The New Sudoku Players' Forum

[ravel]

Thanks udosuk, for pointing out the typo with the puzzle nr (5 instead of 6).

Ocean's gold list can be found here (containing 6 Anemones, 5 Corals and 2 more puzzles). I called it this way, because Ocean mentioned 'More "stuff" was found in the gold mine'.
It is the hardest list posted in this thread so far: The first 6 puzzles cannot be rated by my program (and SE), the RMS ratings for the others are 23,23,18,14,14,14,9

Also the first of JPF's puzzles with 3 diagonal empty boxes qualified with 9 steps.

Ocean's Extreme Jade puzzle for gurth cannot be RMS-rated also.

List updated now.

[tarek]

Fantastic work ravel, This must have taken some time & CPU power to achieve........ Good puzzles Ocean .......It took ArtoI 3 months & 1 billion combinations to get his Escargot where it took us much less than that to beat it

One thing that puzzles me is Ocean's Anemone .... with a low gsfr rating like that.... why did not RMS pick it ??? & how did Ocean pick it up to manually feed it to SE when the rest of the profile of this puzzle fits several others?
tarek

[ravel]

t took ArtoI 3 months & 1 billion combinations to get his Escargot where it took us much less than that to beat it

This is due to the experience you have that puzzles with diagonal patterns tend to be much harder. I suppose that Arto not even was aware that his two hardest puzzles are diagonal (and Escargot is a Fluid Drive). So this is also a confirmation, that it is unlikely to find harder puzzles with other patterns.
A half year since starting this thread now for the first time i suspect that the highest "class" of super hard puzzles is reached now. We started with "the toughest known", then came Ocean's BB, then Tareks "Fluid Drive 1", finally Arto's Escargot and - only a smaller step harder - the 2 current leaders.

One thing that puzzles me is Ocean's Anemone .... with a low gsfr rating like that.... why did not RMS pick it ???

My program is stuck after 5 eliminations. Maybe one good elimination step using a technique i have not implemented could lead to a relatively short solution.

[tarek]

I was under the impression the V3 proposition techniques in gsf's program are included in your techniques ?

I have posted the list (with proper references & links to this thread) on the Programmers forum ..... Let's see if it brings any new ideas or puzzles

tarek

[RW]

Very good job, ravel!

A half year since starting this thread now for the first time i suspect that the highest "class" of super hard puzzles is reached now.

I wouldn't bet my head on that, actually I'm looking forward to the first puzzle that cannot even be solved by multicoloring in the propositions (what happens when we run out of constraints, gsf?). The reason that I believe such a puzzle exists is that these current hardest puzzles were so "easy" to find after fixing the correct pattern. In just a couple of weeks ocean produced 8 puzzles in this category. Another reason why I believe in harder puzzles is that all of these came from the same pattern. Yes, it's the hardest pattern found yet, but apart from the standard diagonal pattern, I think this is also by now the most thoroughly searched variation of the pattern. What about all other different variations of the pattern.. Most have probably been tried, but not searched to this extent.

took ArtoI 3 months & 1 billion combinations to get his Escargot where it took us much less than that to beat it

This is due to the experience you have that puzzles with diagonal patterns tend to be much harder. I suppose that Arto not even was aware that his two hardest puzzles are diagonal (and Escargot is a Fluid Drive). So this is also a confirmation, that it is unlikely to find harder puzzles with other patterns.

With fully random generating, I think it's very unlikely to find a puzzle that hard in 1 billion puzzles. I'm no expert in statistics, but I think it's even unlikely to generate a puzzle with the Fluid Drive pattern in 1 billion random tries. In the original article presenting the puzzle I think it said that the program was optimized for finding hard puzzles, I read this as designed to create diagonal puzzles.

RW

[ravel]

So you think he mangled the puzzle to hide the diagonal pattern ? Cant believe that, there are a lot of more esthetic equivalent variants (Maybe one of the star designers from the rare shape thread could show some?)

[ronk]

In the original article presenting the puzzle I think it said that the program was optimized for finding hard puzzles, I read this as designed to create diagonal puzzles.

Maybe the program just generated mostly puzzles with three or less clues per unit (sector).

[m_b_metcalf]

Very good job, ravel!

took ArtoI 3 months & 1 billion combinations to get his Escargot where it took us much less than that to beat it

This is due to the experience you have that puzzles with diagonal patterns tend to be much harder. I suppose that Arto not even was aware that his two hardest puzzles are diagonal (and Escargot is a Fluid Drive). So this is also a confirmation, that it is unlikely to find harder puzzles with other patterns.

With fully random generating, I think it's very unlikely to find a puzzle that hard in 1 billion puzzles. I'm no expert in statistics, but I think it's even unlikely to generate a puzzle with the Fluid Drive pattern in 1 billion random tries. In the original article presenting the puzzle I think it said that the program was optimized for finding hard puzzles, I read this as designed to create diagonal puzzles.

Nor am I an expert in statistics but, once it is known that these patterns are rich furrows to plough, it seems to be relatively easy to come up with more quickly (see below). However, I'm not intending to make mammoth runs to get harder ones!

Regards,

Mike Metcalf

Snail:

Code: Select all

  4  .  .  .  .  3  .  5  .
  .  3  .  .  9  .  .  .  4
  .  .  7  5  .  .  6  .  .
  .  .  5  6  .  .  1  .  .
  .  6  .  .  3  .  .  .  8
  7  .  .  .  .  4  .  .  .
  6  .  .  .  .  .  .  1  .
  .  4  .  .  .  .  .  .  2
  .  .  8  .  .  .  7  .  .

 Time: 23s  Tries: 40459 (SE 9.1, hardest of 10)



and Fluid Drive:

Code: Select all

  8  .  .  .  .  4  1  .  .
  .  7  .  .  2  .  .  .  .
  .  .  5  7  .  .  .  .  4
  .  .  9  .  .  .  .  .  5
  .  3  .  .  .  .  .  1  .
  6  .  .  .  .  .  9  .  .
  4  .  .  .  .  9  5  .  .
  .  .  .  .  1  .  .  6  .
  .  .  8  5  .  .  .  .  7

 Time:  960s  Tries: 150866 (SE 8.9, hardest of 3)


[ravel]

[Edit:] So did you find 10 snails in 40459 random puzzles or did you pick 10 out of 40459 puzzles with that pattern ?

After all we know now, just searching puzzles with those patterns could be a good method to create puzzles for the hardest list, though the 2 ones are much too easy

... there are a lot of more esthetic equivalent variants

E.g. this one:

Code: Select all

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


[m_b_metcalf]

[Edit:] So did you find 10 snails in 40459 random puzzles or did you pick 10 out of 40459 puzzles with that pattern ?

After all we know now, just searching puzzles with those patterns could be a good method to create puzzles for the hardest list, though the 2 ones are much too easy

Neither. I tried the pattern with different values 40459 times, yielding 10 valid puzzles, of which this (by chance the last) was the hardest.

Regards,

Mike Metcalf

[Ocean]

... List updated now.

Great job again, ravel!

I notice you have divided the ten "Beyond RMS" puzzles in two groups: (1) Need multicoloring in contradiction chains [gsfr Y] and (2) Need Coloring in contradiction chains [gsfr X]. But there is an interesting subgroup (which tarek also pointed at): the three puzzles with gsfr below 99800 - do they actually need coloring in contradiction chains? If not, any explanation then why they are not solved by Explainer, and why they cannot be RMS-rated? The gsfr for these varies significally: #114 (gsfr=99687), #116 (gsfr=99527), #106 (gsfr=99325). tarek: the Anemone scored high on a measure similar to suexrate, and was therefore checked in SE.

[m_b_metcalf]

]... there are a lot of more esthetic equivalent variants

E.g. this one:

Code: Select all

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


I gave your pattern a spin, getting 10 valid puzzles in 157s. The hardest two are below. The others varied from (one) low, to 6.6, 6.7, 7.3, 8.3, and 9.0 (thrice), which I guess isn't too bad for such a small time investment. Maybe I really should run it longer and harder.

Regards,

Mike Metcalf

Code: Select all

  .  5  .  .  2  .  .  .  8
  .  .  6  8  .  .  .  7  .
  4  .  .  .  .  6  9  .  .
  5  .  .  .  .  .  8  .  .
  .  2  .  .  .  .  .  .  6
  .  .  4  .  .  .  .  3  .
  .  .  .  3  .  .  .  6  .
  .  1  .  .  8  .  .  .  2
  9  .  .  .  .  4  7  .  .

 Time:    5.17  Try number: 1536 SE many 9.0 and 9.1

  .  9  .  .  8  .  .  .  4
  .  .  1  7  .  .  .  9  .
  4  .  .  .  .  3  6  .  .
  7  .  .  .  .  .  1  .  .
  .  4  .  .  .  .  .  .  3
  .  .  2  .  .  .  .  4  .
  .  .  .  6  .  .  .  3  .
  .  5  .  .  4  .  .  .  8
  3  .  .  .  .  1  7  .  .

 Time:    3.29 Try number: 11685  SE 9.2



[ravel]

... the three puzzles with gsfr below 99800 - do they actually need coloring in contradiction chains? If not, any explanation then why they are not solved by Explainer, and why they cannot be RMS-rated? The gsfr for these varies significally: #114 (gsfr=99687), #116 (gsfr=99527), #106 (gsfr=99325).

My program is stuck after 15, 4 and 8 eliminations for these 3 puzzles, though it tries all remaining candidates.

I did have a bug, that i found, because it was stuck with puzzle 11/gold list, though Explainer could solve it. Due to this bug it is possible, but very unlikely, that some other puzzles in the list can be overrated (a shorter solution might have been found for them).
But i checked these puzzles after the bug fix. Since Explainer gives the same result, i hope, it is correct. But i cannot explain, why gsf's program could give a rating for the puzzles with standard settings (-q hardest).

If i would add more techniques, of course the ratings would rather differ to the current ones. It is a matter of taste, if a puzzle, that e.g. needs a swordfish in a contradiction chain, but only 10 hard steps, is harder than a puzzle that can be solved with basics in chains, but needs 20 hard steps.

[gsf]

... the three puzzles with gsfr below 99800 - do they actually need coloring in contradiction chains? If not, any explanation then why they are not solved by Explainer, and why they cannot be RMS-rated? The gsfr for these varies significally: #114 (gsfr=99687), #116 (gsfr=99527), #106 (gsfr=99325).

My program is stuck after 15, 4 and 8 eliminations for these 3 puzzles, though it tries all remaining candidates.

I did have a bug

amazing how these puzzles tax the humans and automatons
they uncovered a zeroes bug in my proposition logic where the solver
treated invalid puzzle positions as valid

these three puzzles do not require coloring in the proposition constraints
part of the confusion may be due to the aging solver that I will update shortly
(the update awaits fin logic)

the puzzles require at most triples, box-line, and singles respectively in the proposition constraints

here are the ratings and constraint details
note that the first one has backdoor size 2 (M2, M for magic) and required 8 rounds of propositions (P8)

Code: Select all

99687 FNBTHP C22.m/S4.da/F319.493/N1085.2454/B405.1082.384.30/T126.279.126/H147.238.147/P8.16.991.1.15.3038.14/M2.40.164/V6
99527 FNBP      C22.m/S4.da/F53.135/N318.737/B182.438.176.9/P2.5.365.1.4.893.15/M1.1.91/V5
99325 FNP       C22.m/S4.da/F34.67/N118.364/P2.2.146.1.1.276.11/M1.5.8/V3


[RW]

With fully random generating, I think it's very unlikely to find a puzzle that hard in 1 billion puzzles. I'm no expert in statistics, but I think it's even unlikely to generate a puzzle with the Fluid Drive pattern in 1 billion random tries...

Nor am I an expert in statistics but, once it is known that these patterns are rich furrows to plough, it seems to be relatively easy to come up with more quickly (see below).

That's exactly my point. When you know the pattern, it's not hard to find more. But through completely random generating, without fixing a pattern... I thought a bit about how true my statement above could be. It appears to exist 6 different box constellations with 3 clues "diagonally". This would give 9*6^8=15116544 possible 24 clue masks with one empty box and 8 diagonal boxes. If you found a grid where all these masks give valid puzzles (which I'm sure doesn't exist), removing clues from the full grid toward a minimal puzzle should give 1 or 2 of these in a billion tries (assuming there's 10^16 puzzles in the grid). However, as Mike's tries with the snail pattern showed, only one of 4000 gave valid puzzles, so 1 billion random puzzles from a random grid would probably not find a puzzle with one empty box and 8 diagonal boxes.

RW