The New Sudoku Players' Forum

[RW]

it looks like my solver restricted to singles neglects to look for 'zeros'
this is a flaw in the model that splits each constraint into individual functions

...

after fixing the proposition logic to validate at least one of each candidate for each row/col/box
this puzzle solves with singles/box-line/hidden-pair proposition constraints
so it now agrees with your observations
thanks for pointing this out

Thanks, I suspected something like that was going on, but I didn't dare to go far enough to write the words "your program" and "flaw" in the same sentence...

I suppose #7 from the same list also should solve with the same proposition constraints as #11 now, it had a finned swordfish in exactly the same place and doesn't need quads in SE. Only one question remains, why couldn't ravel's program rate #11?

RW

[gsf]

Thanks, I suspected something like that was going on, but I didn't dare to go far enough to write the words "your program" and "flaw" in the same sentence...

thanks -- regression tests keep most stupid bugs from public view
if I could only get that universal test generator program working ...

I suppose #7 from the same list also should solve with the same proposition constraints as #11 now, it had a finned swordfish in exactly the same place and doesn't need quads in SE. Only one question remains, why couldn't ravel's program rate #11?

#7 needs FNBH2 (singles, box-line, hidden pair)
#11 needs FNBH3 (singles, box-line, hidden triple)

[tarek]

Well spotted RW.......

gsf, I would also think that it would be easy to rate each individual step taken to solve the puzzle then averaging the results....would that correspond to the OVERALL difficulty of a puzzle.... so a puzzle scoring 9 0 may be easier than a 7 20 puzzle. This, along with the current rating system will give us a closer look at puzzles from different angles....

tarek

[RW]

I'm not sure where the minimum RMS now stands..... with all of these ultra ultra hard now creeping up .... Anyway here are 2 puzzles which were interesting

Code: Select all

Fluid Drive #8
 9 . . | . . 1 | 8 . . 
 . 6 . | . 3 . | . . . 
 . . 2 | 5 . . | . . 7 
-------+-------+------
 . . 9 | . . . | . . 6 
 . 5 . | . . . | . 2 . 
 4 . . | . . . | 3 . . 
-------+-------+------
 3 . . | . . 8 | 1 . . 
 . . . | . 4 . | . 8 . 
 . . 7 | 9 . . | . . 5      SE=10.5, gsfr=99789,Suexr=930

As ocean said, these tend to cluster. Change the 7 in r3c9 to a 9 and you'll find this puzzles big brother:

Code: Select all

9....18...6..3......25....9..9.....6.5.....2.4.....3..3....81......4..8...79....5

No logical solution in SE, requires proposition constraint Y in gsf's program.

Is this already posted here somewhere? Or wait a minute... it shows some striking similarities to the other puzzle in your post, the Gyroscope... Are these the same?

RW

[ronk]

I keep thinking difficulty should be calculated like the point-to-point resistance of a network of simple resistors (no inductors, no capacitors, just no other components).

If there is only one technique at each step ... and each technique has difficulty Di ... then the overall difficulty is simply the sum of D1, D2, ...DN for the N steps, however many that might be.

If there are M techniques available at any one of those steps -- almost always the case -- then the overall difficulty for that one step is (D1 * D2 * ... * DM)/(D1 + D2 + ... + DM). With two techniques available of equal difficulty, for example, the overall difficulty would be 1/2 of that for single availability.

However, I've always disliked the seemingly open-ended top-end for that approach. IOW there doesn't seem to be an easy way to normalize "full-scale" to 10 or 100 or 1000 or 100000.

Just thinking out loud ... and maybe gsf is doing this and has found a way to normalize to a top-end of 100000.

[gsf]

gsf, I would also think that it would be easy to rate each individual step taken to solve the puzzle then averaging the results....would that correspond to the OVERALL difficulty of a puzzle.... so a puzzle scoring 9 0 may be easier than a 7 20 puzzle. This, along with the current rating system will give us a closer look at puzzles from different angles....

if you look at the -f%Q output most of the info is there to extend the rating
grouped by Cn.m... where C is the constraint applied,
n is the number of times the constraint was applied,
m is the number of placements or eliminations,
and the remaining numbers count the number of items of order 2,3,4,...
e.g., for W (order n x-wing), Wn.m.i2.i3.i4,
i2 counts the number of x-wings, i3 the swordfish, and i4 the jellyfish,
similarly for T (naked tuples) and H (hidden tuples)

you could play with the rating expression -R 'expression', e.g.:
-R'x*W2+s*W3+j*W4', where x is your weight for x-wings (W2 == #x-wings applied), etc.
--man under -R shows the default expression

[tarek]

Is this already posted here somewhere? Or wait a minute... it shows some striking similarities to the other puzzle in your post, the Gyroscope... Are these the same?

Yes they are..... that 9 is now the 9 in box 9.... which forces the hidden single in box 8 .... I cahanged the shape as it is not a pearl & I thought a new different theme would suit it

if you look at the -f%Q output most of the info is there to extend the rating

Thanx gsf, It seems that the user can do it from the interface, impressive.... I'll try to fiddle with it .... trying to subdivide constraints is probably too much, but i'll follow the simple 0-9 (Y=9) theme with no subdivisions & divide the final number by the number of batch eliminations. I sort of see the whole thing similar to statistical analysis ... at the end A MEAN+/- Standard deviation will help in describing the puzzle.

I'm not sure if anyone remebrs him because he doesn't frequent here anymore but "foxglove" had this cool line diagram that reflects a puzzle difficulty plotted agains step progression

tarek

[tarek]

Apparantly the AI Etana(Escargot, Snail) is all over the news......

I just read an article in the AUSTRALIAN claiming that it has claimed top spot on this site.......Interesting

I wonder would Ocean or myself be interviewed????

tarek

[Karlson]

While solving #5 of Ocean's recently posted Sudokus step-by-step with ER, there was a step which had a hint rating 10.5/10 -> Although ER is not able to solve it completely, we know that it is at least ER 10.5
-> It is also the last step possible
Just a fun fact
Regards,
Karlson

[RW]

I just read an article in the AUSTRALIAN claiming that it has claimed top spot on this site.......Interesting

I wonder would Ocean or myself be interviewed????

I guess it's just a question of marketing... How many newspapers did you call to say "Hey, I just created the worlds hardest sudoku"? The article in the Australian appears to be a little late though, given that both you and Ocean have already posted harder puzzles according to the official rating system in use at the moment... Ravel did ask for ArtoI's ratings on these, but no reply yet. Interesting that after ravel asked for the ratings, on ArtoI's website a short text has been added to the table of "Other famous or the most difficult puzzles by well known sudoku creators " saying "(updated 3 Oct 2006)"...

RW

[ravel]

Since it will take me some time (maybe a week), until i can update my list with the puzzles from the collections posted here in the last 2 weeks, i made a provisional top 8 list at the beginning of the top page.

[ravel]

Since i have seen some discussion about the ratings of hard sudokus, i'd like to summarize some known approaches from my point of.view.

The clearest (easiest to follow and verify) is the one Sudoku Explainer uses: The puzzle is as hard as the hardest step needed to solve it. So the problem is reduced to find a good rating of various techniques, that allow a "move" (which eliminates or forces one or more candidates). To find all possible moves for a given minimal technique difficulty will need some time for hard situations, but programs like gsf's show, that it can be done very fast.
Disadvantage: The solutions found this way (always apply all easier techniques before a harder one) will contain a lot of redundant steps (sometimes more, sometimes less), therefore are far from being optimal. A puzzle, that can be solved with one hard step is rated same as one, which needs 20 of them (and a lot of less hard steps).

On the other side of the spectrum is my own approach: The idea is, that a puzzles hardness is defined by the hardness of the "best possible solution" (the easier the solution, the easier the puzzle). But this is already very vague from the definition. Besides of the fact, that we cannot calculate optimal solutions, we know, that some people spot hard patterns easer, some chains, some ALS's, some long single's chains etc. So also solutions cannot be rated objectively.
So here we also have to rate techniques, but additionally have to do the most time consuming job of finding optimized solutions. Not enough, we have to decide, whether e.g. a solution with 2 very hard and 3 hard moves is easier than a solution with 17 hard moves. I think, to find a good formula here is a job for its own.

gsf's rating lies between these extremes - and it is very fast. The program applies all possible moves of the easiest possible difficulty as one step (batch ove). The rating is calculated with a formula depending on the number of steps and the techniques needed.
I agree with RW, that a second pass, that tries to find a shorter solution by detecting redundant steps could improve the rating. But this is not trivial. E.g. just notice, that an elimination still can be possible, when 4 others are not made before, but it might be a harder step then. This also shows a general problem of the rating (similar to ER): Puzzles, that can be solved with one very hard step and singles only then probably will be overrated.

Both ER and gsf'r use as only tactic, how to proceed, to apply easier techniques before harder ones. Human players would be more sophisticated here.

Ratings, that use guesses, can be good indicators for hard puzzles, but not more.
Similar to ratings based on techniques like tabling, which are nearly impossible for a human to follow.

[Ocean]

I wonder would Ocean or myself be interviewed????

Hope you can take care of the media this week, tarek. Seems that both of us are back to the top of ravel's list - with equally hard puzzles, according to the current rating rules. (Thanks for the provisional list, ravel).

Would be interesting also to see the AI_root ratings for these two puzzles (plus the other new hard ones).

[ravel]

Some intermediate results:

Ocean's list of 14 puzzles with empty boxes and diagoal pattern:
No 2 is the first 13-stepper, i wonder, why i have so much more solutions with an even number of steps, any idea why (hope its no bug:) )?
13: 2
12: 9
11: 11
10: 4,5,6,10
9: 8
8: 7,14

Ocean's list with vertical smmetrical puzzles:
20: 1
11: 3
9: 22
8: 2,7,8,9,12

Ocean's Coral:
16 steps

Tarek's Fluid drives:
20(already in the list),16,15,9,11,10,9,22

RW's non diagonal variant of Ocean's gold #5:
11 steps

When finished with Oceean's gold list and JPF's list with at least 2 empty boxes, i will make an update.

[udosuk]

ravel,

I couldn't find "Ocean's gold list" , could you please provide a link to help us locate it? Thanks!

Also, in your top post on page 1, you showed 2 different "Ocean #5/gold list", one with gsfr=99960 (#1 of "Puzzles, that need multicoloring in contradiction chains") and another 99909 (#2 of "Puzzles, that need coloring in contradiction chains"), so which one is the true #5 and what's the number of the other one?