## The making of a gotchi, a simple way to find extreme sudokus

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

### The making of a gotchi, a simple way to find extreme sudokus

The making of a gotchi
A simple way to find extreme sudokus

In my High clue tamagotchis thread (unfortunately almost lost by the forum crash) i could show, that with a simple method and a few tricks it is possible to find much more minimal 39's on a PC than Intel managed with parallel processing on a super computer. After that i wondered, if the same method could be applied for finding extremely hard sudokus either, and it was.

There is only one significant difference between Havard's work and mine. We both worked up from low clue to high clue puzzles with {-1+2} (replace one clue by two ones and look, if you can get a unique puzzle) and eventually broadened our sets with {-n+m}, n,m being up to 3 or 4. While (as i think) Havard did it linearly (one swap of big sets after the other), i did it in a loop. This has the advantage, that you have much quicker feedback, so that i could experiment, tune and improve the process, while the gotchi already was running and producing results.

It was always clear to me, that i could not be the first one, who used this method. But only recently a mathematician pointed me to the Genetic Algorithm heuristic. It turned out, that my gotchis are something like school examples for it (the funny thing is, that i remembered then to have read about it earlier, but i had found it little attractive and rarely successful at that time).
However i will stick to my own words, when describing it, but it will be easy e.g. to replace "expand" my "mutation" to see the correlation.

"Real" mathematicians dont like such heuristics. They are only vaguely defined and it depends on trial&error, luck, intuition and the skill of the creator, if they give good results. A main disadvantage also is, that the results cannot be used for statistical investigations (e.g. you cannot say something serious about the quality of results, statistical probabilities, barriers etc.).

On the other hand those who had most successfully searched for extreme sudokus all have used the same basic concept of neighbourhood search, with the same disadvantages, from Gordon Royle to ano1, Havard to blue, tarek to coloin. The point is, that extreme sudokus are clustered like the mountains on earth. Near high peaks you have the best chances to find higher ones.

Preferences
The basic operations of a gotchi are to expand, evaluate and filter a set to get the next generation.

Expansion is done with neighbourhood search, for sudokus {-n+m} is the simplest way.
Evaluation of course depends on the target function. For min/max. clue search a puzzle is the better, the less/more clues it has, for hardest sudokus the better the rating is.
Filtering for min/max. clues mainly is already done by removing all duplicates and invalid puzzles in the {-n+m} calculation, for the hard sudokus search i had to find other fast methods, the most important one already had been implemented in Brian Turner's bb-solver (thanks again for this great program), nameley that the puzzle cant be solved with cell forcing chains (STEP 1).

This concept was all i needed to start the gotchis and find much with little effort and a very good fun/frustration ratio. But of course there are other requirements i needed:
- public programs like Brian's bb-solver, dukuso's suexg and gsf's sudoku. Those guys did the main work i needed for fast solving, generating and canonicalizing puzzles.
- a PC, which is rarely shut down, where i could run the gotchis in the background.
- some C/C++ knowledge to write the additional tools i needed, partly by modifying the bb-solver for my purposes. (This did not take me more than 2 weeks each - and was not done in a way i could present)
- some basic knowledge in scripting (batch processing). This is important to be able to make changes on a running gotchi. When you have a script, which calls the scripts expand, evaluate and filter cyclically, you can alter each of them at any time without stopping the program. This is very useful for experiments and improvements. Most useful for me have been the unix commands cp, mv, cat, grep, fgrep, sort, uniq and cut for all the (sudoku) file operations i needed.
- patience you will not find a 39 or 11.9 in a day

Going live
A gotchi is "living", as long it runs (cyclically) and produces something of more or less worth. When you have a living gotchi, you can start to optimize it, mainly by scaling the filters or introducing new ones, but also by making it more complex or improving the expand function.
At the beginning you will use weak filters to get a good starting population (e.g. some 1000 sudokus) and then make them harder for good results. (Of course you can also try more than one starting gotchi with different methods.)
Most important is, that the gotchi does not become too thin or fat. In the first case it might die and you have to restart, in the second one you will have to wait too long for the next generation, where you have the chance to see, where it is going (less than one generation a day normally turned out to be as waste of time). However, when you dont have time for it for a week or two, its no problem, when it produces a big, but less worthful set - this is one of the advantages, also bad gotchis produce useful information.
There is an "inbuilt" nice property for the sudoku problems, when you have managed to keep a minimum and maximum gotchi size. Small sudokus with puzzles in less useful areas will automatically run faster through the space, because the next generations are quicker reached.

This is, how i started the gotchis for the 2 problems:

Starting the high clue gotchi
It was easy for the high clue search. Just start with random puzzles (in my case 28 clues) and do {-1+2} as long as you can find (n+1) clue puzzles, the next generation.
The first problem was, that the number of puzzles exploded up to about 31 clues. My first way to filter them was to make a random selection, later i found, that taking the puzzles with high "eleven weights" lead to better results.
The second was, that the air became thin with 35 clues. No problem, i added a {-1+1} to get a fatter generation. One or two {-1+1}'s for the 36 clue puzzles and i had my first 37 generation (in fact i made 2 of them, with about 1000 puzzles each), the starting set of the gotchi.

Starting the hard sudokus gotchi
In the hard sudokus search i had the advantage, that i could test possible filters with the known "hardest sudokus", given in champagne's ER list with 488 puzzles. None of them could be solved with the "STEP 1" method in the bb_solver (just comment out STEP 2 and GUESSING to see it). But it was clear, that my chances to find such puzzles in random sets were bad. So i had to find a weaker and scalable filter. A quick idea was to count the candidates after basic solving methods (which are also implemented in the solver), which i improved then by evaluating, how much of them could be eliminated with STEP 1 and how much bivalue cells and strong links the grid has. Then i used this trivial rating: # candidates - 3*# eliminations - 4*# bivalues - 3*# links. This is far away from being a good rating, and there will be hundreds of better/quicker ones, but it was fast enough and had some correlation to a serious rating. The hardest known had values of about 150 to more than 200, random puzzles less than 0 - thats good enough for a gotchi's weak filter. (Since at that time i already was quite familiar with the bb-solver, the modifications i needed to count the possible eliminations were done in a day).
Then i started with a set of some 10000 24 clues and a first filter value 0, expanding them with {-1+1} and raising the filter value, until i had found some 1000 STEP 1/filter 140 puzzles. This took some days, maybe a week, then i had my first set of ER 10+ puzzles (the big majority of "STEP 1 puzzles" have ER > 10 also).

Basics
On this way i created a lot of files, most of them i did not not need again, e.g. the "29 clues" or "filter 50" files. So i used different ways to "clean up". Some of them i removed manually, some i overwrote with the next generation, and when i lost the survey, i restarted in a new directory.
When the gotchi is running well then, only the "all" and "current generation" files will remain, containing e.g. the sets of the 37+ sudokus found, the 37 clue puzzles not yet expanded with {-2+2}, and the expanded puzzles of the current generation, pure, canonicalized, with duplicates removed etc. In another directory the current sets of 28+ puzzles working up to 37 to be added to the "high clue gotchi".
Similar with the "hard sudoku" gotchi, where i have the best rated puzzles for 24 down to 21 clues, the weak filter sets needed to recognize duplicates, all ER and q2 rated puzzles and a few more beside of the generation sets.

Beside of the danger, that the gotchi becomes too big, there is the one, that the files become too big. When you look for 17 clues, you can start with an 18 clue, look with {-2+1}, if there is a 17 clue below, and expand it with {-1+1} for the next generation. ano1 has found out, that you can find about 900 mio 18 clues (maybe the half of all exiting ones) and more than 90 % of the 17 clues this way (if you have enough time and CPU). But its not trivial to deal with such big data sets.
When i tried to get more 37's, i noticed, that its faster for me to do a {-2+1}{-1+1}{-1+2} than a {-2+2} to get new ones. But the problem was, that my 36 sets would become that big, that e.g. the test for duplicates would have become more and more costy.
So instead i did it this way then: i made a {-2+2} to all puzzles with {-1+1} neighbours (because they seemed to be in a "denser" region), and if there were less than a lower limit of say 1000, i added the ones with highest "weight" (the average number of solutions a puzzle has, when you remove a clue - the higher it is, the better are the chances on average, that a n+1 clue puzzle is "near").

High clue gotchi
This already describes almost all, i used for the high clue search gotchis. The "bottom up" gotchi was rather slow and needed about 5 days to find about 1000 new 37's. Those were stored in a file and added to the "high clue" gotchi's new generation set. This one tried a {-1+2} on each 37 to find 38's. On all 38's i made {-2+2}, and then up to {-3+4} to find 39's, also {-2+1} to get more 37's. The 39's were tried to expand with {-3+3}.

A half year after i had finished, dobrichev had this nice idea to look at the complement of a puzzle in its solution grid. All its solutions must have a valid puzzle in the original cells (one being the original puzzle). Since the complements of high clues have relatively few givens, you often can find new puzzles this way, and it was easy to implement and fast. In some seconds CPU he could find 27 new 39's (82 known before). I also "dobbed" my sets and added that to the "expand" parts. So (starting with the dobbed set) i could more than double my set of 37's in 2 weeks without doing any {-2+2} operation on them (and found 10 more 39's). This shows, that good ideas also for gotchis are the essential thing for success.
As you can see in my thread, blue did it better later, he found much more 39's than me in shorter time - and did not use a gotchi. But he was so friendly to say, that my puzzles were a big help to achieve that Hardest sudokus gotchi
Now back to the hardest search. The 24 clue gotchi grew fast, and i could raise the filter value to 150. I found many 1000 "STEP 1" puzzles each day.

Now my goal was to find puzzles with high Explainer rating, which is the best accepted public one. It has the disadvantage, that rating a hard puzzle takes minutes. The fastest public filter i had was gsf's q2 rating, which i used for the first weeks to select the puzzles for ER. The correlation between the ratings is not good, but obviously there is some. So i found the first ER 11+ puzzle in less than 2 weeks.

The next steps were to go down to 23 and 22 clues. I took the highest q2 rated puzzles and those with highest filter values and made a {-2+1} to get the starting set for 23 clues, later i did the same for 22. Surprising was, that i had to lower the filter values to 140 and 135 resp. to keep the lower clues gotchis running. But then they developed fine with even more "STEP 1" puzzles daily and - harder puzzles. Since there was such a flood of new puzzles, i needed more (and quick) filters both for selecting the ones for rating and reducing the size of the gotchi generations. Also i could stop the 24 clue gotchi, because i did not expect the hardest there.

An easy to implement filter in the bb-solver was to extend the one cell forcing chains (using basics on the way) to 2 cells in the same unit, which dont have more than 2 different candidates (starting with the possible combinations). This filter eliminates about 70% of the puzzles.
Another filter i made - again by modifying the bb-solver, had the intention to filter out some relatively easy "set techniques", which are not implemented directly in the Explainer. I made some experiments, which showed, that the hardest puzzles even can resist any technique, which does not make use of at least one cell of each box. That means, that if i fade out a box and the six lines connected, i cannot eliminate a single candidate in the reduced grid - each one finds a partial solution in the 21 other units. This filter eliminated more than 90 % of the "STEP 1" puzzles (and a part of the known 11+), but kept some puzzles, the other filter would have eliminated (so it maybe of worth to find hard puzzles for other ratings).

In the 23 clue space it turned out, that the gotchi was living fine, when i only took the puzzles, which passed one of the filter plus some 1000 with the best weak filter value. In the 22 space this would reduce the STEP 1 sets drastically, so i take all STEP 1's of the current generation, when the number of filtered puzzles is below a limit. This gotchi is additionally feeded with the 23 clues' non minimal puzzles and the {-2+1} expanded puzzles, which had been selected for rating.

Both filters are about 10 times faster than q2, so - to save time - i only q2 rated filtered puzzles to select those with high rating (>98000) for the Explainer rating then. This gave me puzzles with an average ER of more than 10.6 and more than 10% have an ER above 11.
The last step then was to go down to 21 clues also a few weeks ago. This was done easily with copy/paste and adjusting the parameters (here i needed weaker conditions again to keep it running).

Much could be improved in this gotchi version, but since i am a lazy person, in the moment i am happy to have found about as much new hard puzzles as known before, and leave it alone.
eleven

Posts: 2283
Joined: 10 February 2008

### Re: The making of a gotchi, a simple way to find extreme sud

Hi eleven,

Congratulations for this very interesting work.

After I completed my work on unbiased classification and on whips, braids and their generalisations to FP-whips and braids, I lost much interest in Sudoku (in addition to having no time for it) :
- all T&E(NS+HS, 1) grids can be solved by nrczt-braids (moreover, the ~10 million randomly generated ones were in practice solved by whips, much simpler in structure than braids; only in very rare cases do braids give a slightly shorter classification)
- long ago, I had checked that all the known puzzles can be solved by (at most) T&E(NS+HS,2), and therefore by braids(braids); moreover, most of them can be solved by braids(FP) for simple FP families of patterns (see http://forum.enjoysudoku.com/abominable-trial-and-error-and-lovely-braids-t6390.html).

I've just checked that this last property [solvable by T&E(NS+HS,2)] remains true of your new hardest ones. But (although I still have no time) your results on hardest have renewed my interest and I have a few questions.

1) I haven't analysed Brian Turner's solver, but, from what you write, I guess that what you call forcing chains step 1 is equivalent to T&E(NS+HS, 1) as defined in the above mentioned thread , i.e. each candidate is eliminated based on only one hypothesis at a time (the assumption that this candidate is true) and no other resolution rule than NS, HS and elementary constraints propagation is used. Can you confirm?

2) Now, the hard one: as I mentioned above, all the known puzzles can be solved with 0, 1 or 2 levels of T&E(NS+HS). But, AFAIK, there has never been any proof that this should be true of ANY valid puzzle. Could your gotchi method be applied to look for T&E(NS+HS, 3) puzzles?
Considering the infinitesimal proportion of T&E(NS+HS, 2) and the time needed to find one, I'm aware that the search for T&E(NS+HS, 3) puzzles may be hopeless (because impractical). Moreover, this search is probably already implicitly included in your search for hardest. What do you think?

3) Could your method be extended to larger boards (e.g. 16x16) ? I mean in practice (of course, it can in theory). Finding a T&E(NS+HS, 3) puzzle could be easier on 16x16 grids. Even if some day it's proven to be true that all the 9x9 puzzles can be solved in T&E(NS+HS, 2), it doesn't have to be true of larger puzzles. Finding a few might give us insights for the 9x9 case: what kind of super-exotic structures can exist on a 16x16 grid, but have no room to exist on a 9x9?
On second thoughts, the case 16x16 can also be interesting for the study of T&E(NS+HS, 2) puzzles, which already contain rather exotic structures. Are these puzzles as rare (in proportion, as roughly estimated by the rate of their production by your gotchis) in 16x16 grids as in 9x9? Which kinds of exotic structures are hard to put in a 9x9 grid, but can easily find their place in a 16x16?
denis_berthier
2010 Supporter

Posts: 1394
Joined: 19 June 2007
Location: Paris

### Re: The making of a gotchi, a simple way to find extreme sud

I have generated a test file of 1000 16x16 grids, 252KB, for anyone who's interested. Just send me a PM (it's too big to post).

Regards,

Mike Metcalf
Last edited by m_b_metcalf on Thu Jan 13, 2011 3:16 pm, edited 1 time in total. m_b_metcalf
2017 Supporter

Posts: 10625
Joined: 15 May 2006
Location: Berlin

### Re: The making of a gotchi, a simple way to find extreme sud

Hi Denis,

denis_berthier wrote:1) I haven't analysed Brian Turner's solver, but, from what you write, I guess that what you call forcing chains step 1 is equivalent to T&E(NS+HS, 1) as defined in the above mentioned thread , i.e. each candidate is eliminated based on only one hypothesis at a time (the assumption that this candidate is true) and no other resolution rule than NS, HS and elementary constraints propagation is used. Can you confirm?

STEP 1 does the following for each unsolved cell (starting with those with few candidates): It tries each candidate using "basics", i.e. NS, HS, locked candidates, subsets, x-wing and swordfish, plus jellyfish. (If this leads to a contradiction, all candidates are removed in this candidates result grid). Then it OR's the candidates in the resulting grids. Thus all candidates are removed, which directly lead to a contradiction (T&E(basics+jellyfish,1)) plus all, which are eliminated, whatever candidate is tried (cell forcing chain).
Remark: Default of the solver is just to use NS, HS, locked candidates and guessing (fastest to solve), subsets, fishies and STEP1 can be added with the use_methods parameter. I had to reset the GUESSING flag from the source, so that it stops, when no elimination is possible with STEP 1.
What i call "STEP 1 puzzle" for short is one, which CANNOT be solved this way (bad name).

2) Now, the hard one: as I mentioned above, all the known puzzles can be solved with 0, 1 or 2 levels of T&E(NS+HS). But, AFAIK, there has never been any proof that this should be true of ANY valid puzzle. Could your gotchi method be applied to look for T&E(NS+HS, 3) puzzles?
Considering the infinitesimal proportion of T&E(NS+HS, 2) and the time needed to find one, I'm aware that the search for T&E(NS+HS, 3) puzzles may be hopeless (because impractical). Moreover, this search is probably already implicitly included in your search for hardest. What do you think?

The bb_solver also has inplemented a STEP 2, which does the same recursively (depth 2). I only verified, that it solved the old known hardest. With minor changes (commenting out locked candidates and reducing the eliminations to the contradiction candidates) i could make it a T&E(NS+HS,2) solver. I have more than 3 mio STEP1 puzzles, which i could try. Maybe thats possible this weekend, but i see little chances, that one could not be solved 3) Could your method be extended to larger boards (e.g. 16x16) ? I mean in practice (of course, it can in theory)...

I dont have any tools for 16x16 puzzles, so this would be too much work for me. Because of the huge space its very unclear for me, what results are possible.
eleven

Posts: 2283
Joined: 10 February 2008

### Re: The making of a gotchi, a simple way to find extreme sud

As expected, all of my 3.15 mio (minimal) step1 puzzles could be solved with T&E(NS+HS,2). bb-solver was very fast here too and did the job in a few hours. In normal mode it leaves depth 1 and 2 as soon as an elimination is possible. Here up to 11 depth 2 calls were made. For those with more than 6 depth 2 calls i also tried it with a "batch mode" version (much slower here), where all possible eliminations in a depth 1/2 call are collected. The puzzles were solved then with a single depth 2 call and up to 699 depth 1 calls. Here are some with much iterations in both cases, ordered by ER:
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`....5..8..56..91.....21.....61..79..5...3..1...........14....976.....4...7...4..1   11.1 1.2 1.21...5..8..56..9......21.....61..79..5...3..1...........14....976.....4...7...4..1   11.1 1.2 1.2..34.....4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7.....5..   11.0 11.0 2.6..3...7....6.8.1..78...1..4...9.....57...8.4.6...2............881...54.........15   11.0 1.2 1.2..34.....4...8..36..8...1...4..6..73...9...1......2.....4.7..686........7.....5..   10.9 10.9 2.6..3..6...4...8..36..8...1...4..6..73...9...1......2.....4.7..686........7.....5..   10.9 1.2 1.2...4....9.5..8.2.6.....7...2........3......1...5.3.8.2....6.3.8..6....95..85.....   10.6 1.2 1.2..34....9.5...92....9.3..4.....4.8...1.........8..5.23..5..4..27...6.5...6.......   10.3 1.2 1.2.2.......4....92.....23..1..7...8.4.3..9..8..8...2......6..4..17..39.4.........5.   10.3 1.2 1.2.........4...89..2..92..6..2....8..7..5....1...8...5..3..8......97.3...4..4.97..3   10.3 10.3 9.9..3..67......8....78.....6..4...1.7...1...4.2..72....1...........4..32.79..5...3.   10.3 10.3 7.8.......8.4....91...89.1....2..3...5..3..9.2..9..5.2...3..9.54....7.4...6.........   10.3 10.3 2.81...5........8.1...8...3..52.....4......4..9..4.3.8..6.7.....6...4.3...7.3.6.7...   10.3 10.3 2.6.2....7..4.6..9.2..9.2......4....8..6....4.9..3.8....1.......5.5..9...3..6...59.2   10.2 1.2 1.21...5......6...1...8...3..52...7.....7.3.5..8..........9...48...4.8..9....7.3...4   10.2 1.2 1.2..34..7.9.5...9.3..........2...6.....6.........13....7..4.9.8.1..8.4.9...1.8...7.   10.2 10.2 9.8`
eleven

Posts: 2283
Joined: 10 February 2008

### Re: The making of a gotchi, a simple way to find extreme sud

jeepers !

suexratt rates highly a few of those critters too - esp number 3 in the list

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`rating:   4923 ,    3209 , ....5..8..56..91.....21.....61..79..5...3..1...........14....976.....4...7...4..1rating:   4918 ,    3189 , 1...5..8..56..9......21.....61..79..5...3..1...........14....976.....4...7...4..1rating:   8042 ,    4534 , ..34.....4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7.....5..rating:   4003 ,    2357 , ..3...7....6.8.1..78...1..4...9.....57...8.4.6...2............881...54.........15rating:   6203 ,    3161 , ..34.....4...8..36..8...1...4..6..73...9...1......2.....4.7..686........7.....5..rating:   5639 ,    3473 , ..3..6...4...8..36..8...1...4..6..73...9...1......2.....4.7..686........7.....5..rating:   4641 ,    2667 , ...4....9.5..8.2.6.....7...2........3......1...5.3.8.2....6.3.8..6....95..85.....rating:   3674 ,    1602 , ..34....9.5...92....9.3..4.....4.8...1.........8..5.23..5..4..27...6.5...6.......rating:   3811 ,    1609 , .2.......4....92.....23..1..7...8.4.3..9..8..8...2......6..4..17..39.4.........5.rating:   2953 ,    1374 , .........4...89..2..92..6..2....8..7..5....1...8...5..3..8......97.3...4..4.97..3rating:   5916 ,    3018 , ..3..67......8....78.....6..4...1.7...1...4.2..72....1...........4..32.79..5...3.rating:   5217 ,    3237 , .......8.4....91...89.1....2..3...5..3..9.2..9..5.2...3..9.54....7.4...6.........rating:   4174 ,    1976 , 1...5........8.1...8...3..52.....4......4..9..4.3.8..6.7.....6...4.3...7.3.6.7...rating:   3164 ,     984 , .2....7..4.6..9.2..9.2......4....8..6....4.9..3.8....1.......5.5..9...3..6...59.2rating:   5527 ,    2429 , 1...5......6...1...8...3..52...7.....7.3.5..8..........9...48...4.8..9....7.3...4rating:   3486 ,    1193 , ..34..7.9.5...9.3..........2...6.....6.........13....7..4.9.8.1..8.4.9...1.8...7.`

just what will champagne make of that one

well done !

C
coloin

Posts: 1864
Joined: 05 May 2005

### Re: The making of a gotchi, a simple way to find extreme sud

And a simple {-2+2} gave these
eek
Code: Select all
`rating:  10378 ,    5710 , ..3......4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7..6..5..rating:   9547 ,    5174 , ..3......4...8..36..8...1...4..6..73...9..........2..5..4.7..686....4...7.....5..rating:   9456 ,    4909 , ..3.9....4...8..36..8...1...4..6..73...9..........2.....4.7..686........7.....5.4rating:   9220 ,    5804 , ..3......4...8..36..83..1...4..6..73...9..........2..5..4.7..686........7.....5..rating:   8900 ,    4556 , ..3.9....4...8..36..8...1...4..6..73...9..........2.....4.7..686........7.....54.rating:   8538 ,    4092 , ..3......4...8..36..8...1...4..6..73...9..........2.....4.7..686........7..6..59.rating:   8507 ,    4354 , ..3......4...8..36..8...1...4..6..73...9...1......2.....4.7..686........7..6..5..rating:   8446 ,    4487 , ..3......4...8..36..83..1...4..6..73...9...1......2.....4.7..686........7.....5..rating:   8342 ,    3752 , ..3.9....4...8..36..8...1...4..6..73...9....1.....2.....4.7..686........7.....5..rating:   8168 ,    4488 , ..3......4...8..36..83..1...4..6..73...9..........2.....4.7..686........7.....59.rating:   8065 ,    3924 , ..3......4...8..36..8...1...4..6..73...9..........7..5..4.7..686....2...7.....5..rating:   7849 ,    3471 , ..3.2....4...8..36..8...1...4..6..73...9....1.....2.....4.7..686........7.....5..rating:   7607 ,    3356 , ..3......4...8..36..8...1...4..6..73...9..........2.....4.7..686...2....7..6..5..rating:   7522 ,    3782 , ..3......4...8..36..8...1...4..6..73...9..........4..5..4.7..686....2...7.....5..rating:   7443 ,    4799 , ..3.9....4...8..36..8...1...4..6..73...9..........2.....4.7..686........7..6..5..rating:   7392 ,    3990 , ..3......4...8..36..8...1...4..6..73...9...1......2.....4.7..686....4...7.....5..rating:   7273 ,    3943 , ..34.....4...8..36..8...1...4..6..73...9..........2.....4.7..686........7.....59.rating:   7069 ,    2829 , ..3......4...8..36..8...1...4..6..73...9.........42..5..4.7..686........7.....5..rating:   7052 ,    3603 , ..3......4...8..36..8...1...4..6..73...9..........2..5....7..686....4...7.....54.rating:   7034 ,    3623 , ..3.9....4...8..36..8...1...4..6..73...9..........2.....4.7..686..4.....7.....5..rating:   6997 ,    2761 , ..3......4...8..36..8...1...4..6..73...9........7.2..5..4.7..686........7.....5..rating:   6957 ,    4279 , ..3.9....4...8..36..8...1...4..6..73...9..........2.....4.7..686........7....65..rating:   6794 ,    3374 , ..3.9....4...8..36..8...1...4..6..73...9..6.......2.....4.7..686........7.....5..rating:   6774 ,    4309 , ..3..6...4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7.....5..rating:   6741 ,    2395 , ..3......4...8..36..8...1...4..6..73...9..........26.5..4.7..686........7.....5..rating:   6727 ,    3417 , ..3.2....4...8..36..8...1...4..6..73..69..........2.....4.7..686........7.....5..rating:   6724 ,    2098 , ..3......4...8..36..8...1...4..6..73...9....1.....2.....4.7..686...9....7.....5..rating:   6720 ,    4539 , ..3.2....4...8..36..83..1...4..6..73...9..........2.....4.7..686........7.....5..rating:   6717 ,    2872 , ..3.2....4...8..36..8...14..4..6..73...9..........2.....4.7..686........7.....5..rating:   6691 ,    2736 , ..3......4...8..36..8...1...4..6..73...9.7........2.1...4.7..686........7.....5..rating:   6685 ,    3350 , ..3.9....4...8..36..8...1...4..6..73...9...5......2.....4.7..686........7.....5..rating:   6568 ,    2192 , ..3......4...8..36..8...1...4..6..73...93.........2.....4.7..686........7.....59.rating:   6523 ,    2997 , ..3......4...8..36..8...1...4..6..73..69..........2.....4.7..686...9....7.....5..rating:   6479 ,    2824 , ..3......4...8..36..8...1...4..6..73...9..6.......2.....4.7..686...2....7.....5..rating:   6438 ,    1755 , ..3......4...8..36..8...1...4..6..73...93..1......2.....4.7..686........7.....5..rating:   6436 ,    3078 , ..3.2....4...8..36..8...1...4..6..73...9...5......2.....4.7..686........7.....5..rating:   6232 ,    2407 , ..3......4...8..36..8...1...4..6..73...9..6.......2.1...4.7..686........7.....5..`

a {2+2} on these to follow

C
coloin

Posts: 1864
Joined: 05 May 2005

### Re: The making of a gotchi, a simple way to find extreme sud

Wow, a suexratt nest this puzzle.

I never had tried this rating. Now i scanned 25000 of the puzzles in this T&E list. Beside of some of the above puzzles i found some more with rating > 6000 or 4000 resp.. These are 'suexratt x.x 10000' ratings:
Code: Select all
`  8917 ,    5333 , ...4......5..8.2.6.....7...2...4....3......1...5.3.8.25...6.3.8..6....95..8......  8568 ,    4143 , 1....6.8...71....66.....15..3.9.....7....184.....2........9.41.5....4..8...8..5..  8508 ,    4880 , .2....7..4....9.3.6..2.3.4.....1......89.....9....4.6..94....5.5.....6.3.....5...  8491 ,    4603 , 1...5.7.9..7.......6.......2...........5.1..2....2.39.3.4.9...15...1...3...8...4.  7927 ,    3770 , ...4......5...9...6...2..1.2...7.9.1..5....7......8.3...6....9.7...3.1......9.327  7799 ,    4027 , ...4......5..8.2.6.....71..2...4....3......1...5.3.8.25...6.3.8..6....9...8......  7515 ,    5454 , 1...5.7.9..71......6.......2...........5.1..2....2.39.3...9...15...1...3...8...4.  7270 ,    3085 , 1...56....5718...66...7.....9.3............9.8....5..35...17..8..2....1.......4..  7140 ,    4410 , 1....6.8...7.....66.....15..3.9.........2....7....854.....9.81.8...41..5.1....4..  6993 ,    4979 , ...4......5..8.2.6.....7...2...4....3......1...5.3.8.25...6.3.8..6..8.9...8......  6952 ,    4241 , ...4......5..8.2.6.....7...2........3.....51...5.3.8.25...6.3.8..6....9...8.7....  6903 ,    3436 , 12..5...9.57...2...9..2..1....8..9.47...6.1.......4............57..9.6....6..3...  6753 ,    4018 , .2.4...8...7.....3.8.237.1.2.1....9..9....8.4...9......1.8...4.5............6...8  6752 ,    4026 , .2.4...8...7.....3...237.1.2.1....9..9....8.48..9......1.8...4.5.8..........6....  6747 ,    4052 , .2.4...8...7.....3.8.237.1.2.1....9..9....8.4...9......1.8...4.5.8..........6....  6727 ,    3848 , 1...5.7.9..7.......6.......2...........5.1..2....2.39.3...9...15...1..23...8...4.  6717 ,    3576 , ...4....94....92.....23...1........5..6..3.1.7..92.3..3...9.8..8..34.....7...8...  6678 ,    4348 , ..3..67.........2.79.2......3....6..5....4..76.7..3.453.5..74...............1...8  6645 ,    4192 , ..3.5.....5.1..2.66...2..4....8...9..8..1.6.5...6.....7.......4..........6...18.2  6628 ,    4182 , ..3.56....5.1..2.6....2..4...68...9..8..1.6.5...6.....7.......4..........6...18.2  6602 ,    4877 , ..3.....945...92....9..3.54....6....6..9..8....5..8.2..1.7................4..5.92  6598 ,    3391 , ...4.6.8.4...8.2..6....2.4.....9...5.3.......9..6.8.2.....7.1...91......7..8...9.  6577 ,    3402 , .2.4..78...6.8...2..92....6.......1..9..4...76....5....7.5...........3..9.2.7...8  6559 ,    3821 , ......7....71.9...86..7......1.6.9535..3.......6.9.8....8.1.6.......2......6...4.  6533 ,    3830 , 1..4....9....8.....98....4...56..19.6...3.5..9.....3.6.7.......5..1..9.3.....2...  6532 ,    2811 , 1...56..9..7.......6.......2...........5.1..2....2.39.3.4.9...15...1...3...8...4.  6528 ,    3822 , .....67....71.9...86..7......1...9535..3.......6.9.8....8.1.6.......2......6...4.  6491 ,    3734 , .....6.....71..2..68......1..59.8.7...8.7.59....5....2..18..92...........4..3....  6482 ,    3628 , .2....7..4....9.3.6..723.4...89.........1....9....4.6..94....5.5.....6.3.....5...  6462 ,    3635 , .2......9...7...2.7...3.6.....6...3...1......6...435..5....8...8....4.5..643..8..  6448 ,    2651 , .2...6.8.4..1.........7...1.84..7.6.......9......3.....76..5.2.8....2.....276..5.  6434 ,    3331 , ..3.5.7.9...1......8.....4...5.9..67.....2...8.....9..3....56......6..94..6.4..7.  6374 ,    4140 , .....6..9..67...3.79...3....1...7.5...752......5.....2..167..2......14..8........  6354 ,    3738 , ...4......5..8.2.68....7...2........3......1...5.3.8.25...6.3.8..6....9...8.7....  6344 ,    4397 , ..34.........8..36..8...1.4.4..6..73...9..........2..5..4.7..686........7.....5..  6338 ,    4433 , ...4......5..8.2.6.....71..2........3.....51...5.3.8.25...6.3.8..6..8.9...8......  6335 ,    3690 , ...4...8..5..8.2.6.....7...2........3......1...5.3.8.25...6.3.8..6....9...8.7....  6294 ,    3338 , ...4....9.5..8.2.6.....7...2........3......1...5.3.8.25...6.3.8..6....9...8.7....  6262 ,    3565 , .....6....5.7...2...7...6...1.3...9.3..9.......5.17.3.53.1...7...2.....8.....43..  6189 ,    3426 , 1..4...8..5...9..2..9.........6..8.36.......4....41.6...2.7.5...7.......8..3...4.  6188 ,    2117 , ..3.........7.....7...1..5...4......5..9.1.2.93..2.8...9..6.5..6....2.9....1.7.6.  6183 ,    3488 , 1..4...8..5...9..2..9.........6..8.36.......4....41.6...2.7.5...7.......8..3...4.  6116 ,    2484 , ...4..7....6...23.7....3..52....83.....9....88.....52.3....587.....4...3..1......  6092 ,    2736 , ......7....71.9...68..7......851.9..5....3.....1.6.85...6.9.12.........4...2.....  6069 ,    4284 , .2.4...8......9..2..9.3............5..8..7....4.5..82...46..21.6.21..4...1......8  6067 ,    4552 , ........9.5.7...2.7.9..2....1.67..5.......4..8....5....7.31....6....7.3..3..6...1  6065 ,    2711 , ..34...8..5..8...37...3.5..23..4..9...19.......9.....1.6..2............2..28.4.3.  6019 ,    3949 , 12..5.7.9..7.......6.......2...........5.1..2....2.39.3...9...15...1...3...8...4.  5995 ,    4032 , ....5.7..4.7..9.3..8....1..2.8..7.....4..8....7..9...3......6...4...2.97..2.....1  5973 ,    4360 , .2.4.6..9..7......6...2..5......15...1.64...28......1..3.26.....6..1...39....3...  5812 ,    4278 , 1....67.9.5.........9.....4....9..3.....1....9..6..8.1..27.....7..8...4.8...6.1.7  5778 ,    4081 , .2..5...9...7.....7.....5..2..........4..8....6..2..91.3.2..9..6...9..13..1.6..2.  5708 ,    4095 , .......8...67......8...36.5.4..3..5......4..66....83.4..1.9..2..3...25..9........`
eleven

Posts: 2283
Joined: 10 February 2008

### Re: The making of a gotchi, a simple way to find extreme sud

I do suexrat9 x.x 20
which quickly trims the top ones
suexratt x.x 1000, and then an accurate 10000 count

we are selectivly getting puzzles which suexratx rates highly.

i cant believe something wont come out of these - or the next batch of mine

this very quickly gets to a stage where it is not possible to search every possibly high rated puzzle 3500/2200 [GN]

all your puzzles could possibly deliver an even better one with expansion

C
coloin

Posts: 1864
Joined: 05 May 2005

### Re: The making of a gotchi, a simple way to find extreme sud

Wow,

The results are certainly ones that I can't match at this moment. I will be publishing what I think can make the Hardest list (although they will look very ordinary next to all of this).

Can we make sure that all puzzles are posted on the Hardest sudokus thread for them to be procesed.

Well done,

tarek tarek

Posts: 3425
Joined: 05 January 2006

### Re: The making of a gotchi, a simple way to find extreme sud

Note, that i already had posted some of the puzzles in the hardest thread (22 clues), including the 11.0 in my T&E post, nr.s 1,2,7,19 in coloins post and 35,40,42 in my last list.
[Added:] Nr 4 in coloin's list is in my Part 3 list.

Another note:
The puzzle
Code: Select all
`..3.9....4...8..36..8...1...4..6..73...9..6.......2.....4.7..686........7.....5.. q1/q2 1612/1440, ER 9.9/1.5/1.5, suexratt 6794/3374 (!)`
can be solved with T&E(basics, 1).
eleven

Posts: 2283
Joined: 10 February 2008

### Re: The making of a gotchi, a simple way to find extreme sud

eleven ive no doubt you have some of the puzzles in your collections ......... the {-x+x} generation methods are indeed not groundbreaking

ive done a furthur {-2+2}x2 on the "best" puzzles from the initial {-2+2} on your "tamagotcha" puzzle. Any one of your puzzles could lead to a higher concentrated region.

First run with {2+2}
Code: Select all
`sxt >24007256      4302         ..3..2...4...8..36..8...1...4..6..73...9..........4.....4.7..686........7.....59. # 85324 FNBP C22.m/M2.9.13122      8399      4167         ..39.....4...8..36..8...1...4..6..73...3...1......2.....4.7..686........7.....5.. # 97517 FNBP C22.m/M2.5.24928      6295      3880         ..39.....4...8..36..8..41...4..6..73.......1......2.....4.7..686........7.....5.. # 98751 FNBP C22.m/M2.7.3748      8649      3845         ..39.....4...8..36..8...1...4..6..738......1......2.....4.7..686........7.....5.. # 95442 FNBP C22.m/M2.11.2384      5580      3759         ..3......4...8...6..83..1...4..6..73...9....1.....2.....4.7..686........7.....54. # 97581 FNBP C22.m/M2.7.1874      5346      3291         ..3.2....4...8..36..8...1...4..6..73...9..........2.......7..686....4...7.....54. # 95046 FNBP C22.m/M2.7.5622      5639      3192         ..3......4...8..36..8...1...4..6..73...9....1.....2.......7..686....4...7.....54. # 97512 FNBP C22.m/M2.5.9184      5235      3174         ..3.....24...8..36..8...1...4..6..73...9..........2.......7..686....4...7.....5.4 # 97564 FNBP C22.m/M2.13.2520      5698      3132         ..3..2...4...8..36..8...1...4..6..73...9..........4..2..4.7..686........7.....5.. # 97648 FNBP C22.m/M2.7.17803      4351      2989         ..3.2....4...8..36..8...1...4..6..73...9..........26....4.7...86........7..6..5.. #  1574 FNBP C22.m/M2.35.374      6090      2984         ..3......4...8..36..8...1...4..6..73...9...1......2.......7..686....4...7.....54. # 98491 FNBP C22.m/M2.1.524880   5701      2979         ..3...9..4...8..36..81......4..6..73.......1......2.....4.7..686........7..6..5.. # 97993 FNBP C22.m/M2.3.48114      5065      2955         ..3..2...4...8..36..8...1...4..6..73...9..6.........1...4.7...86........7..6..5.. # 10080 FNBP C22.m/M2.25.4454      7506      2900         ..3..2...4...8..36..8...1...4..6..73...9.......6........4.7..686........7.....59. # 78304 FNBP C22.m/M2.4.11480      5378      2851         ..3......4...8..36..8...1.9.4..6..73...9..........2.....4.7..686.....5..7..6..... # 95761 FNBP C22.m/M2.16.1640      4261      2836         ..3...5..4...8...6..83..1...4..6..73...9.........32.....4.7..686........7......9. # 95045 FNBP C22.m/M2.34.768      6035      2799         ..3..2...4...8..36..8...1...4..6..73...9.4..............4.7..686........7.....59. # 95082 FNBP C22.m/M2.5.10496      4663      2773         ..3..61..4...8..36..8.......4..6..73...9..........2.5...4.7..686........7.....5.. # 97960 FNBP C22.m/M2.2.52480      5556      2746         ..3......4...8...6..83..1...4..6..73...9..........2.....4.7..686......1.7.....59. # 95065 FNBP C22.m/M2.25.262      4670      2738         ..31.6...4...8..36..8.......4..6..73...9..........2.5...4.7..686........7.....5.. # 97716 FNBP C22.m/M2.6.16395      5028      2720         ..3......4...8..36.68...1...4..6..73..69...1......2.....4.7..68.........7.....5.. # 64237 FNBP C22.m/M2.5.24928      4772      2718         ..3......4...8..36..8...1...4..6..73...9..........2.5.....7..686....4...7.....54. # 98779 FNBP C22.m/M2.4.36080      6356      2708         ..3......4...8..36..8...1...4..6..73...9..........2.......7..686....4.9.7.....5.4 # 97529 FNBP C22.m/M2.8.28700      5137      2686         ..3......4...8..36..8...1...4..6..73.....9..1.....2.....5.7..686...9....7.....5.. #  1425 FNBP C22.m/M2.17.2310      4775      2677         ..3.9....4...8..36..8...1...4..6..73............9.2.......7..686..4.....7.....5.4 # 68420 FNBP C22.m/M2.7.6559      5894      2585         ..3......4...8..36..8...1...4..6..73...9..........2.....4.7..686....45..7......2. # 96998 FNBP C22.m/M2.14.7956      5120      2569         ..3.9....4...8..36..8...1...4..6..73...9..6.......2.....4.7...86........7.....54. #  1351 FNBP C22.m/M2.41.320      4516      2544         ..3.9....4...8..36..8...1...4..6..73............9.2.......7..686..4.....7.....54. # 95157 FNBP C22.m/M2.11.2980      4711      2502         ..3..1...4...8..36.68.......4..6..73...9...5......2.....4.7..686........7.....5.. # 97712 FNBP C22.m/M2.6.16395      4029      2362         ..3......4...8..36..8.9.1...4..6..73...9..........2.......7..686....4...7.....5.4 # 98755 FNBP C22.m/M2.5.51168      q2> 970003708      1787         ..3......4...8..36..8...1......6..73...9..4.......4..5..4.7..686....2...7.....5.. # 98181 FNBP C22.m/M2.2.72160      2704      1488         ..31.....4...8..36..8....9..4..6..73...9...1......2.....4.7...86........7..6..5.. # 97677 FNBP C22.m/M2.15.1311      4720      2025         ..3...2..4...8..36..8..1....4..6..73...9..6.........1...4.7..686........7.....5.. # 97644 FNBP C22.m/M2.8.18040      4964      1256         ..3......4...8..36..8...1...4..6..73...9..........2.......7..686....4...7...2.5.4 # 97621 FNBP C22.m/M2.14.1404      2484      1332         ..3.1....4...8..36..8...1...4..6..71...9..........2.......7..686....4...7.....54. # 97560 FNBP C22.m/M2.12.2730      2710      1218         ..3......4...8...6..8...15..4..6..73...9..........2.......7..686....4.2.7.....54. # 97529 FNBP C22.m/M2.7.9370      2502      1127         ..3......4...8..36..8...1...4..6..73...9..........7.....4.7..186..1.2...7.....5.. # 97513 FNBP C22.m/M2.8.4920      2030      1269         ..3.....44...8..36..8...1...4..6..73...9..........2.....4.7..686...2....7....5... # 97505 FNBP C22.m/M2.23.1140      2199      1475         ..32.....4...8..36..8...1...4..6..73...9....4.....2.....4.7...86........7..6..5.. # 97502 FNBP C22.m/M2.8.1640      3958      1404         ..3......4...8..36..8...1...4..6..73...9..4..........5....7..686....2...7...4.5.. # 97407 FNBP C22.m/M2.7.19677      3617      1762         ..3......4...8...6..8...14..4..6..73...9..........2.....4.7..686......2.7..3..5.. # 97368 FNBP C22.m/M2.12.11466   5313      2444         ..3......4...8..36..8...1.9.4..6..73...9..........2.....4.7..686....45..7........ # 97221 FNBP C22.m/M2.19.1035      3198      1770         ..3......4...8..36..8...1...4..6..73...9..........4..2..4.7..686....25..7........ # 97004 FNBP C22.m/M2.16.8200      `

Second run - x5 more puzzles searched note
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`sxt>24006432      4209         ..39.....4...8..36..8...1...4..6..73.............92.......7..686....4...7.....5.4 # 95122 FNBP C22.m/M2.17.1540   6853      4096         ..3..61..4...8..36..89......4..6..73..............2..1..4.7..686........7.....5.. # 97687 FNBP C22.m/M2.8.13940   6220      3961         ..39.....4...8..36..8...1...4..6..73....9.........2.......7..686....4...7.....5.4 # 95039 FNBP C22.m/M2.7.5622   6105      3825         ..3..61..4...8..36..89......4..6..73........1.....2.....4.7..686........7.....5.. # 98779 FNBP C22.m/M2.5.24928   5865      3791         ..3..4.......8..36..8...14..4..6..13.....1......9.2.....4.7..686........7.....5.. # 93818 FNBP C22.m/M2.9.15309   5349      3547         ..3..4.......8..36..8...14..4..6..83...9..........2.....4.7..686......2.7.....5.. # 96530 FNBP C22.m/M2.10.223045138      3529         ..3...2..4...8..36..8..1....4..6..73...9..........4..2..4.7..686........7.....5.. # 97543 FNBP C22.m/M2.15.874   6656      3524         ..39.....4...8..36......1...4..6..738......1......2.....4.7..686........78....5.. # 95569 FNBP C22.m/M2.12.2184   5410      3486         ..35.....4...8..36..8...1...4..6..73............4.2.....4.7..6869.......7.......4 # 95968 FNBP C22.m/M2.4.67240   5733      3414         ..3...1..4...8..36..6.9.....4..6..73...9...1......2.....4.7..688........7.....5.. # 74898 FNBP C22.m/M2.5.51168   5158      3375         ..3...1..4...8..36..8..2....4..6..73...9...1......3.....4.7..686........7.....5.. # 97877 FNBP C22.m/M2.10.5248   5109      3361         ..3..2...4...8..36..8...1...4..6..73...9..........46....4.7...86........7.....59. # 82438 FNBP C22.m/M2.9.26973   5106      3323         ..3..61..4...8..36..89......4..6..73..............2.9...4.7..686........7.....5.. # 97975 FNBP C22.m/M2.5.28864   4439      3291         ..3......4...8..36..8...1...4..6..73...9..........2.5.....3..676....4...7.....54. # 98510 FNBP C22.m/M2.4.29520   7227      3243         ..3.9....1...4..36..8..21...4..8..73...9................4.7..686........7.....5.4 #   706 FNBP C22.m/M2.15.1311   5539      3209         ..39.....4...8..36..8...1...4..6..73...4..........2.......79.686........7.....5.4 # 95083 FNBP C22.m/M2.22.298   5270      3201         ..3......4...8..36..8...1.4.4..6..73.....9........2.....5.7..686...2....7.....5.. #  1510 FNBP C22.m/M2.14.2340   5801      3169         ..3......4...8..36..8...14..4..6..73.....9........2.....5.7..686...2....7.....5.. #  1441 FNBP C22.m/M2.15.1311   4537      3127         ..34.........8..36..8...14..4..6..73...9..........2.....4.7..686.....5..7......2. # 95453 FNBP C22.m/M2.16.7380   5545      3127         ..3.24...4...8..36..8.......4..6..73......1.....9.2.....4.7..686........7.....5.. # 52795 FNBP C22.m/M2.8.4920   6141      3127         ..341....4...8..36..8.......4..6..73...9.1.........2....4.7..686........7.....5.. # 49411 FNBP C22.m/M2.6.20767   4678      3108         ..3...9..4...8..36..81......4..6..73......6.......2.9...4.7...86........7..6..5.. # 97049 FNBP C22.m/M2.11.137086327      3059         ..3..4.......8..36..8...14..4..6..73.......5......2.....4.7..686..9.....7.....5.. # 98778 FNBP C22.m/M2.7.5622   5588      3054         ..3..9...4...8..96..8...1...4..6..73...9.........3......4.7..686....2...7.....5.. # 78445 FNBP C22.m/M2.5.24928   5108      2964         ..3......4...8..36..8..61...4..6..73...92...........2...4.7..686........7.....5.. # 71176 FNBP C22.m/M2.7.16866   5328      2945         ..39.....4...8..36..8...1...4..6..73......6.1.....2.....4.7...86........7....65.. # 32176 FNBP C22.m/M2.16.410   6180      2924         ..3.4....4...8..36..8...1...4..6..73...9....2....2......4.7..686........7.....5.. #   763 FNBP C22.m/M2.5.5248   4446      2921         ..3..61..4...8..36..89......4..6..73.......9......2.....4.7..686........7.....5.. # 98221 FNBP C22.m/M2.10.4592   5019      2903         ..3......4...8..36..86..1...4..6..73...92...........2...4.7..686........7.....5.. # 73536 FNBP C22.m/M2.12.1638   4506      2900         ..31.....4...8..36..8..3....4..6..73...9...........5....4.7..686....2...7......5. # 46543 FNBP C22.m/M2.13.8064   4492      2886         ..3......4...8..36..8...1...4..6..13...1........9.2.......7..686....4...7.....5.4 # 95208 FNBP C22.m/M2.17.2310   4468      2833         ..39.....4...8..36..8...1...4..6..73.....4........2.....4.7..686.....5..7......9. # 97515 FNBP C22.m/M2.8.15580   4448      2827         ..3......4...8..36..6...1.9.4..6..73...9..........7.....4.7..688....2...7.....5.. # 95045 FNBP C22.m/M2.14.9360   3987      2824         ..3...2..4...8..36..8..1....4..6..73...9...5........1...4.7...86........7....65.. # 97622 FNBP C22.m/M2.10.5248   4529      2823         ..3......4...8..36..8...1...4..6..73...9..........26.1..4.7...86.....5..7..6..... # 26248 FNBP C22.m/M2.42.156   5793      2821         ..3......4...8..36..8...1...4..6..73...92............2..4.7..686...4....7.....5.. #   812 FNBP C22.m/M2.4.11480   3963      2802         ..3.....24...8..36..8...1...4..6..73...9..........26....4.7...86.....5..7..6..... #  2432 FNBP C22.m/M2.67.291   4127      2794         ..3......4...8..36..8...1...4..6..73...9..........2.......3..676....4.9.7.....5.4 # 97603 FNBP C22.m/M2.9.6561   3766      2765         ..3..4.......8..36..89..14..4..6..73....9.........2.....4.7..686........7.....5.. # 97208 FNBP C22.m/M2.5.7872   4711      2760         ..39.....4...8..36..8...1...4..6..73.......1......26......7...86....4...7.....54. # 95327 FNBP C22.m/M2.12.2184   4080      2753         ..3...2..4...8..36..8..1....4..6..73...91.........7.....4.7..686........7.....5.. # 95775 FNBP C22.m/M2.14.468   4693      2732         ..3......4...8..36..8...1...4..6..73...9...2.....2.6....4.7...86........7..6..5.. # 35471 FNBP C22.m/M2.18.1456   4182      2731         ..3......4...8..36..81......4..6..73...9..6.........5...4.7..686....2...7.....5.. # 95093 FNBP C22.m/M2.14.7488   4512      2722         ..3......4...8..36..8...1...4..6..73............9.2.....4.7..686..4..5..7.......9 # 95007 FNBP C22.m/M2.42.312   6480      2702         ..3......4...8..36..8...1...4..6..73...9....2....2......4.7..686...4....7.....5.. #   805 FNBP C22.m/M2.2.22960   3515      2692         ..3......4...8..36..8...1...4..6..73...9....1.....2.......3..676....4...7.....54. # 97556 FNBP C22.m/M2.3.13122   4783      2689         ..3...1..4...8..36..8.......4..6..73...9..........2.....4.7..686....45..7......9. # 97611 FNBP C22.m/M2.19.4140   3930      2688         ..31.....4...8..36..8..3....4..6..73...9..5.............4.7..686....2...7......5. # 73881 FNBP C22.m/M2.11.9536   4501      2674         ..39.....4...8..36..8...1...4..6..73.......1...6..2.....4.7...86........7....65.. #  4066 FNBP C22.m/M2.24.4641   4695      2655         ..3......4...8..36..8...1...4..6..73.....9........2.5...5.7..686...2....7.....5.. #  1059 FNBP C22.m/M2.28.468   4306      2640         ..3..4.......8..36..8...14..4..6..73....9.........2.....4.7..686..9.....7.....5.. # 95301 FNBP C22.m/M2.17.385   4082      2631         ..3......4...8..36..8...1...4..6..73...9........2...5...4.7..986....9...7.....5.. # 95906 FNBP C22.m/M2.2.1246404514      2624         ..3......4...8..36..8...1...4..6..73.....9.5......2.....5.7..686...2....7.....5.. #  1064 FNBP C22.m/M2.28.468   3756      2603         ..3...1..4...8..36..86....2.4..6..73...9..........2.....4.7..686.....5..7........ # 97303 FNBP C22.m/M2.18.2184   4074      2602         ..3......4...8..36..81......4..6..73...9.......6....5...4.7..686....2...7.....5.. # 95093 FNBP C22.m/M2.14.7488   3754      2596         ..34.........8..36..8...14..4..6..73...9..........2.....4.7..686.....52.7........ # 95230 FNBP C22.m/M2.27.729   4645      2596         ..39.....4...8..36.68...1...4..6..73..6....1......2.....4.7..68.........7.....5.. # 52187 FNBP C22.m/M2.4.26240   3844      2592         ..3...2..4...8..36..8..1....4..6..73...91.........3.....4.7..686........7.....5.. # 97055 FNBP C22.m/M2.13.1512   4059      2592         ..3.2....1...4..36..89..1...4..6..73..............2.....4.7..686........7.....54. #   812 FNBP C22.m/M2.21.1248   4586      2587         ..3......4...8..36..8...1...4..6..73.....9.......42.....5.7..686...2....7.....5.. #  1552 FNBP C22.m/M2.17.1155   4454      2586         ..39.....4...8..36..8...1...4..6..73......61......2.....4.7...86........7....65.. #  4066 FNBP C22.m/M2.24.1365   3617      2583         ..3...5..4...8...6..8..31...4..6..73...9.........42.....4.7..686........7......9. #  4346 FNBP C22.m/M2.38.516   4250      2578         ..3..4.......9..36..8...14..4..6.273............9.2.....4.7..686........7.....5.. # 77423 FNBP C22.m/M2.46.284   4503      2575         ..31.....4...8..36..8..3....4..6..73...9...........5....4.7..686....2...7.......5 # 47285 FNBP C22.m/M2.7.14992   5076      2571         ..342........8..36..8...4...4..6..73......1.....9.2.....4.7..686........7.....5.. # 42668 FNBP C22.m/M2.6.21860   4308      2570         ..3......4...8..36..6...1.9.4..6..73...9..........4.....4.7..688....25..7........ # 97610 FNBP C22.m/M2.13.1512   4472      2568         ..3......4...8..36..8...1...4..6..73............9.2.....4.7..686..4..5..7.......2 # 91400 FNBP C22.m/M2.42.312   5378      2557         ..3.2....1...4..36..89..1...4..8..73........1.....2.....4.7..686........7.....5.. #   520 FNBP C22.m/M2.20.328   3713      2529         ..3......4...8..36..8..1.2..4..6..73...9..........42....4.7..686........7.....5.. # 97580 FNBP C22.m/M2.16.1640   5143      2527         ..3.9....4...8..36..8..1....4..6..73...9...4.......2....4.7..686........7.....5.. # 95106 FNBP C22.m/M2.15.3059   4540      2527         ..39.....4...8..36..8...1...4..6..73............4.2.......79.686........7.....5.4 #  6917 FNBP C22.m/M2.22.298   4069      2512         ..3......4...8..36..8...1.9.4..6..73...9..........2.....4.7..686..3..5..7........ # 95844 FNBP C22.m/M2.19.1725   3735      2508         ..34.....4...8..36..8..1....4..6..73...9..6........2....4.7...86........7.....59. # 25651 FNBP C22.m/M2.37.354   4707      2506         ..3......4...8..36..8...1...4..6..73....49........2.....5.7..686...2....7.....5.. #  1559 FNBP C22.m/M2.18.1092   4767      2505         ..3......4...8..36..8...1...4..6..73.....9..1.....2.....5.7..686...2....7.....5.. #  1428 FNBP C22.m/M2.17.2310   4769      2499         ..3......4...8..36..81......4..6..73...92.6..........2..4.7..686........7.....5.. # 92686 FNBP C22.m/M2.22.596   3881      2499         ..31.....4...8..36..8..3....4..6..73...9....2......5....4.7..686....2...7........ # 84805 FNBP C22.m/M2.14.7488   3767      2492         ..31.....4...8..36..8..3....4..6..73...9....1......5....4.7..686....2...7........ # 78243 FNBP C22.m/M2.10.104964066      2477         ..3...1..4...8..36.68.......4..6..73..69...5......2.....4.7..68.........7.....5.. # 56871 FNBP C22.m/M2.6.5465   3454      2472         ..3.2....1...8..36..8...1.4....6..73...9..4.......2.....2.7..686........7.....5.. # 95022 FNBP C22.m/M2.7.9370   3897      2469         ..3......4...8..36..8...1...4..6..73..69..........2.....5.7..486...2....7.....5.. #  1856 FNBP C22.m/M2.8.18040   4580      2465         ..3......4...8..36..81......4..6..73...92......6.....2..4.7..686........7.....5.. # 92686 FNBP C22.m/M2.22.596   3499      2451         ..3......4...8...6..83..1...4..6..73...9....1.....2.....4.3..676........7.....54. # 97518 FNBP C22.m/M2.6.4372   4629      2444         ..3...2..4...8..36..8..1....4..6..73...9.......6....1...4.7..686........7.....5.. # 97644 FNBP C22.m/M2.8.19680   3493      2443         ..3......4...8..36..8...1...4..6..73...9..6.......2..1..4.3...76........7.....54. # 97566 FNBP C22.m/M2.4.6560   3524      2434         ..3..4.......8..36..8...14..4..6..73............9.2.....4.7..686...2....7.....5.. #  1348 FNBP C22.m/M2.32.205   3886      2432         ..3.9....4...8..36..8..1....4..6..73...9.....8.....2....4.7..686........7.....5.. #  1146 FNBP C22.m/M1.1.79   3873      2429         ..39.....4...8..36..8..41...4..6..73........1.....2.....4.7..686.....5..7........ # 95493 FNBP C22.m/M2.15.1748   3422      2420         ..3.2....4...8..36..8...1.4....6..73...9..4.......2.....2.7..686........7.....5.. # 97686 FNBP C22.m/M2.8.7380   3732      2420         ..3..4.......2..36..8...14..4..6.973............9.2.....4.7..686........7.....5.. # 87105 FNBP C22.m/M2.52.252   3773      2401         ..3.9....4...8..36..6...1...4..6..73...9..........2.......7..688....4...7.....5.4 # 95069 FNBP C22.m/M2.5.9184   4154      2401         ..3.9....1...8..46..8...1...4..6..73.....9...8....2.....4.7..686........7.....5.. #  1550 FNBP C22.m/M2.15.874   q2>970002475      1961         ..3......4...8..36..84..1...4..6..73...9.2.5............4.7...86........7.....54. # 98753 FNBP C22.m/M2.10.4592   4432      1807         ..3...2..4...8..36..8..1....4..6..73...9..6..........2..4.7...86........7.....52. # 98753 FNBP C22.m/M2.8.18040   3369      2340         ..3......4...8..36..8..21...4..6..73...9.........2........7..686....4...7.....5.4 # 98708 FNBP C22.m/M2.6.24046   2175      1727         ..3......4...8..36..84..1...4..6..73............9.2.5.....7...86....4...7.....54. # 98673 FNBP C22.m/M2.11.4172   3326      2287         ..39....4....8..36..8..41...4..6..73.......1......2.....4.7..686........7.....5.. # 98168 FNBP C22.m/M2.20.1968   2681      1287         ..3......4...8..36..81....2.4..6..73...9..6.............4.7..686....2...7.....5.. # 98122 FNBP C22.m/M2.18.728   2767      1263         ..3......4...8..36..81....2.4..6..73...9.......6........4.7..686....2...7.....5.. # 98122 FNBP C22.m/M2.18.728   3230      2350         ..3...2..4...8..36..8..1....4..6..73...9........7...1...4.7..686........7.....5.. # 97991 FNBP C22.m/M2.9.5103   2507      1139         ..3......4...8..36.681....2.4..6..73...9.......6........4.7..68.....2...7.....5.. # 97980 FNBP C22.m/M2.18.728   3120      1835         ..39.....4...8..36..8...1...4..6..73........9.....24......7..686....4...7.....5.. # 97876 FNBP C22.m/M2.6.6558   3545      2039         ..3......4...8..36..8..1....4..6..73...9..........42....4.7..686........7.....5.2 # 97815 FNBP C22.m/M2.19.2070   4047      2206         ..34..2..4...8..36..8..1....4..6..73...9...2............4.7..686........7.....5.. # 97812 FNBP C22.m/M2.6.6558   3851      2151         ..3......4...8..36..8..1....4..6..73...9.4.........2....4.7..686........7.....52. # 97743 FNBP C22.m/M2.20.656   3824      2061         ..3......4...8..36..8..1....4..6..73...9.46........2....4.7...86........7.....52. # 97743 FNBP C22.m/M2.20.656   3404      2081         ..3......4...8..36..8..21...4..6..73...9.......6........4.7..686..5.....7......9. # 97725 FNBP C22.m/M2.1.2165131839      1328         ..3..2...4...8..36..81....4.4..6..73..............9.1...4.7..686........7.....5.. # 97714 FNBP C22.m/M2.27.972   1895      1307         ..31.....4...8..36..8....5..4..6..73...9........3....5..4.7..686....2...7........ # 97708 FNBP C22.m/M2.34.960   1939      1276         ..3...2..4...8..36..8..1....4..6..73...9..6.........1.....7...86..4.....7.....54. # 97678 FNBP C22.m/M2.17.3465   2728      1407         ..3..2...4...8..36..81......4..6..73...9..6..........5..4.7..686.....5..7........ # 97648 FNBP C22.m/M2.19.1035   2696      1388         ..3..2...4...8..36..81......4..6..73...9.......6.....5..4.7..686.....5..7........ # 97648 FNBP C22.m/M2.19.1035   2302      1140         ..3..2.......8..36..8.4.1...4..6..73...9...........45...4.7..686........7.....5.. # 97630 FNBP C22.m/M2.8.4100   2189      1344         ..314........8..36..8...4...4..6..73...9..........2.5...4.7..686........7.....5.. # 97609 FNBP C22.m/M2.8.1640   3446      1922         ..3......4...8..36..8...1...4..6..73...9..........2.....4.7..286....45..7..2..... # 97601 FNBP C22.m/M2.4.36080   3894      2115         ..3...2..4...8..36.68..1....4..6..73...9.......6....1...4.7..68.........7.....5.. # 97588 FNBP C22.m/M2.10.157442620      1759         ..3..1...4...8..36..8.....4.4..6..73...9..........2.....4.7..686.....5..7......2. # 97584 FNBP C22.m/M2.26.252   2411      1513         ..3...2..4...8..36..8..1....4..6..73...9..6.........1...4.7...86........7..6..5.. # 97563 FNBP C22.m/M2.28.468   2833      1443         ..3...9..4...8..36..81......4..6..73.......1......26....4.7...86........7.....54. # 97558 FNBP C22.m/M2.12.4368   3043      2176         ..3...2..4...8..36..8..1....4..6..73...9....2...3.......4.7..686........7.....5.. # 97552 FNBP C22.m/M2.15.874   2573      1303         ..39.....4...8...6..83..1...4..6..73..............2..1..4.7..686......9.7.....5.. # 97547 FNBP C22.m/M2.31.422   2671      1895         ..3..72..4...8..36..8..1....4..6..73...9............1...4.7..686........7.....5.. # 97537 FNBP C22.m/M2.20.984   2592      1893         ..3..1...4...8..36..8.......4..6..73........5...9.2.....4.7..686..4..5..7........ # 97537 FNBP C22.m/M2.5.3936   3304      1939         ..31..5..4...8..36..8..3....4..6..73...9...2............4.7..686....2...7........ # 97534 FNBP C22.m/M2.16.820   3070      1904         ..3......4...8..36..8..1....4..6..73...9..........42....4.7..686........7.....5.1 # 97534 FNBP C22.m/M2.25.1048   3014      1704         ..31..5..4...8..36..8..3....4..6..73...9....2...........4.7..686....2...7........ # 97532 FNBP C22.m/M2.16.820   2242      1390         ..3...2..4...8..36..8..1.9..4..6..73...9............1...4.7...86........7....65.. # 97529 FNBP C22.m/M2.14.2808   2220      1313         ..3...9..4...8...6..81...2..4..6..73.......1......2.5...4.7...86........7..6..5.. # 97529 FNBP C22.m/M2.14.2340   3492      2280         ..31.....4...8...6..8..3....4..6..73...9.............5..4.7..686....23..7.....5.. # 97528 FNBP C22.m/M2.14.468   2860      1498         ..3......4...8..36..81......4..6..73...9..6..........9..4.7..686....2...7.....5.. # 97528 FNBP C22.m/M3.1001.5303017      1418         ..3......4...8..36..81......4..6..73...9.......6.....9..4.7..686....2...7.....5.. # 97528 FNBP C22.m/M3.1001.5302743      1865         ..3......4...8..36..8..1....4..6..73...9..........42....4.7..686.....5..7......9. # 97521 FNBP C22.m/M2.12.2730   2561      1167         ..3..4..9....8..36..8...14..4..6..73..............2.....4.7..686..9.....7.....5.. # 97519 FNBP C22.m/M2.19.1725   2581      1720         ..3......4...8..36..8...1.9.4..6..73...9...........6....4.7...86....25..7..6..... # 97518 FNBP C22.m/M2.11.1788   2820      1700         ..3..2...4...8..36..8...4......6..73...9..1.......4..2..4.7..686........7.....5.. # 97517 FNBP C22.m/M2.5.19680   3459      2116         ..3......4...8...6..8...14..4..6..73.......1....9.2.....4.7..686..4..5..7........ # 97503 FNBP C22.m/M2.6.19674   2104      1446         ..3......4...8..36..8..1.9..4..6..73...9..........42....4.7..686........7.....5.. # 97503 FNBP C22.m/M2.17.1540   3764      2203         ..31...8.4...8..36..8.......4..6..73...9...1............4.7..686....2...7.....5.. # 97501 FNBP C22.m/M2.4.27880   1646      1089         ..3...5..4...8...6..83..1...4..6..73.....96.......2.....4.7...86.......17......9. # 97305 FNBP C22.m/M2.19.1035   3158      1765         ..3..4.......8..36..8...14..4..6..73..............2.9...4.7..686..9.....7.....5.. # 97215 FNBP C22.m/M2.30.654   3269      1718         ..3...1..4...8..36..83......4..6..73..............26....4.7...86...9.5..7......9. # 97193 FNBP C22.m/M2.7.5622   3198      1606         ..31.....4...8..36..8.......4..6..73...9...14...........4.7..686....2...7.....5.. # 97179 FNBP C22.m/M2.8.14760   2868      1573         ..31.....4...8..36..8.......4..6..73...9...1........5...4.7..686....2...7.....5.. # 97174 FNBP C22.m/M2.13.3024   3328      1927         ..3..4.......8...6..8...14..4..6..73...9..........2.....4.7..686......2.7.....51. # 97164 FNBP C22.m/M2.12.114662912      2126         ..32.....4...8..26..8...1...4..6..73............9.2.......7..686....4...7.....54. # 97107 FNBP C22.m/M2.5.9184   2710      1292         ..3..2...4...8..36..81......4..6..73...9..6.............4.7..686.....5..7.......1 # 97035 FNBP C22.m/M2.16.820   2482      1434         ..3..2...4...8..36..81......4..6..73...9...8............4.7..686........7.....5.1 # 97017 FNBP C22.m/M2.34.1152   2259      1304         ..31..4..4...8..36..8.......4..6..73...9...1............4.7..686....2...7.....5.. # 97016 FNBP C22.m/M2.14.2808   `

It would seem that the high rated suexratx puzzles are petering out - but i suppose they have to. Lingering doubts however exist that "lesser" rated puzzles that i havent extended would lead to another high rated region.

Of course we only have here puzzles which suexratx rates highly - and it brings about a long muted discussiuon as to how to rate a puzzle.

It could be that there is a possible flaw in the suexratx program which these puzzles have exposed. The reaching of the 10000/5000 sxt rating perhaps will justifiably allow the great Guenter Stertinbrink aka dukuso to perhaps comment as to why his program thinks this particular puzzle is significantly [x2] harder than Golden Nuggett.

I will politely point out this thread to him.
regards
C
coloin

Posts: 1864
Joined: 05 May 2005

### Re: The making of a gotchi, a simple way to find extreme sud

eleven wrote:
denis_berthier wrote:1) I haven't analysed Brian Turner's solver, but, from what you write, I guess that what you call forcing chains step 1 is equivalent to T&E(NS+HS, 1) as defined in the above mentioned thread , i.e. each candidate is eliminated based on only one hypothesis at a time (the assumption that this candidate is true) and no other resolution rule than NS, HS and elementary constraints propagation is used. Can you confirm?

STEP 1 does the following for each unsolved cell (starting with those with few candidates): It tries each candidate using "basics", i.e. NS, HS, locked candidates, subsets, x-wing and swordfish, plus jellyfish. (If this leads to a contradiction, all candidates are removed in this candidates result grid). Then it OR's the candidates in the resulting grids. Thus all candidates are removed, which directly lead to a contradiction (T&E(basics+jellyfish,1)) plus all, which are eliminated, whatever candidate is tried (cell forcing chain).
...
What i call "STEP 1 puzzle" for short is one, which CANNOT be solved this way (bad name).

If no guessing is allowed in your algorithm (which is how I understand it), then what remains is what can't be solved by generalised braids[NS+HS+BI+subsets+fish].
In your context of finding hardest puzzles, it makes sense to eliminate all the puzzles that can be solved by these relatively simple generalised braids (instead of by only elementary braids). I consider these extended braids simple because inferences bearing on several candidates at the same time are localised within short patterns.

eleven wrote:
denis_berthier wrote:2) Now, the hard one: as I mentioned above, all the known puzzles can be solved with 0, 1 or 2 levels of T&E(NS+HS). But, AFAIK, there has never been any proof that this should be true of ANY valid puzzle. Could your gotchi method be applied to look for T&E(NS+HS, 3) puzzles?
Considering the infinitesimal proportion of T&E(NS+HS, 2) and the time needed to find one, I'm aware that the search for T&E(NS+HS, 3) puzzles may be hopeless (because impractical). Moreover, this search is probably already implicitly included in your search for hardest. What do you think?

The bb_solver also has inplemented a STEP 2, which does the same recursively (depth 2). I only verified, that it solved the old known hardest. With minor changes (commenting out locked candidates and reducing the eliminations to the contradiction candidates) i could make it a T&E(NS+HS,2) solver. I have more than 3 mio STEP1 puzzles, which i could try. Maybe thats possible this weekend, but i see little chances, that one could not be solved eleven wrote:As expected, all of my 3.15 mio (minimal) step1 puzzles could be solved with T&E(NS+HS,2). bb-solver was very fast here too and did the job in a few hours.

Yes, from the (much smaller) already available collections of hardest, which could all be solved by T&E(NS+HS, 2) or equivalently by braids[braids], this was expected. But it remains better to be sure by checking. Thanks for doing these calculations. The size of your collection makes more likely the conjecture that there is no T&E(NS+HS, 3) 9x9 puzzle.

eleven wrote:
denis_berthier wrote:3) Could your method be extended to larger boards (e.g. 16x16) ? I mean in practice (of course, it can in theory)...

I dont have any tools for 16x16 puzzles, so this would be too much work for me. Because of the huge space its very unclear for me, what results are possible.

Can't Brian Turner's solver be easily adapted to 16x16 boards? Combined with a fast generator (suexg), there may be a chance that it produces a T&E(NS+HS, 2) - which never happened in the 9x9 case.
denis_berthier
2010 Supporter

Posts: 1394
Joined: 19 June 2007
Location: Paris

### Re: The making of a gotchi, a simple way to find extreme sud

coloin wrote:Any one of your puzzles could lead to a higher concentrated region.

Yes, but i stick to the gotchi method, which still is producing 30 ER 11+ puzzles a day.

denis_berthier wrote:Can't Brian Turner's solver be easily adapted to 16x16 boards? Combined with a fast generator (suexg), there may be a chance that it produces a T&E(NS+HS, 2) - which never happened in the 9x9 case.

Unfortunately it needs to rewrite about half of the code of the bb-solver to get a 16x16 solver. I also dont know, if there is a public program to normalize 16x16. Anyway such a gotchi would be more work than the 9x9. But in the moment the old one is still running and i am more interested to make a gotchi for a non sudoku problem.
eleven

Posts: 2283
Joined: 10 February 2008

### Re: The making of a gotchi, a simple way to find extreme sud

good to still see progress in sudoku-theory after all these years !

These results are unexpected to me ... did eleven expect it when he/she started ?

I havn't checked all the details of the description but it seems that
it was hard word, trial and error, rather than a few decisive brilliant ideas ?!?

Is the same method maybe useful to find hard exact-cover problems or hard
SAT-problems in general ?
dukuso

Posts: 479
Joined: 25 June 2005

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