The New Sudoku Players' Forum

[Mathimagics]

At the end of week 8, we have:

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 known 17-19C:   144,490,098
 added    19C:   975,263,602  Week 1
                 917,301,757  Week 2
                 451,939,607  Week 3
                 507,056,483  Week 4
                 358,256,360  Week 5
                 543,137,278  Week 6
                 467,361,125  Week 7
                 211,939,044  Week 8
               =============
               4,576,745,354  Total resolved
                 895,985,184  Unresolved


A slow week - not because of reducing yields so much as a reduced batch production level (we've lost one of our 3 data mining sites!):

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Week 8:
       Date  Grids   New   Yield
  ------------------------------
  1   4 Oct    805    50   0.062
  2   5 Oct    800    46   0.057
  3   6 Oct    772    37   0.0482
  4   7 Oct    810    41   0.0504
  5   8 Oct    805    39   0.0478


Good news, perhaps, in the last 3 yield figures - all ~4.8%. Explicit grid testing based on current sampling costs 40ms/grid, and this corresponds (roughly) to worker yields of ~2%, so we will keep on going with the current mining operations!

[blue]

It looks like the "relative yield" -- (% yield)/(% unresolved) -- has stabilized at ~30%.
That's good !

--

Updated Blue19 :

Blue19-new.zip

(137.96 KiB) Downloaded 283 times

Blue18.zip

(91.31 KiB) Downloaded 260 times

[coloin]

It looks like the "relative yield" -- (% yield)/(% unresolved) -- has stabilized at ~30%.
That's good !

Updated Blue19 :

Blue19-new.zip

Yes ... because its as predicted 250-300k will be no 19C grids ....
and the new 19C finder will surely be an improvement too !

The no 19C grid solutions will be known soon.

Regarding the 18C - i wonder what proportion of 18C puzzles are "untouchable" ? [ no non-isomorphic puzzles within {-1+1} ] - these wont be found as easily as the rest !!!

I found an untouchable 21C some time ago - which might be rare - or maybe just flukey

here i posted - "new " challenges !!!

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+---+---+---+
|...|...|...|
|12.|3..|8..|
|34.|12.|...|
+---+---+---+
|...|.6.|..7|
|..9|..7|..8|
|6..|...|5..|
+---+---+---+
|..5|..3|..4|
|.1.|...|...|
|...|8..|.9.|
+---+---+---+ untouchable 21C

[Mathimagics]

The state of affairs at the end of week 9 ....

This week we produced 6 batch sets (each set has 128 batch files), the grid counts are millions, rounded sometimes, the yields quoted are exact however):

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       Date  Grids   New   Yield
  ------------------------------
  1  10 Oct    800    35    0.0433
  2  11 Oct    784    30    0.0387
  3  12 Oct    784    30    0.0387
  4  13 Oct    736    24.5  0.0333
  5  14 Oct    641    21.6  0.0337
  6  15 Oct    630    18.9  0.0301


We resolved 160 million grids:

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    975,263,602  Week 1
    917,301,757  Week 2
    451,939,607  Week 3
    507,056,483  Week 4
    358,256,360  Week 5
    543,137,278  Week 6
    467,361,125  Week 7
    211,939,044  Week 8
    160,648,812  Week 9


The current LCT catalog state:

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 Totals:
     17C:      46301
     18C:   85663604
     19C: 4651798500       59233 have no 18C
     20C:  735222129        4814 have no 19C
     21C:          4
          ----------
 Puzzles: 5472730538 ( 100.00%)
     unk:          0 (   0.00%)
          ==========
   Grids: 5472730538


The "No 18C" count appears for the first time. I'm slowly working my way through the automorphic grids (as I did for 19C), testing them with the new Find18C provided by blue. I've only tested around 10%, but clearly the great majority have no 18C puzzle. (is the actual count known?)

The unresolved 20C grid count is 735222129 - 4814 = 735,217,315. The rate of yield decline is low. So we push on!

[Mathimagics]

The average expected time for explicit grid testing of the unresolved 20C grids remains at 38ms.

As blue pointed out, Find19C times are generally higher for grids with low numbers of 19C puzzles. The morphing process tends to favours grids with many 19C puzzles. So there would be a tendency for the unresolved grids to have lower 19C puzzle counts, and we were concerned that this could become a significant problem.

Find19C is very slow on grids with no 19.

• 250 random such grids, took ~3.33 seconds each, on average, to process.

• Grids with a small number of 19's, can take just as long.

The correlation between 19C puzzle counts and testing times is complicated (fortunately, as it happens)

Consider the pattern-based search as a simplified linear model, ie "for each possible clue pattern, does that pattern on this grid give a valid puzzle?". The ultimate cost-determining factor is the pattern index of the "best" puzzle, the one that has the lowest pattern index.

A grid with 50 puzzles might take longer than a grid with only 1 puzzle, if that 1 puzzle happens to have a lower pattern index.

This creates an "amelioration" factor, a blurring of the puzzle count/time relationship, the effect of which cannot be predicted, but can be clearly observed in our LCT-19 case. In other words, we got lucky!

[blue]

It looks like the "relative yield" -- (% yield)/(% unresolved) -- has stabilized at ~30%.
That's good !

I was wrong, I see.
It's under 25% now.

[Mathimagics]

A better indication of the efficacy of the LCT-19 morph workers is obtained by looking at the estimated completion times (ECT). That is the number of core-days required to do all the unresolved grids:

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        Added   
    467,361,125  Week 7   ECT = 487
    211,939,044  Week 8   ECT = 394     (-93)
    160,648,812  Week 9   ECT = 323     (-71)


For the past 2 weeks we have been running Gen19C on 8 cores (I think that's right, if coloin is running 4) so any reduction of 56 core-days or more indicates that it's still worth running.

[Mathimagics]

Some news of interest for this project!

New PC

I am investing in a new PC, an AMD Ryzen 2950X ("ThreadRipper") with 16 cores (32 threads), which has ~4 times the processing capacity of my current system (Intel i7-7700K, 4 cores, 8 threads). It will have 64Gb RAM against my existing 32B, and a couple of other useful extras that I hadn't thought of when ordering the current system (a 1TB fast-access SSD drive just for the ED+LCT catalogues, and a better sound-card). All this for around 1.7 x the current PC cost, which seems like a reasonable deal.

LCT-18

I've been doing a little bit of preliminary testing of the Gen18C code, which is essentially the same as Gen19C but with different seed generation. Have produced some batches (have got 127 million 18C grids, which is maybe 13% of the estimated total). I'll post about this below.

LCT-17

blue has kindly offered to hijack my new system for 3 months or so in order to finish off the 17C search with his "divide and conquer" app. Between us we have 20 cores - and 2200 core-days is the estimate to complete the search - so that's roughly 110 days. Hopefully we can reduce that with a little boost from hyper-threading, charity donations, begging, etc ("spare some core-days, mister?").

And of course there are the negative factors like power outages, breakdowns (human and/or computer), entropy, Brexit, etc etc

For the LCT project, completion of this job means knowing we have all grids with 17C puzzles identified, and that any 18C grids we identify apart from these are the "best possible #clues", and that's effectively LCT-17.


The "Little Ripper" will initially be used to:

• do Find18C on the remaining automorphic grids (est 1/2 days, a gentle warmup exercise)

• do Find19C on the unresolved 20C grids (est 2-3 weeks)

• perhaps do a little bit of LCT-18 batch production

Then, in say 4 weeks time, it will be kickoff-time for the big one, LCT-17 !

[Mathimagics]

LCT-18 Overview

The software components involved here are:

• Gen18C: the batch generator, a clone of Gen19C, slightly modified

• Find18C: blue's explicit-grid tester function

• UpdateCat: updates the catalog from batch-sets (64/128), no change needed

Gen18C does just the same {-1,+1} multi-pass propagation process as does Gen19C. The only difference is that we use Find18C for 18C-puzzle seed generation, since finding them by reduction methods is hard.

Seed generation will be done here (ie my PC) where we have access to the catalog (for every seed we generate we get ~6 grid resolutions). coloin will be provided with "seed pods" ...

As with LCT-19, we would hope to find most 18C's quickly by this method - prelim testing (more on this to follow) suggests that we get lower yields, but we have a much smaller target (~0.97 billion) so I'm guessing (wildly) that these will balance out ...


LCT-18 - The Longer View

blue's estimate of the number of 18C grids (~0.97 billion) means that there will then probably be, say, ~4.5 billion grids, for which all we know is that they will have a 19C, and almost certainly have no 18C. And only Find18C can tell us for sure..

February 2020 might see us reach that position, given fair winds. Then only this last step will remain, we will have finished both LCT-17 and LCT-19. Mind you, back in June, I never thought I'd be even contemplating getting to this point. Now I find myself estimating a notional "time to completion".

Ok, simple maths, assuming we get there, 4.5 billion grids to check at 4.23s is roughly ~600 core-years. Urrrgh, I hear you say, but consider this - it is 200 less than the legendary "No 16C" job took!

"LCT - The Complete Series". Direct to DVD. Featuring blue as "Shelley".

I can see it now! Ok, I am using a large telescope ...

[Mathimagics]

LCT-18 Batch properties

I have produced some test batches, rather slowly, using mostly the old (but soon to be "ex") PC, enough for 4 or 5 decent update runs.

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                                                             new/#ED   new/#Raw
 Set Batches  Date  Raw grids   ED grids               New    Yield     Yield       nSeed
 --------------------------------------------------------------------------------------------------
   1   128  Oct 10  268435122   65811495 (0.245)  61766034   0.9385    0.2301       10
   2   128  Oct 13  268435328   30340535 (0.113)   7255723   0.2391    0.0270       10
   3   128  Oct 16  264241026   27598684 (0.104)   5971153   0.2163    0.0226       10
   4    64  Oct 17  368440278   93852582 (0.254)  34165952   0.3640    0.0927       20
   5    32  Oct 18  186574856   63881415 (0.342)   7776707   0.1217    0.0417       40


I have added columns showing the number of grids in the raw batch files. That's because the resulting ED grids actually resulting from the merge is neither stable, nor large. LCT-19 had both of these right through to the end, but we are in a different world here.

The {-1,+1} connectivity of the 19C grids is complete, and most grids have 100's if not thousands of direct connections. It's pretty easy to get around.

Planet LCT-18, on the other hand, is over 80% ocean, with the grids scattered across a sprawling archipelago of islands, some large, some barely there at all. There is no boat technology here, the inhabitants completely isolated. Road connections are barely sufficient to connect the grids on these islands. Rumour has it that there is a small continent, which might have 50% or 60% of the population. But nobody really knows ..

Ok, we get it! Most grids don't have any 18C, those that do don't have many, and have limited direct {-1,+1} connections.

Some rough sample data for 18C puzzle counts (blue made an Enum18C for us). Two sets of 100 pseudo-random grids, all having an 18C:

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   n18C     Grids
   ---------------
     1     41   27
     2     19   24
     3     15   13
     4      8    7
     5      3   11
     6      4    4
     7      1    3
     8      -    1
     9      1    1
    10      1    1
    11      1    1
    12      2    -
    13      1    2
    14      -    2
    15      -    1
    20      1    1
    21      -    1
    43      1    -
    49      1    -
   ---------------
          100  100


I did a Gen19C using one seed at a time, which gives us some sort of vague idea of the "island" distribution. ~130 seeds were tested individually. In a fractal kind of way, some converged, other did not. I used a bailout initially of 16K grids, but that's too slow, and got the following results with a 5K bailout:

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Island sizes for individual seeds:
    Size    Count
  ---------------
       1      27
       2      11
       3      15
  4 -  9      14
 10 - 50       9
     137       1
     971       1
     BIG      56 (> 5000)


coloin will be pleased to see so many "untouchables", I trust?

The raw data and results for each seed are here:

The Gulag: Show

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1.............9.2.78..3......4..5.9....81.......2...5...2...6....5............3.8 #    3
...4..78..56...................7.....61.....5..48...3.3.....84.....6..1.....9.... #    2
12....7......89...7........2..........4....98....4..5...85......6.....4......12.. #      Big
1...5.......7....3.......6..37......6...1........2.4.......491..683.............5 #      Big
.2...67..........3..91............916....7....4..2..5....5...1.....9.....7....4.. #      Big
1....6......7...2..8....5....794....5.......8...2.......2........45..........38.1 #    2
...4...8...6......7...3.........5..6..58...........3.7..4.6..12....71.....8...... #    5
.....67......8......91......4....6.8...........12......7.9...1286..4...........3. #    2
1......89.............32......8....5.37...2...4....6.............4.7.3..8..9....1 #      Big
..3....8....7......8.....642.....9......6..4...75..3..5.....2.7.............48... #    1
1....6....5.....2.........4....1.9....8..73....45.....3.....6.5...24........7.... #      Big
....5...9...7......89.....4.6....35..1...8.......2..7.5.....2....4...........4..6 #      Big
12.......4..7.9..3...........83....7.........9...2..1......1.4...58..3....7...... #      Big
.........4...8...3..91...6..6.........1...4.......3..8......91.8...75..2.3....... #    1
12....7......89..3....3.....7..1..........4...6...52..3.......8.4..........2.4... #    1
..34............2.7......6.......41...85..3......7.....1.....76...3.8....6.2..... #    1
.2.4...........1.3......56...59...4.3.1..5...6...............9.......2......138.. #    5
1.....7.9.5............2..4...3.5........4...9.......6....7....6...9..1...2...35. #   38
..34...8........2.7..........8....4....2.19..6....7.....49......1....3.6........7 #      Big
.2....7..4....91...8......4.......5....2....89.1.........6........82..3...4...9.. #      Big
..3...7...5..........1...6.2...7...1........8....43....4.8.....6..9.5..2.7....... #    3
.23........67..........15.4............1...3.8....4....4...8...5.......7...3..61. #    1
12....7..4...89.........5....5.....6....1..9...73.........7.......5.3...9......4. #      Big
1............89...7......64.......1...8.429.............2...8..6..5........1..47. #   46
..34....9....8....7......6.....6..1............4.2.8...9....4....2...3..6...15... #    1
1......89.......2.7...31......9....76...4..........3....28......97..........6..5. #    9
...4..78.45...9..........6....8..31..........9....5.............186......7...4..5 #    3
1.....78.4.6..9...............64.......8....2.39....1.........6.7....9...8.5..... #      Big
.2...6.8....7.....7..1....5...5....7.4........3..2..........6..5.1......9.....23. #      Big
.2.4.6............7.8..........98.3..4.........7....9.5...73...........29.....6.4 #   15
1.3..6......78..2................3...7.........5..34.1..........8..9..7....5.16.. #      Big
............78...3.9....54.2....4............867.....2...6....7.4...5...9......1. #      Big
....5...9...7......98.....62........5.............4.18.6...1.......9..7...1...35. #    1
1.3........6....2......254......5...6.......79....4....4.....9....69.8.....3..... #    1
...4.......6....2..9.13.....3....4.15.9..7.........2....1......8....5.7..4....... #      Big
............7...23.98......2......7.6..9...5......4....81...4.....3..8.....26.... #    7
...45..........1.3........6.3...7.....5...8......6..9......1....6.2.3...9.4....5. #    1
...4..7.9.5.7.............6.3..6..5..1.2...3.....9......2.........3.....9.7..4... #    4
..3.....94...8.1..................35.........86..1........4.6...1.9.......52.3..7 #    1
...4...8......9...7.....5.6.453......1...........2...7....6...2.3........84..7... #      Big
....56...4......23...1...4....8...978.......4.6..2.....1....6..............9....8 #    3
....5..........1.379........4.9.8.......2..7..3......5.........5.2...9....13.4... #    1
...45...9..6.8....7.....5...4..1..........3.........753...27..........648........ #    1
..3.....9....8.1..7....2.....49.7..5..........81...6..3....5..7.1...............2 #      Big
......7.94.6.8......8...5...7...5..........6....3.72....42.........6..5.......3.. #    3
1...56....5.....23.......4.....1.9....5.......3..........2.8..7...3.....9.7...6.. #      Big
..3..6....5.7...2.........4.14...6.8......3..8...2........48........1.....7....3. #    1
.2......9...7......9.1....4....6......5........78...1...1....5.....2.....6..943.. #      Big
.....6...4......2.7.......42...4..9..3...8.........3...81.....6.6...39......7.... #    3
..3.....9....8.1..7....2...21..4..7.............6...35.8....9.....3........5.1... #    1
1...5.......7....3.9.....6....9...........41..6.3.....5...4.....3...8..7....1...6 #      Big
..3......4......2....1...6..1...8....6.5...1......43......2..9..7.9.....8.....4.. #      Big
.....6....5.7......9......42...48...3.....9.......1.5....92....8.......1..2....7. #    1
..34.6.....67...2.......5..2.......75...1.....8..9........2......73....69........ #    4
1.3.56......7...2...8..........18........3....7........6....9.1.4.2...7.........8 #    3
.2..5....4.......3...1..5....5..........24.7.8..............94......38....167.... #    9
............7...23.98......2.....4...6....9....53.....3.2.....5....9.6......4...7 #      Big
.......894........7...32.....95........8...........37.3...78.....59....6....4.... #    2
1...5......6.....3........42.....95......8.1......4....3......7.84........762.... #      Big
........9....8.1..7...32...2..9...5.38..........5....6..96.........1.3....4...... #      Big
...4....9.5..8....7...3......9........4...6......7..3...29..4.......1....8...5.7. #      Big
12.......4....9.........56...9...3......6.......21...7.......1...5.4...2..7..5... #    2
..34.........8....7......6.21.9..........5.3.8.....4.....5.7.........8..9....1..2 #    1
.23...7.......9...........4....6.....8.37....9......51.........5.1....9..6..2.3.. #    2
.2...6...45.....2.....1........4.8........9.1.75...........2.56..1......9...7.... #    3
.2..........7....3..8.1.......5....65..9......4....2.83......95..........1..24... #      Big
......7...5...9....9...3....3.....98..4......6...2...1..267...........3...7.4.... #   27
1...5......6....2.....1..64.....4.........9..9.....37..62.....5...89.....4....... #  137
....5...94........7.8...........8..5....9...6.1...4......1.....8.....47...2.6.3.. #    3
.2...6.........1........5....5...91...7.3........28.....91....6.8..67..2......... #      Big
.2...6........91........5........94..4..7...8...3.5.......2...75........9.1.....6 #   11
...4...8...67......9....5..24.......8............61.7.......2.7.8..9...6....3.... #    1
...4.6.8..........7.....5..2....7.......9.....3.1...4...9..52.7..........143..... #      Big
...45......6...1..7.8.......45.....7.....2..8.3........1.....4......7.3.....38... #    2
.23...7...5..............6..........6.95.....8....72.1...6...9......2....7..41... #      Big
1.......9...7...2...8..3...........5.3.92..........6.......584..7....3..9...6.... #   52
...4...8......9.2.7..........18....7......6...841.....5...2....6...7.....3.....4. #      Big
...4...8...6......7.....5.....3.......7.....6.3.1.8.....2.7.....8....41.......93. #   53
1.34..........9.2........6..7.....9...48.......51........5....1........8.69.7.... #      Big
.....67.94...8..........5..2....5...38.....4......7.1.......83...9.......17...... #      Big
12.....8....7.9..........6..84...........29...6......2...........7.6..4.9..3.5... #    8
.234...8....7.9.....8.......1......6..432.....3.............24........3.9....5... #    1
123.....................654...56...........4.8.7.....1.....1......3.7...96....2.. #    3
1........45......3...2..6.......5....67...9.....8.1...3....4..1...6....7..9...... #      Big
...4......5......3...2..6..2.4......6..9..........1..7.....7..5..9...4..81...5... #      Big
..3....8......912.7..2.....2....8...6....4.......3...5...67......9...3..........7 #   22
..3.56.........1.....2....424......1......37.6............9....81......2....35... #    3
.2....7...5...9.......3..6....5.8...6......1......2...3.9.1.......6..8...4......5 #      Big
....5...9..67..1...98......2..6.......48.......7.....253..2.......1..8........... #      Big
...4.......678..........5...17.....6.8...2........53..5...23..............4....17 #      Big
.23.........78.....9.........75...........2...6...24....18....7.4...36..........5 #    6
..34.........8.1........5..2...6...............43.7....6.1...478...2..9........3. #      Big
.......8.4....9...7..2...6..3..7.4.....61..........9...6..4.........3.....2.6..1. #      Big
1......8....7.9......2....4........76..5.....84.....1...7.4........6.83...2...... #    9
.....6...4......2....2.15......4.9...8..9.....1.....5......8..6..2.....19...7.... #      Big
.2..........7....3.9...1.......6........249..8.5....7.3.7.....55...9.6........... #    3
...4.67...5.....2.....3..........8..37....6.5..91.........9..1.68..............4. #    2
..3.5.7........1.....2..5..2.......6....75...8...4.......9....8.71........4.....2 #      Big
..34.....4......2......1.6.....6...............5.2.3.7...8.74..6.9.......1.....7. #    1
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Two questions to which I currently do not have answers:

• why are the ED/Raw yields so low? In some sets there were nearly 90% grid duplicates.

• The New/ED yields are also anomalous - the first looks normal (there were barely any to start with), but to immediately plunge to 24% from 92% seems a little premature!

As you can see, I am looking at these for the first time myself basically ... still have this ^%%$%^$ flu-thing-bug going on. Maybe it's obvious to someone else .. sure hope so!

(I have also done a quick health check on some indivdual batch files in each set - all look kosher, no grid duplicates).

[dobrichev]

I would suggest checking for "twin" puzzles and for minimality, if not already done.

[Mathimagics]

Ok, I will do that, Mladen, thanks.

I'm sorry to have to ask, but what does "twin" meaning here?

[Update]
Ok I do have a couple of thousand 17C grids in each batch, they do turn up in the morph process, obviously.

But in pretty small numbers ... the update process ignores them ultimately when it checks the catalog entry and discovers that its a known 17. So they certainly have a yield-reducing effect but a very small one.

[dobrichev]

I meant producing 18s by 19s which by chance have a redundant clue.
"Twins" are puzzles with same exterior (cell values for the initially non-given cells) but different interior (some givens are changed). They are easy to produce by a single solver call. For small number of givens they are not very frequent but make a bridge to a valid puzzle that differs from the original by several values at once.

[Mathimagics]

Rebooting ... 64kb Ram available

I would suggest checking for "twin" puzzles and for minimality, if not already done.

Like, for example, producing 18s by way of 19s which have a redundant clue?

I knew that the 19C workers would in fact turn up some 18C's this way, as indeed they did. While I was waiting for blue's Find18C to arrive, I found that I could get some 18C seeds for test purposes, very quickly, by simply looking in the LCT catalog, checking random entries until I found a 19C with a redundant clue. The success rate was, I believe, about 1 in 2000.

But perhaps I have failed to exploit this resource.

I really do need to look further into this. How many valuable 18C's has Gen19C (the batch producer) actually been throwing away?

[Mathimagics]

"Twins" are puzzles with same exterior (cell values for the initially non-given cells) but different interior (some givens are changed). They are easy to produce by a single solver call. For small number of givens they are not very frequent but make a bridge to a valid puzzle that differs from the original by several values at once.

Thanks, Mladen, this is also an interesting idea ...