Abominable TRIAL-and-ERROR and lovely BRAIDS

Advanced methods and approaches for solving Sudoku puzzles

Postby denis_berthier » Wed Nov 05, 2008 9:53 pm

Deleted: superseded by modifications in the previous post.
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Postby denis_berthier » Mon Nov 10, 2008 12:35 am

Deleted: superseded by modifications in the previous post.
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Postby denis_berthier » Wed Nov 12, 2008 11:05 pm

Deleted: superseded by modifications in the previous post.
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Postby DonM » Thu Nov 13, 2008 6:51 am

denis_berthier wrote:[b]One way these results shouldn't be interpreted is as any form of support on my part for nets. I've always said I didn't like nets, but there's no formal logic reason for this, it is just a personal opinion. And it seems that some form of nets is necessary if one wants to solve the hardest puzzles. Of course again, I doubt any normal player wants to solve the hardest puzzles.


Approximately, what difficulty, say ER, level are you considering the hardest puzzles? (Serious question of interest.:) )
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Postby denis_berthier » Thu Nov 13, 2008 7:17 am

DonM wrote:Approximately, what difficulty, say ER, level are you considering the hardest puzzles?

I'm not a specialist of the hardest puzzles. The hardest ER I know is 11.6. But I think ER is not very meaningful at such levels.
AFAIK, no such puzzle has ever been been solved manually.

The hardest puzzles that are solved manually by excellent players I know are at ER 9.3 or 9.4.
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Postby re'born » Thu Nov 13, 2008 9:27 am

denis_berthier wrote:
DonM wrote:Approximately, what difficulty, say ER, level are you considering the hardest puzzles?

I'm not a specialist of the hardest puzzles. The hardest ER I know is 11.6. But I think ER is not very meaningful at such levels.
AFAIK, no such puzzle has ever been been solved manually.

The hardest puzzles that are solved manually by excellent players I know are at ER 9.3 or 9.4.


Presumably this is, at least, modulo the occasional 10 or 11+ solved using Gurth's symmetry techniques. Even I can do those by hand.
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Postby denis_berthier » Thu Nov 13, 2008 8:55 pm

re'born wrote:
denis_berthier wrote:
DonM wrote:Approximately, what difficulty, say ER, level are you considering the hardest puzzles?

I'm not a specialist of the hardest puzzles. The hardest ER I know is 11.6. But I think ER is not very meaningful at such levels.
AFAIK, no such puzzle has ever been been solved manually.

The hardest puzzles that are solved manually by excellent players I know are at ER 9.3 or 9.4.


Presumably this is, at least, modulo the occasional 10 or 11+ solved using Gurth's symmetry techniques. Even I can do those by hand.


Right, but this will be true of any technique: if specific patterns (based on some form of symmetry or other) are present in a puzzle and allow specific eliminations, the difficulty of the puzzle measured by a rating that doesn't take the corresponding specific rules into account looses much of its meaning.
I'm not proficient in Gurth's techniques, but rules based on specific symmetries may be an interesting topic as an exercice of rule writing (AI teacher speaking). Do you have references?
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Postby 999_Springs » Sat Nov 15, 2008 11:35 am

denis_berthier wrote:The hardest puzzles that are solved manually by excellent players I know are at ER 9.3 or 9.4.

I'm quite surprised - is the mid-9s really the cap on manual solving? I wouldn't consider myself a particularly excellent player, but two and a half years ago I found a neat solution to a puzzle which I recently learnt was #2 from the top1465 (ER=9.5) and I posted it here (5th post on the page).
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Once upon a time I was a teenager who was active on here 2007-2011
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Postby DonM » Sat Nov 15, 2008 1:30 pm

999_Springs wrote:
denis_berthier wrote:The hardest puzzles that are solved manually by excellent players I know are at ER 9.3 or 9.4.

I'm quite surprised - is the mid-9s really the cap on manual solving? I wouldn't consider myself a particularly excellent player, but two and a half years ago I found a neat solution to a puzzle which I recently learnt was #2 from the top1465 (ER=9.5) and I posted it here (5th post on the page).


SE is not perfect and it is possible that this an aberration because ordinarily any puzzle roundabout ER= above 8.6-9.0 can't be solved without a net. The 2nd possibility to be perfectly honest is that your solution has an error mainly because the two critical chains do not have complete notation which means that the eliminations can't be easily verified. I say this with the greatest of humility because I have submitted more than one solution for puzzles at ER >= 8.3 that I thought was the best of the bunch only to be informed that I had made an error- and that was after having checked it several times.
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Postby denis_berthier » Sat Nov 15, 2008 8:46 pm

999_Springs wrote:
denis_berthier wrote:The hardest puzzles that are solved manually by excellent players I know are at ER 9.3 or 9.4.

I'm quite surprised - is the mid-9s really the cap on manual solving? I wouldn't consider myself a particularly excellent player, but two and a half years ago I found a neat solution to a puzzle which I recently learnt was #2 from the top1465 (ER=9.5) and I posted it here (5th post on the page).

I've just checked: top1465 #2, SER 9.5, can't be solved with mere nrczt-whips but it can be solved with zt-braids(ECP+NS+HS+BI) i.e. hinged-nrczt-braids.

Could you be more explicit on the following two chains in your solution and what they eliminate?
Code: Select all
r5c2-7(-r5c4)-r5c789=7=hidden pair r46c7-7-r2c7=7=hidden pair r2c89=5=r2c5-5-r4c5-9-r5c4-4-r5c7-1-r5c8, no value for r5c9
hidden pair in c2
r8c2=8
3 is locked in c3b7
r2c7-7(-r7c7)-naked triple r456c7-1-r7c7-2(-r7c5)-r7c1-1(-r4c1)-r7c5-5-r4c5-9(-r5c4)-r4c1-8-r4c7-1-r5c7-4-r5c4-7, no place for 7 in b6

They look like some zt-whip with Pair and Triplet components. Could you try to re-write them as such?

As for the highest SER accessible to human solvers, the good news of this thread is that, if you accept nets (which are anyway necessary for extreme puzzles), then you can't refuse braids (which are the mildest kind of nets one can imagine - there is still some linear structure) and you can hardly refuse Trial and Error (with no recursion and no guessing). As a result, using T&E in combination with relatively simple patterns, you can solve all the puzzles.

Of course, one can refuse nets for puzzles that can be solved without them (and I am personally on this side). Looking for whips based on different families of basic patterns is then the most powerful technique as of today. But we have no idea of how powerful exactly (probably much beyond SER 10).
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Postby denis_berthier » Sat Nov 15, 2008 8:48 pm

DonM wrote:ordinarily any puzzle roundabout ER= above 8.6-9.0 can't be solved without a net.

Puzzles upto SER 9.3 can be solved with nrczt-whips - no net is necessary.
And, if you put more complex components in the whips, then you can go much beyond SER 9.3.
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Postby Allan Barker » Sat Nov 15, 2008 10:37 pm

I think I understand Denis's view that 9.5 seems to be some kind of barrier. There is an immense change of difficulty between about 9.5 and 11.5 as if SE compresses the top of the scale above 9.5. If the scale went from 1 to 30, with 10 to 30 covering the existing 9.5 to 11.5 range, maybe the scale would look more linear.

denis_berthier wrote:I've just checked: top1465 #2, SER 9.5, can't be solved with mere nrczt-whips but it can be solved with zt-braids(ECP+NS+HS+BI) i.e. hinged-nrczt-braids.

I took a look at the same and found a short, non-symetrical rank=0 SK-like loop that blasts the puzzle to singles.
I posed it here in the Monster Loop thread, top1465 #2 loop solution.
.
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Postby ttt » Sat Nov 15, 2008 11:04 pm

Hi All,
For #2 of top 1465, based on 999-Springs, I present as below (using Eureka! – AIC notation):
Code: Select all
 *-----------*
 |7.8|...|3..|
 |...|2.1|...|
 |5..|...|...|
 |---+---+---|
 |.4.|...|.26|
 |3..|.8.|...|
 |...|1..|.9.|
 |---+---+---|
 |.9.|6..|..4|
 |...|.7.|5..|
 |...|...|...|
 *-----------*
After SSTS
 *--------------------------------------------------------------------------------------*
 | 7        126      8        | 459      4569     4569     | 3        1456     1259     |
 | 469      36       3469     | 2        34569    1        | 4679     45678    5789     |
 | 5        1236     123469   | 78       3469     78       | 12469    146      129      |
 |----------------------------+----------------------------+----------------------------|
 | 189      4        1579     | 3579     59       3579     | 178      2        6        |
 | 3        1267     12679    | 479      8        24679    | 147      1457     157      |
 | 268      25678    2567     | 1        2456     24567    | 478      9        3        |
 |----------------------------+----------------------------+----------------------------|
 | 128      9        12357    | 6        125      2358     | 127      1378     4        |
 | 12468    12368    12346    | 3489     7        23489    | 5        1368     1289     |
 | 12468    1235678  1234567  | 34589    12459    234589   | 12679    13678    12789    |
 *--------------------------------------------------------------------------------------*

Move 1: present as Kraken cell => r5c236<>7
Code: Select all
(7)r5c4
 ||
(4)r5c4-(4=ht157)r5c789
 ||
(9)r5c4-(9=5)r4c5-(5)r2c5=(hp58-7)r2c89=(7)r2c7-(7)r456c7=(7)r5c89

Move 2:
Code: Select all
(5)r2c5=(hp58-7)r2c89=(7)r2c7-(7=hp12)r7c17-(12=5)r7c5

=> loop => r1469c5<>5, r456c7<>7, SSTS to the end

Edit:
Other way for thinking on Move 1, look 5’s & 7’s and bilocation 8’s at row 2 => at least one of r2c5=5 & r2c7=7 must be true
Code: Select all
(quad1457=9)r5c4789-(9=5)r4c5-(5)r2c5=(hp58-7)r2c89=(7)r2c7-(7)r456c7=(7)r5c89 => r5c236<>7


BTW, I think that is not much puzzles with ER9.5 like this...:D

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Postby DonM » Sun Nov 16, 2008 6:52 am

denis_berthier wrote:
DonM wrote:ordinarily any puzzle roundabout ER= above 8.6-9.0 can't be solved without a net.

Puzzles upto SER 9.3 can be solved with nrczt-whips - no net is necessary.
And, if you put more complex components in the whips, then you can go much beyond SER 9.3.


I think you know that I was talking about the limits of typical manual solving as we know it on both major forums. I'd be interested in seeing an example of a manually solved ER=9.3 puzzle solved using nrczt-whips.
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Postby denis_berthier » Sun Nov 16, 2008 7:03 am

DonM wrote:
denis_berthier wrote:
DonM wrote:ordinarily any puzzle roundabout ER= above 8.6-9.0 can't be solved without a net.

Puzzles upto SER 9.3 can be solved with nrczt-whips - no net is necessary.
And, if you put more complex components in the whips, then you can go much beyond SER 9.3.

I think you know that I was talking about the limits of typical manual solving as we know it on both major forums. I'd be interested in seeing an example of a manually solved ER=9.3 puzzle solved using nrczt-whips.

I don't know what "both" major forums are.
I've already given you references on the sudoku-factory forum, but you seem to be suffering from the NIH syndrome:

DonM wrote:
D.Berthier wrote:Concerning my rules, other human players use them daily and they combine them freely with other rules. See the sudoku-factory forum.

Let's just keep this real. This is a bare handful of people.
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