postby m_b_metcalf » Sat Dec 16, 2017 3:48 pm

FLOCKMAN wrote:Hi Mike,
Thank you for your valuable comment that no. 31 was not minimal. Do you have a program that did this for you? If so, could you e-mail it to me at david [at] flockman [dot] com? When you deleted r7c8, did the minimal puzzle have a different ED score than the original? Perhaps someone else will let me know if they are morphs of specific existing sudokus in the Hardest Sudoku database?

Yes, as stated, the ED changed from 10.8 to 2.6.

An exec file is on its way.

Regards,

Mike Metcalf
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Re: Easter Monster Derivatives

Postby champagne » Sat Dec 16, 2017 6:00 pm

m_b_metcalf wrote:Yes, as stated, the ED changed from 10.8 to 2.6.


which makes sense.

When you have redundant clues, the corresponding clue is often easy to find and many minimal puzzles with high ratings gave an ED 1.2.

BTW, this is one weakness of the data base of potential hardest on the bottom side where the filter is done on diamonds. a 10.5/1.2/1.2 is ignored although, after several assignments selecting easiest moves it becomes a 10.5/10.5/10.5 non minimal puzzle.

Happily, this is only for ratings below 10.8 and I did want to change the filter when I have seen my mistake.
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Re: Easter Monster Derivatives

Postby FLOCKMAN » Sat Jan 13, 2018 1:06 pm

Over the Christmas holiday, I found over 250 derivatives from another existing hard Sudoku, of which 15 rated over 10 ED with one rated at 11.9/11.9/11.7 by skfr, which is second only to one other SE rating. It was: -

9..7.....78....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2 and its canonical format was 98.7.....6.....9....7....5..4..3...5..95..6.......2.1...86..5......1...3.....4.2.

However, in 2015, Eleven produced another with the same ED rating, the same canonical format and the same SE rating of 11.8;11.8;11.6 which was 1.......9..67...2..8....4......75.3...5..2....6.3......9....8..6...4...1..25...6., so they are morph of each other, although possible arrived at by different routes. Eleven may wish to comment?

I used skfr to rate it as it is over 100 times faster than Sudoku Explainer, which is not practical to use to evaluate large numbers of derived sudokus. I am told there are programming bugs in both rating systems, so they may not give identical ratings.

So I decided to produce the table attached that sets out and compares the SE and skfr ratings for the published 11.9 and 11.8 sudokus. This took some time, so a complete table for all published sudokus of SE 10 and over would be a herculean task! However some conclusions can be drawn from the 62 listed.

1) There were only 3 examples (Numbers 10, 12 and 15) where the skfr rating exceeded the SE rating. These were from Filmer, Eleven and Tarek.
2) There were 16 examples where the ratings from both systems were equal and another 7 where they were almost equal.
3) There were 37 examples where the SE rating exceeded the skfr rating.
4) The SE rating exceeded the skfr rating for the 9 11.9 SE sudokus: 6 @ 11.8, 1 @ 11.7 and 2 @ 11.6. So SE is statistically significantly higher than DE for the 11.9 SE puzzles.
5) The frequency of skfr ratings equalling SE ratings seemed to increase as the ratings decreased. This will need to be confirmed when someone compares the ratings for sudokus below SE = 11.8.

I have been striving to produce high rating sudokus that are not morphs of existing ones for some time and so far have produced only one so far rated at 10.6;10.6;10.6 from a group of 15 above 10 ED; (see above) last December.

I am informed that the high value sudokus were extensively researched some years ago so possible most, if not all of them have been found! Eleven said "If someone finds a 10.6+ puzzle by himself, the chance is far less than 1:10000 to get an equivalent of Arto's puzzles". Am I therefore wasting my time? Advice from other members would be welcome!

I have a question and a comment

1) Is there a complete list of hard sudokus in canonical format (see last column in the attachment)? If so a copy would enable me to evaluate further ones > 10 ED
2) I was impressed that 30% 0f the 53 puzzles rated at 11.8 were ED rated exactly the same as the SE rating and 43% were almost the same. However 52% were rated 11.2 to 11.7, some 0.1 to 0.6 below the SE rating. Perhaps it may be possible for a future programmer to resolve the differences so that both give the same rating.

See attachment for the table
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Re: Easter Monster Derivatives

Postby eleven » Sat Jan 13, 2018 4:09 pm

FLOCKMAN wrote:However, in 2015, Eleven produced another with the same ED rating, the same canonical format and the same SE rating of 11.8;11.8;11.6 which was 1.......9..67...2..8....4......75.3...5..2....6.3......9....8..6...4...1..25...6., so they are morph of each other, although possible arrived at by different routes. Eleven may wish to comment?

This is long ago (2011), and therefore out of time. I wrote a summary of my search here.
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Re: Easter Monster Derivatives

Postby FLOCKMAN » Sat Jan 13, 2018 5:26 pm

Thanks Eleven. You have put in a tremendous amount of time and programming skills starting with very large numbers of random puzzles and a high proportion of the hardest puzzle are yours, Since 2011 the numbers of 11.9 and 11.8 puzzles have grown.

ER.............11.9 11.8
Others..........1.....9
Eleven..........3....20
Sum 2011......4....29
Now 2018,,,,,,9....53

I believe Champagne will be updating the list, so the numbers may increase. Where can I find that when it is published? I saw that OW found an 11.9 puzzle in 2015 , so perhaps there ARE more to be found. Do you think that a 12.0 SE puzzle will ever be seen? My efforts are puny compared with others as all my work is done manually. So finding just one new one over 10.0 is perhaps surprising!

Can you tell me if the table that I published for just 11.9 and 11.8 SE puzzles is already extended to include ALL puzzles > 10.0 SE?

Lastly can you tell me where to locate all the published puzzles in canonical form as I have dozens of ones over 10 SE and need to test if any are not morphs?
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Re: Easter Monster Derivatives

Postby eleven » Sun Jan 14, 2018 6:22 pm

FLOCKMAN wrote:I believe Champagne will be updating the list, so the numbers may increase. Where can I find that when it is published? I saw that OW found an 11.9 puzzle in 2015 , so perhaps there ARE more to be found.

champagne holds a hardest database. He made an update in December (after 2 years), see the Hardest thread here.
Do you think that a 12.0 SE puzzle will ever be seen?

No. But don't believe me. I also thought, there would not be a minimal puzzle with 40 clues, but dobrichev found a two of them.
My efforts are puny compared with others as all my work is done manually.

Impressing.
Can you tell me if the table that I published for just 11.9 and 11.8 SE puzzles is already extended to include ALL puzzles > 10.0 SE?

I don't think so. champagne's list goes down to 10.3.
Lastly can you tell me where to locate all the published puzzles in canonical form as I have dozens of ones over 10 SE and need to test if any are not morphs?

champagne's canonical form is a bit different, starting with the highest possible numbers. But it schould be easy to convert them to another canonical form.
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Re: Easter Monster Derivatives

Postby FLOCKMAN » Tue Jan 16, 2018 12:41 pm

Thank you eleven for answering all my questions.

Champagne sent me his skfr and skmpp programs so I can now rate my efforts as well as produce their canonical formats.

As you instructed, I downloaded the latest list of potentially hardest sudokus. The readme file was very interesting. Over the last 2 years 306,677 new sudokus were added (=18.7%) but few in the high rating ones as seen below. File 1 shows the sudokus and their SE ratings while file 2 contains their canonical format and their ranking order (highest 2,105,269!).

.SE……..No……Increase
11.9…….9………….0
11.8…….53………..0
11.7…….114…….+1
11.6…….189…….+2
11.5…….579…….+30. So I conclude that there is still scope for finding high ranking sudokus.

I was pleased to see my first included .2.3.....4...5......6..17..5..2......3.....4...1..68....9....7.7..1..9.......9.68;10.60;10.60;10.60;FLK;2017_12_11;1884993;22;*

With programs sent me, I have now ranked the 43 Easter Monster Derivatives and find that 15 ranked over 10 using the skfr program. Their canonical formats enabled me to search file 2 above, which I how I located my first entry. I searched all 15 formats several times but could only find 6 listed so I wonder if my search technique is in error.

The details are in the attached file and I would be grateful if any member with better searching skill than me can find them? If any of them are really not there, perhaps they should be!

Easter Monster Derivatives with ED over10.docx
(12.06 KiB) Downloaded 3 times
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