The New Sudoku Players' Forum

[Pat]

try this:

5....78...1..8..2...46....7..34.6...............2.86..1....59...5..6..4...23....1

Pat # 289 # (258812) #

Code: Select all


 5 . . | . . 7 | 8 . .
 . 1 . | . 8 . | . 2 .
 . . 4 | 6 . . | . . 7
-------+-------+------
 . . 3 | 4 . 6 | . . .
 . . . | . . . | . . .
 . . . | 2 . 8 | 6 . .
-------+-------+------
 1 . . | . . 5 | 9 . .
 . 5 . | . 6 . | . 4 .
 . . 2 | 3 . . | . . 1



[Alpxcx]

.....1....29.3.4....452..6...7.......62...38.9.....2...8..635....5.8..4.7..9.....

it is on the list
becuase it requires a Quad;

and yes, i put it at the top of my list
because it requires several more steps...
that's what makes it interesting

I just looked at the puzzle again. The first step was the hidden quad, and rated as the harded step.
However, it wasn't. Most people with a little experience on subsets should be able to spot it, because it was distributed around the middle.
2368r5 and 2368c5 makes the clues and those was the only numbers on r5 and c5. There was no interference at all so very easy.
The next 3 steps (naked triple, locked candidates, hidden pair) were all dependent on the quad, this means you couldn't find them if you couldn't find the quad.
They were autually harder than the quad to human, but the exsiting rating systems would rate them below the quad, simply because they are generally simpler to find by a machine.
I can put an image of the puzzle here so everyone can see.

[StrmCkr]

Hierachy solving is indicitove as they form the foundations for the bigger step as you move up the list

Often many substeps are covered under the large technique base and 1 application can skip many basics (subsets etc)

However having a flexible hierachy to find that pigeonhole solution also results in a Np complete problem
Trying to make a solver that shows the easiest path possible.

[Alpxcx]

Hierachy solving is indicitove as they form the foundations for the bigger step as you move up the list

Often many substeps are covered under the large technique base and 1 application can skip many basics (subsets etc)

However having a flexible hierachy to find that pigeonhole solution also results in a Np complete problem
Trying to make a solver that shows the easiest path possible.

I don't think it is another NP-complete problem, unless there is a mathmatical proof.
Anyway, we don't need to run it on every occasion, but just the time we need finer analyses.
And the most important part is to avoid the stupid thing I montioned. Don't have any skippable step on the solution path output.
When you are just making improvements on a current solution path, rather than searching for everything, it would be much easier to do, and faster.
I think we shouldn't really call it a solution path, but a solution tree, if you find out the dependence among all steps.
I will probably make a prototype solver in the next year, not for the speed but beautifulness.

[StrmCkr]

it is a np- complete problem i my self wanted a more robust system that could account for sub-step difficulty then realized in coding it wasn't actually needed as the max length actually resolved all the smaller techniques as well. { ill link mythread on the idea from 08 when i purposed it}

given how many technique sets overlap each other and how many of them can reduce the puzzle to singular solutions skipping some successive steps directly

blr
hidden subsets {2-4}
naked subsets {2-4}
multiple size 2-4 fish

how so
a singular aic chain length 3
on the same grid can have 37k valid chains

how do you pick the simplest of them with the same length?

or is it more complicated then applying a size 2 fish twice for similar eliminations
or perhaps an als size 3 does the same job for again another 37 k options

funny part of all of this
is that the als chain algorithm will also find the size 3 aic chains
it also finds the size 1-3 fish as they use the same mapping just different translation methods
it also finds the {1-3} naked/hidden subsets

they are all interchangeable increasing size is directly quantitative

just because the puzzle uses multiple steps doesn't make it any harder if the longest step also finds all the smaller steps in successive search runs

looking for 1 step out of 67k thousand examples {as this simplistic example} is harder then actually searching in an incremental pattern

filtering through every possible combination to find the absolute minimal path is Np-complete given the total number of valid paths{order of application} to choose from.

i have personally attempted this on my own solver with some grids producing 37K x 14 pages of different chains from 1 application of a technique set. many of which have the same eliminations just different positions selected same length or slightly longer.

I have played on many grids that involve multiple steps to solve including basics and circumvented all of that with 1 well placed chain.
just cause 1 chain skips lets say 20 sub steps, 20 of which are basics of some form but this doesn't mean everyone can spot the 1 off method i used, when 1 slightly smaller method was needed on top of 20 sub steps. however that size of step also found all the other 20 sub steps.

They were actually harder than the quad to human, but the existing rating systems would rate them below the quad, simply because they are generally simpler to find by a machine.

the size changed to find the max step however the subsets are still included meaning that you would find anything below size 4 with the same logic used to find size 4: they aren't harder, they follow the same logic already required to advance.
more steps doesn't mean harder - indicates more work ie applications of the same difficulty level or lower. ie Tediousness if you know how to do something repetition doesn't mean harder work in fact repetition of the same level makes the task easier to execute.

if really want to be technical Hidden quad is really
ahs size (1-2) and ahs size (2-3) - xz removals: this can be used to find the subset "naked" removals with out actually needing the hidden quad.
also a naked subset is the inversion of a hidden set (9 - x) and these are also just als-xz functions.

but then this raised the question does the solver actually know this?

again ambiguity.

Here are the solution paths on some solvers, at the time of this post:

an inherit issue with many of these is they don't place Hidden subsets ahead of naked:

why -
from a coders point of view naked subsets are easier to as its whats left on directly in the RC space of a grid
a hidden set is RN,CN,BN space or twiddling RC space to whats off. <- slightly harder to code

from a players point of view whats left on is easier to spot directly on a grid as it uses the givens {not the pm's}
very few solvers{coders} realized this and its reflected in the hierarchy

Hodoku can remap its solving order by user preferences and this often drastically changes for better or worse any given grids listed difficulty.

the break points in a fixed solving order a coder first needs to know what can solve what else using the same code structures will also find

{not limited to the following}
BLR is also Naked/hidden singles
naked pair / hidden pair is also a single digit x-wing
Naked/hidden triple is also Finned/sashimi X-wing , sword fish

naked/hidden quads also jelly fish, Finned/sashimi sword fish

subsets Naked are als-xz
subsets Hidden are ahs - xz

subsets are also A.I.C of length x

naked and hidden subsets also form a balance on the sector: ( Given + Naked + Hidden ) = (9 digits + 9 cells)

anyways - long enough post for now.

ps

Code: Select all

.------------------.-----------------------.---------------------.
| 3568   357   368 | 4678    479    1      | 789   23579  235789 |
| 1568   2     9   | 678     3*     678    | 4     157    1578   |
| 138    137   4   | 5       2*     789    | 1789  6      13789  |
:------------------+-----------------------+---------------------:
| 13458  1345  7   | 123468@ 1459   245689@| 169   159    14569  |
| 145    6*    2*  | 147     14579  4579   | 3*    8*     14579  |
| 9      1345  138 | 134678@ 1457   45678@ | 2     157    14567  |
:------------------+-----------------------+---------------------:
| 124    8     1   | 1247    6*     3      | 5     1279   1279   |
| 1236   139   5   | 127     8*     27     | 1679  4      123679 |
| 7      134   136 | 9       145    245    | 168   123    12368  |
'------------------'-----------------------'---------------------'


if you change Hidden sets above naked sets - required # moves ends up lowering but rating is way higher
{hodoku has hidden subsets as "higher" scores then naked"} {flip them} and the scores will be more accurate { at least in my point of view}
ie hidden is easier to find then naked as the latter requires pms to be filled in! { for example it uses the * givens for 4 @ cells left open in the box}

Or if your good you realized the 5 cells in box 5 (or 10 cells from r5, c5 contain an intersecting quintupplet)
as a hidden quad is a naked size 5 set.
.. But I'll digress until you respond...

[StrmCkr]

generalized ratings are systemically bad as a generalized "rating" {as mentioned by eleven}
- but they do form a bases of expected skill set in incremental order of what tools should be required to solve, this dose not indicate that beyond the listed tools could solve it quicker.

case point:

Code: Select all

.--------------------.------------------.-------------------.
| 5      14   14     | 6      9      2  | 3    7      8     |
| 8      124  123479 | 1347   1347   34 | 5    1269   169   |
| 1239   6    12379  | 8      137    5  | 4    129    19    |
:--------------------+------------------+-------------------:
| 7      5    14     | 9      14     6  | 8    3      2     |
| 12346  9    1234   | 12347  12347  8  | 67   46     5     |
| 2346   8    234    | 5      2347   34 | 1    469    4679  |
:--------------------+------------------+-------------------:
| 249    7    6      | 234    5      1  | 29   8      349   |
| 124    3    8      | 24     6      9  | 27   5      147   |
| 1249   124  5      | 234    8      7  | 269  12469  13469 |
'--------------------'------------------'-------------------'

Locked Candidates Type 1 (Pointing): 4 in b2 => r2c23<>4 (50)
Locked Candidates Type 2 (Claiming): 1 in r1 => r2c23,r3c13<>1 (50)
Naked Single: r2c2=2 (4)
Hidden Single: r3c8=2 (14}
Finned Swordfish: 1 c148 r259 fr8c1 => r9c2<>1 (200)
singles to the end. {190}
==> 508 rating

this is one of many short solution paths, skipping many sub-steps.

Compared to {default settings} hodokus 19 steps to singles

dose this mean this puzzle is drastically over rated from default 1184
or
dose it mean my skill set is beyond what minimal levels this puzzle could be solved with.

it also raises many questions of:{ but not limited to}
- what steps can be skipped?
- would a player skip steps found or apply it.
- dose a player follow incremental tool box or apply skills in random order based on what they happen to spot at any instance
- do they cycle: singles, blr, hidden subsets, naked subsets until pm's are fully developed
- once pms are established is it free game for any technique as mentioned above or is it also hierarchy based

- or can they spot more advanced logic without pm's or minimalism {synder notation} - {like the fish on 1's that tripped the singles solution}

[Alpxcx]

generalized ratings are systemically bad as a generalized "rating" {as mentioned by eleven}
- but they do form a bases of expected skill set in incremental order of what tools should be required to solve, this dose not indicate that beyond the listed tools could solve it quicker.

...

it also raises many questions of:{ but not limited to}
- what steps can be skipped?
- would a player skip steps found or apply it.
- dose a player follow incremental tool box or apply skills in random order based on what they happen to spot at any instance
- do they cycle: singles, blr, hidden subsets, naked subsets until pm's are fully developed
- once pms are established is it free game for any technique as mentioned above or is it also hierarchy based

- or can they spot more advanced logic without pm's or minimalism {synder notation} - {like the fish on 1's that tripped the singles solution}

You are actually right. Not all skippable steps will be skipped by a human player.
When we are not given the level of difficulty of a puzzle, we generally find all simple steps first.
We don't know what is dependent on what until we go through the steps. Definitly, when you find a technique to use, you will just use it. Why not?

However, finned swordfishes are generally very difficult to be found by human without fully filled pm's. This is very different from finned X-wings.
My previous example did not show the problem you mentioned. To that puzzle, I still have the same opinion, because the pattern on 7 wasn't difficult to see.

The actually thing happening is, we are usually hinted with how difficult a puzzle is before we start.
We usually find a difficult puzzles either on a Sudoku app/website, or on a post of something like "help: how to solve this".
Most of these would tell you how difficult a puzzle is waiting for you to be solved. Then you may know what techniques are potentially on the solution paths.
For example, if we already know a puzzle is extremely hard, we may be interested with exocet patterns first, before a lot of simpler steps.
I don't know if this example works: 98.7..6..7......9...6.5.....4......3..75...8......2.....96...5...89..16.....1....
When you don't know exocet, you just don't know, the puzzle will be never solved.
Once you find out where it is, it instantly becomes a easy puzzle. You don't even need to do all the pm's to solve it.
On this occasion, this puzzle is dead easy. It would be even simpler than the finned swordfish in your example.

[Alpxcx]

I have seen quite interesting responds this week, but unfortunately I don't have much personal time at this moment. I will try to respond to all comments when I have spare time. Please don't worry or be annoyed when some of your comments get ignored.

[Hajime]

My 2 cents: SER to be extended?

It is about extending SER, but into another direction as discussed above.

SER is a number from 1.0 to 12.0 and is the number of the highest (most difficult) method needed.
1. So if VWXYZ-Wing method is needed to solve the puzzle (and no more difficult method is needed) the SER will be 6.2-6.4 .
This is independant of how many "less difficult" methods are used.
So if 0 or 5 Jellyfish methods (SER=5.2) are also needed to solve the puzzle, the rating will remain 6.2-6.4 .
2. The SER is calculated for 1 Sudoku or Sukaku puzzles. SE does not rate overlapping Sudoku's.
So a Samurai is equal difficult rated as a Single Sudoku using the same (maximal) method?

The difficulty can be discussed, but the Labour sure is more !
Labour rating?

If you have to "solve" 5 Jellyfish and 1 VWXYZ-Wing a lot more work has to be done.
Also a Samurai (Gattai of 5 overlapping Sudoku's) more labour is needed to solve the puzzle.
In my solver/generator SiSeSuSo I introduced SER * Eliminated_Candidates per method, a kind of sumproduct to indicate the needing Labour.

[Alpxcx]

My 2 cents: SER to be extended?

It is about extending SER, but into another direction as discussed above.

Labour rating?

If you have to "solve" 5 Jellyfish and 1 VWXYZ-Wing a lot more work has to be done.
Also a Samurai (Gattai of 5 overlapping Sudoku's) more labour is needed to solve the puzzle.
In my solver/generator SiSeSuSo I introduced SER * Eliminated_Candidates per method, a kind of sumproduct to indicate the needing Labour.

I know. As the things discussed on this topic, it couldn't be done by just to extend the rating system, but to redesign it.
Yeah, I wasn't good at thinking of a title.

Talking about labour rating, it really is different before making pencilmarks and after.
Jellyfishes sometimes can be found without pencilmarks. They are not as visible as X-wings and swordfishes, but you don't have to do pencilmarks when you don't need to.
VWXYZ-Wings are very different, because they are not just wings, but also complex chains or forcing chains. You always need to have full pencilmarks to find them.
If you are using an app which automatically fills pencilmarks for you, then VWXYZ-Wings can be very easy sometimes.

I can't find a good example to compare them yet, but I will use a post on reddit for a VWXYZ-Wing.
Puzzle in text: ....8..2..8..59..1..32..8.5...4.....8....59329.....1.71.............6..35261.....
You can probably find it very easily after simple steps (locked candidates, triples). How would this compare to a not-so-visible jellyfish which you need pencilmarks to find?
See, it's not what SE rating system can do. SER gives fixed ratings for every technique so it can't do anything when a high-rating step is actually obvious to see.
This one is not actually an extreme puzzle, but none of the existing software will give you a simple path.
I can give my solution path here:

Code: Select all

Hidden Single: 1 in b9 => r8c8=1
Hidden Single: 3 in b7 => r7c2=3
Hidden Single: 4 in b6 => r6c8=4
Hidden Single: 9 in b5 => r4c5=9
Hidden Single: 3 in b4 => r4c1=3
Hidden Single: 2 in c1 => r2c1=2
Locked Candidates 1 (Pointing): 5 in b6 => r4c2<>5,r4c3<>5
Locked Candidates 1 (Pointing): 6 in b6 => r4c2<>6
Locked Candidates 1 (Pointing): 8 in b6 => r4c6<>8
Locked Candidates 2 (Claiming): 9 in r9 => r7c8<>9,r7c9<>9
Locked Candidates 2 (Claiming): 6 in c1 => r1c2<>6,r3c2<>6
Naked Triple: in r1c1,r2c3,r3c1 => r1c2<>47,r1c3<>47,r3c2<>47,
Naked Triple: in r1c4,r2c4,r5c4 => r6c4<>36,r7c4<>7,r8c4<>7,
Naked Single: r6c4=8
Hidden Single: 8 in r8 => r8c3=8
Locked Candidates 2 (Claiming): 3 in c4 => r1c6<>3
XYZ-Wing: 147 in r5c3 r2c3 r4c2 => r4c3 <> 7
Almost Locked Set XZ-Rule: A=r6789c5 {23467},B=r5c4 {67}, X=6, Z=7 => r5c5<>7
Almost Locked Set W-Wing: A=r257c3-{1479}, B=r3c2-{19}, connect by 1c5  =>
 r1c3<>9 r8c2<>9
Hidden Single: 9 in b7 => r7c3=9
Hidden Single: 9 in b8 => r8c4=9
Hidden Single: 5 in b8 => r7c4=5
Hidden Single: 5 in b9 => r8c7=5
Hidden Single: 2 in b9 => r7c7=2
Hidden Single: 2 in b8 => r8c5=2
Hidden Single: 5 in b6 => r4c8=5
Hidden Single: 8 in b6 => r4c9=8
Full House: r4c7=6
Hidden Pair: 47 in r2c3,r5c3 => r5c3<>1
W-Wing: 67 in r2c8,r5c4 connected by 7c3 => r2c4<>6
Hidden Single: 6 in r2 => r2c8=6
Hidden Single: 6 in b9 => r7c9=6
Locked Candidates 2 (Claiming): 4 in r7 => r9c5<>4,r9c6<>4
XY-Chain: (7=4)r2c3 - (4=7)r5c3 - (7=1)r4c2 - (1=9)r3c2 - (9=7)r3c8 => r2c7,r3c1<>7
WXYZ-Wing: 3479 in r2c47,r1c9,r3c8,Pivot Cell Is r2c7 => r3c56<>7
Hidden Single: 7 in r3 => r3c8=7
Hidden Single: 7 in b9 => r9c7=7
Hidden Single: 4 in b9 => r9c9=4
Full House: r1c9=9
Hidden Single: 9 in b9 => r9c8=9
Full House: r7c8=8
Hidden Single: 8 in b8 => r9c6=8
Full House: r9c5=3
Hidden Single: 3 in b5 => r6c6=3
Hidden Single: 2 in b5 => r4c6=2
Hidden Single: 1 in b5 => r5c5=1
Hidden Single: 7 in b5 => r5c4=7
Full House: r6c5=6
Hidden Single: 2 in b4 => r6c3=2
Full House: r6c2=5
Hidden Single: 6 in b4 => r5c2=6
Full House: r5c3=4
Hidden Single: 7 in b4 => r4c2=7
Full House: r4c3=1
Hidden Single: 7 in b7 => r8c1=7
Full House: r8c2=4
Hidden Single: 6 in b2 => r1c4=6
Full House: r2c4=3
Hidden Single: 3 in b3 => r1c7=3
Full House: r2c7=4
Full House: r2c3=7
Full House: r1c3=5
Hidden Single: 7 in b2 => r1c6=7
Hidden Single: 7 in b8 => r7c5=7
Full House: r7c6=4
Full House: r3c5=4
Full House: r3c6=1
Hidden Single: 1 in b1 => r1c2=1
Full House: r1c1=4
Full House: r3c1=6
Full House: r3c2=9


You can actually just do works around r34c2 and r25c3, except the ending WXYZ-Wing.
Depending on how you usually solve puzzles, it can be easy to solve.

[Alpxcx]

it is a np- complete problem i my self wanted a more robust system that could account for sub-step difficulty then realized in coding it wasn't actually needed as the max length actually resolved all the smaller techniques as well. { ill link mythread on the idea from 08 when i purposed it}

given how many technique sets overlap each other and how many of them can reduce the puzzle to singular solutions skipping some successive steps directly

blr
hidden subsets {2-4}
naked subsets {2-4}
multiple size 2-4 fish

how so
a singular aic chain length 3
on the same grid can have 37k valid chains

how do you pick the simplest of them with the same length?

or is it more complicated then applying a size 2 fish twice for similar eliminations
or perhaps an als size 3 does the same job for again another 37 k options

funny part of all of this
is that the als chain algorithm will also find the size 3 aic chains
it also finds the size 1-3 fish as they use the same mapping just different translation methods
it also finds the {1-3} naked/hidden subsets

they are all interchangeable increasing size is directly quantitative

...

Okay. I had a look at this 2 days ago but I didn't understand what you said. Now I see.
I didn't actually say we have to find the technically simplest path, but just any path without a skippable step.
Well, as I said, you will apply any technique you find when you don't know the difficuty.
Therefore, it is acceptable to hint the extra steps in a special colour.
I don't think we need a solver looking for even 100+ chains right at the start to achieve this.

And the most important part is to avoid the stupid thing I montioned. Don't have any skippable step on the solution path output.
When you are just making improvements on a current solution path, rather than searching for everything, it would be much easier to do, and faster.

The "current solution path" I mentioned can be done by searching in an incremental pattern. I didn't actually mean we should deny all efforts we have done so far, but make improvements.

In my point of view, writing this kind of dependency-detection algorithm isn't rocket science. There are at least two ways of implementation:
1. Scan a few techniques further on each step, if a "higher" technique can be detected with substraction of candidates, then mark it. If the technique is used later, then go back and only apply this technique. If the puzzle rating gets decreased, then apply this technique at an earlier stage.
2. Add substraction of candidates done by simpler techniques back when a "higher" technique is applied. If the technique is still valid and decrease the puzzle rating, then apply this technique at an earlier stage.

Doing it in a "chain" way won't work, because most chains found by a machine are almost invisible to human.
We still scan technique-by-technique, but a bit further every time.
By doing it this way, we know how likely the next step is to be skipped by a human player.
For example, if there is a naked subset, and the next step is a cell forcing chain, we will apply the naked subset, even if they are independent steps and the cell forcing chain will cause stte without the naked subset (but it should be hinted by an ideal solver).

[eleven]

Some more remarks:
If you have a solution path, it's of course no problem to leave out unnecessary steps. All do that in the Puzzles thread (unless someone just tries to eliminate a backdoor).
There are good manual solvers, who already in early solving stages enter (quickly) all candidates, and thus have a different view as the ones, who only enter say 2 or - if needed - 3 candidates, or use markers for strong links.
Also the hierarchy of the order, which solving techniques are tried, is different. And it may depend on, what the puzzle looks like (e.g. few or many open candidates left). And they may look for a cracking elimination (at least giving a number) more than trying to find any elimination.
Concerning StrmCkr's swordfish example it is very unlikely, that manual solvers would not do it with the obvious pairs and triple, and UR's (or 3 strong links, if they don't like UR's).
In the exocet example (definitely a rarity, that it directly solves such a hard puzzle), it is all but easy to find it manually. I think, even David himself used his excel sheet as a help (though i don't doubt, that he could do it on paper - but not quickly).
In the above sample the steps "Almost Locked Set XZ-Rule/W-Wing" are also wxyz-wings or - more generally (and how i find it) of the form 'n candidates in m cells (m>=n)', where either all must be in the set or (at least one) must be twice (first example: 23467 in 5 cells, only 7 can be twice -> one of r5c4 and r789c5 must be 7).
Last but not least: There is more than one way to skin a cat. Though having my priorities, in many puzzles i could not say, which of the solution paths would be the easiest or best (and that's a very positive fact).

[Alpxcx]

Some more remarks:
If you have a solution path, it's of course no problem to leave out unnecessary steps. All do that in the Puzzles thread (unless someone just tries to eliminate a backdoor).
There are good manual solvers, who already in early solving stages enter (quickly) all candidates, and thus have a different view as the ones, who only enter say 2 or - if needed - 3 candidates, or use markers for strong links.
Also the hierarchy of the order, which solving techniques are tried, is different. And it may depend on, what the puzzle looks like (e.g. few or many open candidates left). And they may look for a cracking elimination (at least giving a number) more than trying to find any elimination.
Concerning StrmCkr's swordfish example it is very unlikely, that manual solvers would not do it with the obvious pairs and triple, and UR's (or 3 strong links, if they don't like UR's).
In the exocet example (definitely a rarity, that it directly solves such a hard puzzle), it is all but easy to find it manually. I think, even David himself used his excel sheet as a help (though i don't doubt, that he could do it on paper - but not quickly).
In the above sample the steps "Almost Locked Set XZ-Rule/W-Wing" are also wxyz-wings or - more generally (and how i find it) of the form 'n candidates in m cells (m>=n)', where either all must be in the set or (at least one) must be twice (first example: 23467 in 5 cells, only 7 can be twice -> one of r5c4 and r789c5 must be 7).
Last but not least: There is more than one way to skin a cat. Though having my priorities, in many puzzles i could not say, which of the solution paths would be the easiest or best (and that's a very positive fact).

I totally agree.
I just wanted to share my ideas when I found them interesting, and this was why I posted. You and many others actually pointed out that some of my original thoughts were naive. I really appreciate your help.
A very important thing I learnt was that, not everyone solves puzzles in the same way. This makes a uni-rating reflecting every individual's effort needed to solve a puzzle a non-existance.
However, existing rating systems have too many problems, so it's needed to redesign them.

What I have listed so far:
1. Some high-rating steps are easier to find than a lot of low-rating steps
2. Some steps are more likely to be skipped than others
3. Sometimes applying a more advanced technique can decrease the overall rating
4. Puzzles which don't need pm's are generally easier than ones require.

The one which require a VWXYZ-Wing (ALS XZ/W-Wing) was a very good example of showing the above 3.
The default solution path given by HoDoKu/YZF-Sudoku was rediculous, a piece of non-sense.
A solver which does incremental search on pre-numbered techniques won't find a readable/satisfying solution path on this one!
YZF-Sudoku625 gave a HoDoKu-type rating of 3620 on the default path. However, with my own path there, it suddenly dropped to 2380!
This was enough to make it from a "upper tough" puzzle to a "upper moderate" one. How did the solvers not discover this?

generalized ratings are systemically bad as a generalized "rating" {as mentioned by eleven}
- but they do form a bases of expected skill set in incremental order of what tools should be required to solve, this dose not indicate that beyond the listed tools could solve it quicker.

This was a great con to this opinion, wasn't it?

[StrmCkr]

I don't see how that's a con, you just reaffirmed what I said.

This was enough to make it from a "upper tough" puzzle to a "upper moderate" one. How did the solvers not discover this?

Most of us veterans are aware of the blunders of hierarchy solving and how easily it çan be skewed higher or lower by changing order
Play around with hodokus none fixed path in the settings and this becomes very apparent.

Mostly we use it as a generalized guide line evaluating with se we could be given at the very least a top end skill set needed to advance the puzzle.

Knowing it's fixed order also establishes a consensus reference point to compare all puzzles.
- hence why se is used over others.

The only part I know se needed fixed as at least in my opinion is the following

Hidden Before naked subsets (to fix the oversight issues)

Multiple modern techniques added:
Barns ie(als wings, xy, xyz, wxyz,... Stuvwxyz wing)
Strong wing, W, M, S, L(2,3,), h(1-6) ,iw - wings and Rings added
Als xz, als Xy, Aals 2rc, N als Nrc, DDs, adds, msls, exceots, broken wings, oddigons, thors hammer, nxn+k fish
Ahs-xz, ahs-xy, fireworks
Mugs, reverse bug, revers bug lite
(All the Bugs in bug, bug+n fixed.)
Als +aic chains
Als chains
Extended UR types beyond 1-6

Ps: with a solver aid pms filled in cycle Blr, subsets etc finding eliminations that are from the start affecting full board.

However if we consider synder Notation as the rising go to method of choice
Marking Blr, strong link digit spots
Making Hidden subsets + complimentary naked subsets
Naked subsets + complimentary hidden subset
Then filling in Bi valve cells.
Completes the pms stage of setting up a puzzle all while skipping what a solver finds as basics after initiating pms as these moves are already noted and eliminations performed without erasing anything
Which is interesting as it leaves the subset applications of inital moves.

Pss. Some of us can solve advance moves without any pms: can everyone definitely not.

Hopefully you saw my remarks on the uwxyz wing as these are als Xz functions I call them barns. (same search method as eleven

Another point of why a flexible path isn't the best solution either as we cannot guess what a player would or wouldn't do or decipher how they fill the initial pms in or don't.

here is this grid with synder notes: {in progress}

Code: Select all

000000000000000000000000000000000000000000000000000000000000000000000000000000000
+------------+------------------+------------+
| .   7   .  | .     4*      1   | 79  29  29 |
| .   2   9  | 7     3      678 | 4   .   .  |
| .   7   4  | 5     2      9*   | 7   6   .  |
+------------+------------------+------------+
| 8   .   7  | 2368  1459   268 | 6   .   46 |
| .   6   2  | 147   14579  45  | 3   8   4  |
| 9   .   38 | 368   1457   68  | 2   .   4  |
+------------+------------------+------------+
| 24  8   1  | .     6      3   | 5   79  79 |
| 26  9   5  | 17    8      27  | .   4   .  |
| 7   34  36 | 9     15     45  | 8   2   28 |
+------------+------------------+------------+



* cell is a single found
this mark up system
singles
bi local strong links first
bivalves
blr {2-3 cells in a box/row or row/box}
hidden subsets and marking the naked subset at the same time {cycle till cant find any more}
next is Naked subsets that are exposed -> mark the hidden subset with it

at this point it cycles top down
finishing the pencil mark setup {or in this case solves the puzzle}
- it minimizes erasing : increases solving time

more advance players increase bi-locals to include all 5 types of strong links on a single digit.

before moving into full pencil markups {for als moves}

problem with this markup approach is that it can be easy to mistake bivalves for overlapping strong links. {or a player doesn't move to the next step finalizing all pms} --- i see this frequently on reddit where players stall on synder notes and lock them selves up.

[Alpxcx]

Most of us veterans are aware of the blunders of hierarchy solving and how easily it çan be skewed higher or lower by changing order
Play around with hodokus none fixed path in the settings and this becomes very apparent.

Mostly we use it as a generalized guide line evaluating with se we could be given at the very least a top end skill set needed to advance the puzzle.

Knowing it's fixed order also establishes a consensus reference point to compare all puzzles.
- hence why se is used over others.

I know what you were always trying to say. There is indeed an issue on the priority right now.
However, for my previous examples, I could have been this, or that.
I'm still not certainly believing everytime it's because of the priority issue.
On my earlier comment on dynamic contradiction chains, you can see it probably should be given a really wide range of ratings, rather than a fixed rating.
I'm going to find more examples if I can.
If in 10 examples it's like 8/10 the occasion like you said, then I may say "yes, it is the case". But if it's more like 5/10, then I will say no.