The New Sudoku Players' Forum

[denis_berthier]

.
Just out of curiosity, I've coded the "weak" version upto depth 2.
At least, we agree on level 1.

2nd 100
-------
level 2 : 100 (100.00%)

But even on level 2, I find 12 puzzles in weak-T3

So, let's start again from the basics (they should be the same in both approaches):
1) Occurrence of template[1] = 1 digit nb1 + 9 cells that don't "see" each other; nb1 must still be a candidate or a decided value in each of the 9 cells; no other condition.
2) Occurrence of template[k] = k different digits and k templates[1] resp. for the k digits + only compatibility condition: the k sets of cells don't overlap.

Now, in the "weak" approach:
3) A candidate with number nb is eliminated at depth k>0 is there is a set of k digits containing nb such that there is no template[k] for this set.
4) No template[k] is ever eliminated, except indirectly via the elimination of a candidate or of a template[1] that is part of it.

Do we agree on these four points?
.

[blue]

Thanks P.O., that's good to know.

I (just now) had to correct my table of results for Denis' cbg-000 list, here, after fixing a stupid bug.

[denis_berthier]

Thanks P.O., that's good to know.

I (just now) had to correct my table of results for Denis' cbg-000 list, here, after fixing a stupid bug.

That was for the weak version.
Does it imply any similar change in your results for my version of templates (wrt to the larger list (254,760 puzzles) ?
.

[denis_berthier]

.

Any template[k] is the extension of a template[k-1] by a compatible template[1] for a different number.

But the reverse isn't always the case: that the extension of a template[k-1] by a compatible template[1] for a different number, is (still) a member of the relevant template[k] list.

There must be something different somewhere in our definitions. It seems you put more restrictions on the "relevant" templates.
How could the extension, which is a template[k] (this is exactly how I define a template[k]), could be not relevant?
What do you mean by "relevant"? Where does the additional information about "relevant" come from?
.

[blue]

Thanks P.O., that's good to know.

I (just now) had to correct my table of results for Denis' cbg-000 list, here, after fixing a stupid bug.

That was for the weak version.
Does it imply any similar change in your results for my version of templates (wrt to the larger list (254,760 puzzles) ?
.

Nothing changed.

[blue]

.

Any template[k] is the extension of a template[k-1] by a compatible template[1] for a different number.

But the reverse isn't always the case: that the extension of a template[k-1] by a compatible template[1] for a different number, is (still) a member of the relevant template[k] list.

There must be something different somewhere in our definitions. It seems you put more restrictions on the "relevant" templates.
How could the extension, which is a template[k] (this is exactly how I define a template[k]), could be not relevant?
What do you mean by "relevant"? Where does the additional information about "relevant" come from?
.

Don't read too much into the term "relevant".
If I say "relevant template[?] list", I'm just refering to the list for a (particular) digit set ... where the digit set should be obvious from the context.

What I was getting at in the quote, is this: if (t1,t2) is a pair of compatible templates, with t1 in the template[1] list for d1, and t2 in the template[1] list for d2, then (t1,t2) [ "(d1:t1,d2:t2)" ] would have been in the template[2] list for {d1,d2}, when it was first built, but it may have been removed later on, by a "T3-delete" application. If that's the case, then (t1,t2) is still a "compatible extension of t1" (in my mind) ... but it doesn't actually appear in the {d1,d2} list. It's "physically compatible" (as always), but it has been seen as being "not logically compatible" (as a pair of templates that could actually be part of a solution to the puzzle).

[blue]

.
Just out of curiosity, I've coded the "weak" version upto depth 2.
At least, we agree on level 1.

2nd 100
-------
level 2 : 100 (100.00%)

But even on level 2, I find 12 puzzles in weak-T3

So, let's start again from the basics (they should be the same in both approaches):
1) Occurrence of template[1] = 1 digit nb1 + 9 cells that don't "see" each other; nb1 must still be a candidate or a decided value in each of the 9 cells; no other condition.
2) Occurrence of template[k] = k different digits and k templates[1] resp. for the k digits + only compatibility condition: the k sets of cells don't overlap.

Now, in the "weak" approach:
3) A candidate with number nb is eliminated at depth k>0 is there is a set of k digits containing nb such that there is no template[k] for this set.
4) No template[k] is ever eliminated, except indirectly via the elimination of a candidate or of a template[1] that is part of it.

Do we agree on these four points?
.

Well, I'ld agree that it's a "weak" approach, but it isn't the one used by eleven and P.O..

In the "slightly stronger" approach:
1) "singles and ECP" are used at level 0.
2) T1-assert (in particular) and T1-delete rules are used at level 1.
3) Template[1] lists are trimmed whenever the pencilmark state changes.
4) At levels > 1, it's template[1] items that are eliminated, not candidates.

At level k, if a template[k] list for digits {d1,d2,..,dk}, with items (d1:t1,d2:t2,...dk:tk), doesn't have an entry using a particular (di:ti) in the template[1] list for {di}, 1<=di<=k, then (di:ti) is eliminated.

Your "T2" rules, match its levels 0,1 & 2 rules.

Side note: I don't know what eleven and P.O. do, but I don't actually maintain template[k] lists for k >= 2.
They're there in principle only, and the main reason for removing something, would be a template[1] item being removed.

[eleven]

I don't know what eleven and P.O. do,

Well i don't remember the details, i had lost the interest, because it seemed to be no benefit for manual users, so i did not keep the program over the years. I can only say, that there were no discrepancies with P.O.'s and my results.

[denis_berthier]

.
Blue, thanks for your explanations.

So, finally, we have three different techniques for templates, based on equivalent definitions of a template[k]:
- the strongest one, introduced at the start if this thread;
- the old one, used by eleven and P.O.;
- the weakest one, defined while I tried to understand the latter.

In the three approaches, templates[1] eliminate candidates.
As for templates[k+1], k≥1:
- in the weakest approach, they can only eliminate candidates;
- in the medium approach, they can only eliminate templates[1]; (my cbg-000 results a few posts above show this is strictly stronger than the weakest approach, already at level T2);
- in the strongest approach, they can only eliminate templates[k].

The reasons for increasing power should be clear. Once level k+1 is reached and all the templates[k+1] are computed (which all the approaches must do):
- the weak approach can do nothing if it can't directly eliminate a candidate;
- the medium approach can do nothing if it can't directly eliminate a template[1] (which is easier than eliminating a candidate);
- the strong approach will not directly eliminate more candidates or templates[1], but is has a chance of eliminating templates[k], which may later lead to still more eliminations of smaller templates.

I'll now stick to the strong approach defined at the start. Notice that it is computationally simpler than the other approaches, as in all the approaches, the use of some level k requires knowing all the templates at this level, but the strong approach requires lower levels (for puzzles above T2).
.

[P.O.]

Side note: I don't know what eleven and P.O. do, but I don't actually maintain template[k] lists for k >= 2.
They're there in principle only, and the main reason for removing something, would be a template[1] item being removed.

i retrieve template sets on two occasions, at initialization and when candidates are asserted to a value
then this set is constantly updated by the template eliminations performed by the combinations
and i only use these templates directly when making the combinations of 2 which index the templates,
then i combine these indexes: the combinations of 3 are formed from the combinations of 2, those of 4 from those of 3 etc. from level 2 i only handle indexes
when templates are eliminated by the analysis of combinations whatever the level, i start again at combinations of 2 to reindex the new and reduced set of templates

this reduction in the number of templates can be seen in the resolution paths i give, for example in my solution to the first puzzle of Denis' third list, where there is no assertion of candidates until the end the templates are only retrieved once, at initialization:

Hidden Text: Show

Code: Select all

initialization
#VT: (2 5 23 21 15 15 4 250 5)     #templates from 1 to 9
 2combs
#VT: (2 5 21 19 12 12 4 191 4)
 2combs
#VT: (2 5 21 19 12 12 4 190 4)
 3combs
#VT: (2 3 19 15 10 12 4 78 4)
 2combs
#VT: (2 3 12 15 10 12 4 71 4)
 2combs
#VT: (2 3 12 15 10 12 4 57 4)
 3combs
#VT: (2 3 12 14 10 12 4 31 4)
 4combs
#VT: (2 3 3 8 6 6 4 5 3)


what remains after solving a puzzle is
for a single-solution puzzle, if i let the combinations go up to 9, a single set of indexes indexing 9 templates
for a multi-solution puzzle as many sets of indexes as solutions, indexing a variable number of templates

for example this same puzzle without n2r2c8 has 15 solutions
the last state of the puzzle:

Code: Select all

Left in pool: (15)
#VT: (3 7 8 7 4 4 4 11 3)

128    289    3      4      15     568    7      568    269             
248    5      6      378    378    9      1      248    23             
7      489    19     16     2      358    348    458    369             
23     1      49     5      34     7      69     26     8               
6      348    458    238    9      234    25     1      7               
258    279    57     16     18     26     59     3      4               
13458  67     2      9      57     345    348    468    136             
1458   3678   157    2378   3457   2348   23468  9      1236           
9      348    48     28     6      1      2348   7      5               
154 candidates.


15 solutions:

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823415769456739182791628453319547628684392517275186934562973841137854296948261375
823415769456739182791628453319547628648392517275186934562973841137854296984261375
823415769456739182791628453319547628648392517275186934562973841187254396934861275
293418756856739142741625389319547628684392517527186934472953861165874293938261475
293415786856739142741628359319547628684392517527186934472953861165874293938261475
293418756456739182781625349319547628648392517527186934872953461165874293934261875
293418756456739182781625349319547628648392517527186934872953461165274893934861275
893415762256879143741623859319547628684392517527186934172954386465738291938261475
293418756856739142741625389319547628684392517527186934172954863465873291938261475
293415786856739142741628359319547628684392517527186934172954863465873291938261475
283415769456739182791628453319547628648392517527186934172953846865274391934861275
293418756456739182781625349319547628648392517527186934172954863865273491934861275
293418756456739182781625349319547628648293517527186934172954863865372491934861275
293418756456379182781625349319547628648293517527186934172954863865732491934861275
123456789456789123789123456214537968635894217897612534362975841571348692948261375


15 sets of indexes:

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 ((0 1 3 4 1 2 3 9 1) (0 1 3 5 1 2 3 7 1)  (0 2 2 5 1 2 3 8 1)
  (0 4 6 1 0 0 2 5 2) (0 4 6 1 2 0 2 4 2)  (0 4 6 2 0 0 2 3 2)
  (0 5 6 2 0 0 2 2 2) (1 0 1 0 2 1 0 10 2) (1 4 5 0 0 0 2 5 2)
  (1 4 5 0 2 0 2 4 2) (1 5 2 5 2 1 2 6 1)  (1 5 5 3 0 0 2 1 2)
  (1 6 4 3 0 0 2 1 2) (1 6 7 3 0 0 0 1 2)  (2 3 0 6 3 3 1 0 0))


the sets of templates:

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1: ((20 4 15 28 48 43 63 77 62) (20 4 15 28 48 43 54 77 71)
    (0 21 15 28 49 43 65 77 62))
 
2: ((9 22 8 46 41 34 56 75 69) (1 22 17 45 41 34 56 75 69)
    (1 22 17 45 41 34 56 66 78) (1 22 16 27 50 42 56 75 71)
    (0 22 17 46 41 34 56 75 69) (0 22 17 46 41 34 56 66 78)
    (0 22 17 46 39 34 56 68 78))
   
3: ((2 23 17 37 31 52 54 66 78) (2 23 17 27 39 52 73 67 60)
    (2 13 26 27 39 52 73 59 69) (2 13 26 27 39 52 64 59 78)
    (2 13 24 27 41 52 73 66 62) (2 13 24 27 39 52 73 68 62)
    (2 13 24 27 39 52 73 59 71) (2 12 24 27 41 52 73 67 62))

4: ((19 3 16 38 31 53 63 59 78) (19 3 16 38 31 53 54 68 78)
    (9 3 25 37 31 53 74 68 60) (9 3 25 37 31 53 74 59 69)
    (9 3 24 38 31 53 73 68 61) (9 3 24 37 31 53 74 68 61)
    (9 3 24 29 41 53 73 67 61))
   
5: ((10 23 7 45 30 42 65 58 80) (10 5 25 47 30 42 54 67 80)
    (10 5 25 45 30 42 65 58 80) (10 4 25 38 30 51 63 59 80))

6: ((11 21 8 36 50 33 64 76 61) (11 21 7 36 50 33 64 76 62)
    (11 21 7 36 50 33 55 76 71) (11 5 26 36 48 34 55 76 69))

7: ((18 13 6 47 32 44 55 66 79) (18 12 6 47 32 44 64 58 79)
    (18 12 6 47 32 44 55 67 79) (18 12 6 46 32 44 65 58 79))

8: ((19 13 7 45 39 35 74 68 60) (19 5 16 38 49 35 63 75 60)
    (19 5 16 38 49 35 54 75 69) (19 5 16 38 49 35 54 66 78)
    (9 23 7 37 49 35 74 66 60) (9 5 25 37 49 35 74 66 60)
    (1 23 16 38 49 35 63 75 60) (0 23 16 38 49 35 73 66 60)
    (0 23 16 38 49 35 64 75 60) (0 23 16 37 49 35 74 66 60)
    (0 12 24 37 49 35 74 68 61))

9: ((20 14 8 46 40 33 72 57 70) (19 14 8 29 40 51 72 57 70)
    (1 14 26 29 40 51 72 57 70))


[denis_berthier]

.
I gave a first idea of what happens to puzzles in T&E(3) here: http://forum.enjoysudoku.com/templates-as-patterns-t44896-14.html
I've now completed the calculations of the template-depths (according to the definitions at the start of this thread) for the full collection of 158,276 min-expand puzzles in T&E(3) (all of which have a non-degenerate tridagon). The above results are not fundamentally changed: the template-depths are only 3 or 4; most of the puzzles are in T3, with only 134 in T4, i.e. 0.085 %
Here's the list of the 134 in T4. Apart from being in T&E(3) and having a tridagon, they don't seem to have much in common.

Hidden Text: Show

Code: Select all

......7..4....9...6.8..7.......1537.3.5.2..91...9.35.2...3.19.7.3.5..12..1...2.53;893;16198  #4956
..34.678...718..36....374.129..6....5........73....6.837..4.........3.......718.3;933;22275  #5067
..34.678...718..36....374.129..6....37....6.85........73..4.........3.......718.3;934;22276  #5074
.2345.78.4.7.8.2...8..........5.4.7.....6....7..91....3.5...4.78....532...2..3.58;1245;23134  #6120
.2..5.......1....6.8.73.....1........98...62...4...8.1.61..49..8.2...46..4...8.12;1247;29659  #6124
.2..5.......1....6...73.....1........98...62...4...8.1.61..49.88.2...46.94...8.12;1247;28794  #6125
12..56......1.92.6...23.1........5.1.4.......87...2.....2.9.36....3..9.2..962..15;1449;62715  #6696
1..45....4.71.9.......271.42.4...........16.8......3...4279..1.57..1..9.9.15.....;1451;62714  #6700
12.4.........8...6....731..2.45..96....9...1.91....5...4....62.59....4.16........;2317;298786  #9524
1.....789.....9..3.9....56.24..938..3.981.24..81........294...8...3.1.......28...;2607;46716  #11225
.2...6...4.7....366.8.......79.346.1...7.1.94.4196.37.......46.7...1.9.3.....3.17;2673;35030  #11595
.2...6...4.7....366.8.......79.316.4...9.4.71.4176.39.......46.7...1.9.3.....3.17;2674;34944  #11599
.2...6...4.7....366.8.......79.613.4...9.4.71.4173.69.......46.7...1.9.3.....3.17;2675;34945  #11603
.2...6...4.7....366.8.......79.346.1...9.1.74.4176.39.......46.7...1.9.3.....3.17;2676;35031  #11607
.2...6...4.7....366.8.......79.643.1...9.1.74.4173.69.......46.7...1.9.3.....3.17;2677;35032  #11611
.2...6...4.7....366.8.......79.316.4...7.4.91.4196.37.......46.7...1.9.3.....3.17;2678;34946  #11615
.2...6...4.7....366.8.......79.613.4...7.4.91.4193.67.......46.7...1.9.3.....3.17;2679;34947  #11619
.2...6...4.7....366.8.......79.316.4...9.4.17.4176.39.......46.7...1.9.3.....3.71;2681;35034  #11627
.2...6...4.7....366.8.......79.613.4...9.4.17.4173.69.......46.7...1.9.3.....3.71;2682;35035  #11631
...45.78........31........6...87.....98.25.745.79.4.2...429....8.25.7...9...48...;2779;169974  #12113
...45.78........31........6....7.....98.25.745.79.4.2...429.8..8.25.7...9...48...;2779;170412  #12114
...4........18.2.6....3.14..6.3.8.14....613.2.3.24.86..8.......51.82....7.96.....;2781;82835  #12166
.23..67...5.........92.365.....3..75.35...29.......3.6...1.4.........96..72.98...;2914;52641  #12919
.23..67.9.5.......7.92...5.....3..75.35...29...7...3.6...1.4......3..96..72.98...;2914;50247  #12925
.2...6......18.2......7.4.524....5..3.6...9...95..........9.3.2.345..69.9.263..54;3192;46647  #14164
....56.8...71.........3..4.24.8..9...98.....27.1...4.8....9..24..2..419.......8.7;3597;55563  #16622
....56......1..2.3..8.27...24.9..13..8.2..9.49......2831....8.2......34.8.4..2...;4046;63402  #19201
...45.7..45.....23.9.....6..4.5.8....8197......5.41....74........9....1881..9....;4419;63712  #21429
...4.678.4...89.......3.....3.8...47...3..69..7...43.8..29.....5.16.....7.....86.;4604;89628  #22639
.2.45.........92..9..3.....27.....68.9687.12.8.1.......8....6.16....187.71.....92;4628;142642  #22775
1...56.8..5.18..6..6.3.7.....6......3.5.....171.5.8..653......2...7.5..8.7....954;4698;84195  #23102
12......9..7.89...6.9..........34......5.8.3...579..4.......8.454.8.3.97.7..4.35.;4863;86676  #23820
......7.9.571...3696.37.51..35....7.61.....9.7.9.........84.9..5.6..3.......2.3..;5412;87304  #26299
1.3..67.9.57..9.36......5...79.1...53.6.....151.......73..6.......2.4.5....8...6.;5413;89019  #26302
1.3..67.9.571.9.36......51..79.....53.6.....151.......73..6.......2.4.5....8...6.;5413;87305  #26304
12......9...1.9.3....2..54121........86.....77.9.....8...8.1....71.926....267....;5471;88966  #26473
12....78..5.1..2.66..2...152...7.8...1.......78....56..6..94...8....3......7..65.;5601;153126  #27059
12....78..5.1..2.66..2...152...7.8...1.......78....65..6..94...8....3......7..56.;5603;153125  #27101
...45.7.9....8.2.6.........21..9...3.........7.6.....23.1...6.7.72..3.9196...132.;5877;88718  #28090
1.....78.4.6....2..8...........7893..3.59.2...9.2.3.5........955.8...3.29...2587.;6883;145241  #34042
1.345...945..89..3..9.......319.58...4.83.1....8.14..........7....5..9..8.5....26;6905;143295  #34146
1.3.5......6789....89.........94..78.4..2.9.5.9.5..42...2.94......27....9.48.5...;7216;145397  #35059
1.3.5......6789....89.........94..78.9..2.4.5.4.5..92...2.94......27....9.48.5...;7217;145398  #35061
...4..78.4.71..2.6.......14...8.5......67.82.8...13.....4.6.1.26.2....787........;7985;174808  #38385
...4..78...71..2.6.......142..8.5......67.82.8..213.....4.6.1.26.2....787........;7985;173396  #38399
1.3.56......1.9..6...27.....14..59..5.9..4..163....4.53.....69..........94....5.3;7988;174799  #38443
1.3456......1.9..6...27.....14..59..5.9..4..163....4.5...54.69..........9.....5.3;7988;173397  #38449
1.3456......1.9..6...27.....14..59..5.9..4..163....4.53...4.69..........9.....5.3;7988;173398  #38450
.23....8945..89......2.3.4529.....673.......1....9.4...8..24....3.9.5......8..5..;8349;174771  #40201
...4..78.4.7.....6.89...4.1.46.9...87.1.6.9.489..........9.21...7..1.......5.3...;8707;174763  #41946
....567.9..71.9.63...73.15.24956......1...69..8.91....3...95....7.3.1......67....;8975;182385  #43294
...456...4.7.....6.8.......2..96.5......1492....2.5.6..9154.6.2..26.149........15;9244;186815  #44654
12....78.......2.66.82...1....34856....59.87.8..7.....5.2..7..878...5....61....57;9299;183524  #44876
12....78.......2.66.82...1....34856....59.87.8..7.....58...7...7.2..5..8.61....57;9556;183526  #45877
1.3...78........3668.3..1.....79.85....24867.8..5.....5.8..7...73...5..8.16...5.7;9558;183528  #45884
1.3...78........3668.3..1.....79.85....24867.8..5.....53...7..87.8..5....16...5.7;9559;183529  #45887
....56....5.1....668.3.7..1.157.8.6.37.56.8..8.6.......3.....4.7.....92.....7...3;11263;294151  #55048
...4.678...718.2....8.27.1.......8.1....1246....8.4.7.53.......7.62......92....4.;11551;288750  #56018
.2....78..56.......9..13....4.13..78.8..72....718.423........42....4.3.7....2.81.;12490;275306  #59372
1.....7......89.63....2..5....8..9...719.24..9.8..4.....2.4....7.4.98..18..2.7...;13092;295729  #60929
1.3.5.7..........368....1.5..8....173.1..76.876.8.1...5....2......9.4.......3..76;13093;295730  #60930
1.....7......89.36....2...5...9..8...718.24..8.9..4.....2.4....7.4.98.1.9..2.7...;13094;295731  #60931
1..45.7.9...1.9.......37.5.....95..3.3.7.19.4...34.5..3.2......8.6......91..73...;14523;504659  #65852
1..45.7.9...1.9.......73.5.....95..3.3.7.19.4...34.5..3.2......8.6......91..37...;14524;504660  #65857
1..45.7.9...1.9.....9.7..5.....95..3.3.7.19.4.9.34.5..3.2......8.6......91..37...;14524;502077  #65858
1.3..678..57....3668...35.1.18.6.......94..1.....2...5.......6..61....53...63...7;16019;427606  #71540
1..4.6.894...891.2...21.64..376.......58......9....2.......491....9........1.8.26;16067;437068  #71648
1.3.5.7.9.57.....669..7.1...16...5.3..9.......7....69...1..4......9..3...652.8...;16079;441004  #71679
1...5.78....18..36...7..1.5.76.........57.6.3...6.8...3.2......51....36..98......;17049;442234  #74766
...45...945.1.92.3....23...2.5......31.5...2..943.2.1....2.48.7...93.6...........;17226;440426  #75199
..3.56......1..23....3.7...2.9...3.831.8..49..489...12..4...9........84.8.1....23;17415;429241  #75812
.....6...4.7.89.3..8..3.....7869....3.6.748..94.3.86......479.........21........5;17615;440941  #76252
.....6...4.7.89.3..8..3.....7869....3.6.478..94.3.86......749.........21........5;17616;440942  #76258
1.3.......5.......79....5462...7...5.........6...259.4.....749..7..9.6.2....64.57;18187;442073  #77683
1.3.5.....5.1.9....8973..1..95..3...3.15..9..87.9.1......8.7.....8....62......84.;19755;436616  #81655
.2.4.67.9.......63.9.73.4..2....7...8.5.....4..1.........97.6.2..2.64.37...2.3.4.;19756;436617  #81658
1.3..67.9.57..9.36......51..16...3.5..9....7..7....96...1.4....7..82.........3.57;20018;436526  #82242
1.345..8945....13..89.............98...6.......427....54...38.1.3....94.9....4.53;20021;427031  #82251
1.345..8945....1.3.89.............98...6.......427....54...381..3....9.49....4.35;20022;427032  #82255
..345........89....891.354..349....581.54...39.5.3.........527.......6...98.....1;20023;429973  #82258
1.345........89....891.354..349....581.54...39.5.3.........527.......6...98......;20023;427033  #82259
..34..7....71.923.....37.41....14.93...3.2..7.......2..81....7456.....1...9..1...;20216;436805  #82652
.2.....8.4.7.89..668..2....24..7.....98.64...7.6..24......4.951....9...397....8..;20627;475529  #83361
1.3..67.9.57..9.3696....15....84..6.....27...5........6.5....7173.....9.........3;20765;440690  #83666
...4.6..9......2.17.....5...3.84..9....9.3....9..67...3..6.89.7.78.94..396....8.4;20919;427265  #83894
....56789..6.........23..46.47....6.6.1..7..489...4.71.68...49....9..6.8.......1.;20920;427266  #83897
12..56....5678....7.82.1..52.5.7..........2..86..12.......6.9.8......43..8....5.1;21099;436280  #84275
.23...7..4..78.....9....6...156.78.....84.5.1.......67....68.5....1.4.78...57...6;21176;436427  #84389
1...56.....7.8.......3..41.2.....19.7...9..43.........37.2..9.4.429...719.1...32.;21237;480479  #84529
1...56.....7.8.......3..41.2.....19.7...9..43.........3.1...92..429...7197.2..3.4;21238;480480  #84542
..3......4.71.9...8.6........4.15.97...72.......9.45.2.4.29..71...5.7..4....41.5.;21612;504397  #86484
..3........71.9...8.6......2.4.15.97...72.......9.45.2.4.29..71...5.7..4....41.5.;21612;504333  #86486
...4..7.9..7....36......41.2..9.....7.......38.53........79.6.1.7.6.439..6..13.74;21958;480277  #87811
...4.6...4.7.892.6.8.27....2.46.7.9...8.92.4.9..84.......72..6.......5........1.3;22132;504318  #88434
1.345.7.9...1.9.......37.5.2.6.......1..73.....8..........95..4.9.34.5...4.7.19.3;22133;504319  #88440
.2.45..89....8923....3.25.4..6..3.........34.731............4.5......89.9.48...23;22159;480303  #88513
...4567.9....8....69.3.....2.6..1.9337......1.19..3.7.76....9.2.31....679.2......;22185;469696  #88656
1.345.7.9...1.9.......37.5.....95..3.3.7.19.4.9.34.5...1..74...8.2........6......;22396;486938  #89564
1.3.......57..9...69....5.....84.3..3..7.1......2...6.71.5..69..36.7.1.5.......73;22631;482175  #90345
...45...9......2..6.9..7...2.18......68.1....79........16....928.2...1.797...186.;23577;482541  #93174
...45...9......2..6.9..7...2.18......68.1....97........16....9279...186.8.2...1.7;23578;482542  #93175
.........4.7.8..3668......5.465...783.87..65.57....3.4...6.2.......91..7..4......;23655;482172  #93358
.........4.7.8..3668......5.467...583.85..67.57....3.4...6.2.......91..7..4......;23656;482173  #93360
1.3..6...45.1.9....963..1...45...6.1.......28......57.31.69....5.4.......695.4.13;24219;799234  #95659
........9...18..3...8...5.42..76.....6.2.8.7.78..31.2...682....81.6.73.2....13...;24295;486356  #95970
........9...18..3...8...5.428..13.7..6.7.8.2.7..26......682....81.6.73.2....31...;24296;486357  #95971
........9...18..3...8...5.42..76.....6.2.8.7.78..13.2...682....81.6.73.2....31...;24297;486358  #95972
........9...18..3...8...5.428..31.7..6.7.8.2.7..26......682....81.6.73.2....13...;24298;486359  #95973
12....7.9.5.1..26.6..2...5129...16.5.15......7.6.25......7.2....6..34...97...8...;27070;528242  #107650
.....6.89...18.........3.542.....5.1.952.1.48...5.492..8.........2...8...19...4.5;27100;542310  #107731
1.3..67.9.57..9.3669....15....6.....7618.5...9..24....3........5.93...17..69.....;27856;525787  #110052
1.3...789...18.2..........4...6.5.....681......5.32.......218...325.86.18.136.5..;27857;525788  #110053
...4.6.8...7.89.2....27....2.869.....64..89..97........46....7.....6.3.5.......61;31027;765769  #119327
...4.6.8...7.89.2....27....2.869.....647.89..9.........46....7.....6.3.5.......61;31027;654865  #119328
..3.567....718.......7.3....8567....6.13.8..5....15.......6.5...16....92..8...64.;31298;589784  #120074
...4.67......892.66..27...4.6.9.8...8.5......931.......4276.9.8.86.94.27...8.....;31659;602843  #121672
12..567...5718.2..6.8......2.6...85.....6.9.4.........56..78...7.1.2.....82..1.7.;32944;741985  #126009
.......8.4.......6....27.45..476.85.....48.72..82.56.431.....2...5..2...9.2....67;33560;614487  #127717
....5678..5.18.3.6.8.7.3.152.4..1...86.......9...7..........6.1.....783...83...5.;33886;619170  #128738
1.....78....1.92.6........52.6.....4.71....6.94.........4.126..61.7.4...7.296....;33921;621552  #128882
....567.....7..13....2.....29.1..47.3.4....21.17...9.3.4..9..1..32....97........4;34104;620977  #129414
1.3...78....1..2.6......5......384..3..74.......9.1..7.183.4.7.7.489....93..17.4.;34920;641335  #132296
1.3...78....1..2.6......5......384..3..74.......9.1..7.183.7.4.7.489....93..14.7.;34921;641336  #132300
...4.67.9......12.......564...8.3...84.69..7..3..74...3..9.7..6.9.36...767..48...;34970;640208  #132447
......789......13.7.9...6.42.5.......47.95.6.96..2.....72.4...659..67...6.4..2..7;34972;640210  #132454
1.3......45.78....789........4.75.68...8.4..2...26.......6.8.74.4..27..5.7.54..2.;34974;640211  #132474
...4...8..571.9......23.....18....6.5.6.....879......5.75...6.168..1..97...67.8..;35637;757228  #134365
.......8945..891.2...2.154....19.4.5....24..8...8.52..37.......6.1........291....;36257;756364  #136451
1.3......45..89....89..3.45.4583......19.54...9..14....1.....6.....9.8..93.....72;36314;647332  #136614
.2....7.94.7..9....89....45..8.35......961......8...9..752..9.8...5..47..4.....52;36778;755908  #138583
......78..571...3686.3..1.5.7.831......795..1...624.57.18...67..3....5...........;37086;730144  #139746
.......8945..891.2...2.154....91.4.5....24..8...8.52..37.......6.1........219....;37767;756365  #142095
....56.8..5.18.....8.7.3.15....3.86.........7..167..53..2.......6.31....9.4....7.;40112;765332  #148909
1.3.567.....1.9...9..73.1...96.....353.69...77.1............5.16.5...9.8.......42;43138;816555  #155879

[Edit: 2024 Nov. 3]: following the discovery of missing eliminations in SudoRules for T3, all the above puzzles are now solved in T3. All the known puzzles in T&E(3) are in T3.
.

[blue]

Those too, I have as all in T3.

I applied a random relabeling to each of the puzzles.
Would you check whether they still come out as "T4" ?

Hidden Text: Show

Code: Select all

......8..5....7...2.6..8.......1498.9.4.3..71...7.94.3...9.17.8.9.4..13..1...3.49
..98.276...746..92....978.431..2....5........79....2.697..8.........9.......746.9
..35.689...829..36....385.241..6....38....6.97........83..5.........3.......829.3
.9358.71.5.7.1.9...1..........8.5.7.....2....7..46....3.8...5.71....839...9..3.81
.9..3.......7....5.6.41.....7........86...59...2...6.7.57..28..6.9...25..2...6.79
.7..3.......4....8...52.....4........16...87...9...6.4.84..91.66.7...98.19...6.47
31..76......3.81.6...12.3........7.3.9.......45...1.....1.8.26....2..8.1..861..37
1..86....8.21.9.......521.85.8...........14.7......3...8529..1.62..1..9.9.16.....
51.9.........3...7....465..1.92..87....8...5.85....2...9....71.28....9.57........
2.....174.....4..9.4....36.58..497..9.472.58..72........548...7...9.2.......57...
.1...7...9.4....377.8.......45.397.6...4.6.59.9657.34.......97.4...6.5.3.....3.64
.2...9...5.6....199.3.......68.179.5...8.5.67.5769.18.......59.6...7.8.1.....1.76
.6...3...2.9....733.1.......94.387.2...4.2.98.2897.34.......23.9...8.4.7.....7.89
.1...8...3.4....988.5.......42.938.6...2.6.43.3648.92.......38.4...6.2.9.....9.64
.1...9...8.7....599.2.......74.985.6...4.6.78.8675.94.......89.7...6.4.5.....5.67
.9...8...6.1....588.7.......12.548.6...1.6.24.6428.51.......68.1...4.2.5.....5.41
.3...5...7.9....455.6.......92.514.7...9.7.21.7124.59.......75.9...1.2.4.....4.19
.6...1...9.2....811.3.......27.841.9...7.9.42.9421.87.......91.2...4.7.8.....8.24
.5...6...8.3....266.7.......34.612.8...4.8.13.8132.64.......86.3...1.4.2.....2.31
...26.95........31........4...59.....75.86.926.97.2.8...287....5.86.9...7...25...
...62.78........93........5....7.....18.42.762.71.6.4...641.8..8.42.7...1...68...
...1........45.3.8....6.41..8.6.5.41....846.3.6.31.58..5.......74.53....9.28.....
.92..63...8.........59.268.....2..38.28...95.......2.6...4.1.........56..39.57...
.84..57.1.2.......7.18...2.....4..72.42...81...7...4.5...9.6......4..15..78.13...
.6...8......97.6......2.5.165....1..4.8...3...31..........3.4.6.451..83.3.684..15
....54.9...18.........7..2.32.9..6...69.....31.8...2.9....6..32..3..286.......9.1
....51......4..7.6..9.73...72.8..46..9.7..8.28......7964....9.7......62.9.2..7...
...17.3..17.....58.6.....4..1.7.9....9263......7.12....31........6....2992..6....
...7.495.7...52.......1.....1.5...79...1..42..9...71.5..32.....8.64.....9.....54.
.4.76.........94..9..5.....48.....13.9138.24.3.2.......3....1.21....238.82.....94
8...52.4..5.84..2..2.9.3.....2......9.5.....838.5.4..259......1...3.5..4.3....657
57......9..8.39...2.9..........16......4.3.1...489..6.......3.646.3.1.98.8..6.14.
......9.1.296...8515.89.26..82....9.56.....1.9.1.........47.1..2.5..8.......3.8..
5.4..12.9.62..9.41......6...29.5...64.1.....565.......24..1.......8.7.6....3...1.
9.1..86.4.769.4.18......79..64.....71.8.....979.......61..8.......5.3.7....2...8.
85......4...8.4.6....5..29858........31.....77.4.....3...3.8....78.451....517....
94....85..6.9..4.22..4...964...8.5...9.......85....62..2..73...5....1......8..26.
69....15..8.6..9.33..9...689...1.5...6.......15....38..3..72...5....4......1..83.
...29.6.3....5.4.1.........48..3...7.........6.1.....47.8...1.6.64..7.3831...874.
3.....24.1.6....5..4...........2478..8.97.5...7.5.8.9........799.4...8.57...5942.
9.687...587..25..6..5.......695.72...8.26.9....2.98..........4....7..5..2.7....13
4.6.5......9187....87.........72..18.2..3.7.5.7.5..23...3.72......31....7.28.5...
2.7.9......3615....15.........54..61.5..8.4.9.4.9..58...8.54......86....5.41.9...
...3..84.3.86..7.5.......63...4.1......58.47.4...62.....3.5.6.75.7....848........
...5..94...93..7.8.......357..4.6......89.47.4..732.....5.8.3.78.7....949........
1.4.58......1.7..8...62.....19..57..5.7..9..184....9.54.....87..........79....5.4
3.8926......3.4..6...15.....39..24..2.4..9..368....9.2...29.64..........4.....2.8
9.3627......9.5..7...81.....96..25..2.5..6..973....6.23...6.75..........5.....2.3
.46....7839..78......4.6.3948.....216.......5....8.3...7..43....6.8.9......7..9..
...7..16.7.1.....5.64...7.8.75.4...61.8.5.4.764..........4.38...1..8.......2.9...
....196.8..65.8.92...62.51.34819......5...98..7.85....2...81....6.2.5......96....
...631...6.2.....1.8.......9..51.3......7659....9.3.1..5736.1.9..91.765........73
97....25.......7.33.57...9....68543....41.52.5..2.....4.7..2..525...4....39....42
83....56.......3.99.63...8....21649....47.65.6..5.....46...5...5.3..4..6.98....45
1.6...24........6774.6..1.....29.45....38472.4..5.....5.4..2...26...5..4.17...5.2
9.5...71........5881.5..9.....73.12....46187.1..2.....25...7..17.1..2....98...2.7
....94....9.3....447.2.8..3.398.7.4.28.94.7..7.4.......2.....1.8.....65.....8...2
...5.784...864.9....4.98.6.......4.6....6957....4.5.8.12.......8.79......39....5.
.2....74..53.......8..16....9.16..74.4..72....714.926........92....9.6.7....2.41.
2.....3......61.78....5..9....6..1...321.54..1.6..4.....5.4....3.4.16..26..5.3...
3.5.1.2..........578....3.1..8....325.3..27.827.8.3...1....6......4.9.......5..27
5.....3......67.98....1...2...7..6...356.14..6.7..4.....1.4....3.4.76.5.7..1.3...
9..16.8.5...9.5.......38.6.....56..3.3.8.95.1...31.6..3.7......2.4......59..83...
5..71.9.3...5.3.......94.1.....31..4.4.9.53.7...47.1..4.2......6.8......35..49...
4..38.1.6...4.6.....6.1..8.....68..9.9.1.46.3.6.93.8..9.2......5.7......64..91...
3.8..162..56....8112...85.3.32.1.......97..3.....4...5.......1..13....58...18...6
9..3.1.423...429.8...89.13..751.......64......2....8.......329....2........9.4.81
2.8.1.6.3.16.....553..6.2...25...1.8..3.......6....53...2..7......3..8...519.4...
2...5.83....23..47...8..2.5.87.........58.7.4...7.3...4.1......52....47..93......
...61...261.7.25.8....58...5.1......87.1...5..268.5.7....5.64.3...28.9...........
..3.18......2..63....3.4...6.9...3.532.5..79..759...26..7...9........57.5.2....63
.....4...7.8.59.3..5..3.....8549....3.4.875..97.3.54......789.........12........6
.....5...6.7.92.8..9..8.....7952....8.5.679..26.8.95......762.........43........1
1.2.......9.......46....9857...4...9.........5...796.8.....486..4..6.5.7....58.94
3.6.9.....9.3.2....5246..3..29..6...6.39..2..54.2.3......5.4.....5....18......57.
.6.2.75.8.......74.8.54.2..6....5...3.9.....2..1.........85.7.6..6.72.45...6.4.2.
3.8..47.6.57..6.84......53..34...8.5..6....7..7....64...3.2....7..19.........8.57
8.624..5924....86..59.............95...1.......273....42...65.8.6....92.9....2.46
8.146..2746....8.1.27.............72...9.......453....64...128..1....7.47....4.16
..627........34....345.672..624....735.72...64.7.6.........719.......8...43.....5
3.629........17....173.692..627....913.92...67.9.6.........954.......8...71......
..38..2....26.153.....32.86....68.13...3.5..2.......5..76....2849.....6...1..6...
.7.....9.6.4.93..229..7....76..4.....39.26...4.2..76......6.381....3...534....9..
5.4..32.8.12..8.4383....51....79..3.....62...1........3.1....2524.....8.........4
...1.3..7......9.82.....5...6.41..7....7.6....7..32...6..3.47.2.24.71..673....4.1
....75916..5.........43..25.29....5.5.8..9..216...2.98.51...26....6..5.1.......8.
13..98....9857....5.73.1..93.9.5..........3..78..13.......8.2.7......64..7....9.1
.89...5..1..52.....3....4...674.52.....21.7.6.......45....42.7....6.1.52...75...4
6...13.....4.8.......5..76.2.....69.4...9..75.........54.2..9.7.729...469.6...52.
2...75.....9.1.......8..62.4.....23.9...3..68.........8.2...34..643...9239.4..8.6
..9......3.76.4...1.8........3.65.47...72.......4.35.2.3.24..76...5.7..3....36.5.
..7........63.5...2.9......8.1.34.56...68.......5.14.8.1.85..63...4.6..1....13.4.
...9..2.8..2....14......97.6..8.....2.......13.51........28.4.7.2.4.918..4..71.29
...4.9...4.7.135.9.1.57....5.49.7.3...1.35.4.3..14.......75..9.......8........2.6
4.291.7.5...4.5.......27.1.8.3.......4..72.....6..........51..9.5.29.1...9.7.45.2
.4.18..53....5342....2.48.1..7..2.........21.629............1.8......53.3.15...42
...8196.3....5....93.4.....2.9..7.3446......7.73..4.6.69....3.2.47....963.2......
9.476.5.1...9.1.......45.6.....16..4.4.5.91.7.1.47.6...9..57...3.2........8......
2.8.......96..1...51....9.....73.8..8..6.2......4...5.62.9..51..85.6.2.9.......68
...78...3......1..2.3..6...1.54......24.5....63........52....314.1...5.636...542.
...64...8......2..9.8..5...2.31......91.3....85........39....8258...319.1.2...3.5
.........5.6.3..2993......1.591...632.36..91.16....2.5...9.4.......87..6..5......
.........6.5.8..4998......2.695...284.82..95.25....4.6...9.7.......31..5..6......
6.8..9...14.6.5....598..6...14...9.6.......37......42.86.95....4.1.......954.1.68
........4...72..3...2...8.19..56.....6.9.2.5.52..37.9...629....27.6.53.9....73...
........7...43..6...3...8.923..46.1..5.1.3.2.1..25......532....34.5.16.2....64...
........7...29..4...9...8.51..36.....6.1.9.3.39..24.1...691....92.6.34.1....42...
........8...25..3...5...7.615..32.4..9.4.5.1.4..19......951....52.9.43.1....23...
47....6.3.2.4..79.9..7...2473...49.2.42......6.9.72......6.7....9..51...36...8...
.....2.35...13.........6.987.....9.1.597.1.83...9.857..3.........7...3...15...8.9
9.1..68.4.38..4.1664....93....6.....8697.3...4..25....1........3.41...98..64.....
1.8...267...16.3..........9...4.5.....461......5.83.......316...835.64.16.184.5..
...6.2.8...3.84.5....53....5.824.....26..84..43........62....3.....2.1.9.......27
...7.9.3...8.32.6....68....6.392.....978.32..2.........79....8.....9.4.5.......91
..4.635....571.......5.4....1635....3.74.1..6....76.......3.6...73....82..1...39.
...1.82......437.88..72...1.8.3.4...4.5......369.......1728.3.4.48.31.72...4.....
58..962...9257.8..6.7......8.6...79.....6.3.1.........96..27...2.5.8.....78..5.2.
.......5.2.......8....79.23..298.53.....25.97..57.38.261.....7...3..7...4.7....89
....5726..5.36.4.7.6.2.4.358.1..3...67.......9...2..........7.3.....264...64...5.
2.....67....2.89.3........49.3.....5.62....3.85.........5.293..32.6.5...6.983....
....863.....3..72....4.....41.7..93.2.9....47.73...1.2.9..1..7..24....13........9
5.9...37....5..4.6......2......971..9..31.......8.5..3.579.1.3.3.178....89..53.1.
9.4...78....9..6.3......1......485..4..75.......2.9..7.984.7.5.7.582....24..95.7.
...1.38.5......72.......631...4.9...41.35..8..9..81...9..5.8..3.5.93...838..14...
......473......21.4.3...6.85.9.......84.39.6.36..5.....45.8...693..64...6.8..5..4
9.7......51.63....632........5.61.83...3.5..4...48.......8.3.65.5..46..1.6.15..4.
...7...4..653.9......28.....34....1.6.1.....459......6.56...1.314..3..95...15.4..
.......7548..752.6...6.284....25.4.8....64..7...7.86..13.......9.2........652....
8.9......31..57....57..9.31.3159......87.13...7..83....8.....4.....7.5..79.....62
.7....9.68.9..6....36....84..3.54......612......3...6..947..6.3...4..89..8.....47
......43..645...8939.8..5.6.4.385......416..5...972.64.53...94..8....6...........
.......6145..618.2...2.854....18.4.5....24..6...6.52..39.......7.8........281....
....16.5..1.25.....5.9.3.21....3.56.........9..269..13..4.......6.32....7.8....9.
2.3.571.....2.4...4..13.2...47.....353.74...11.2............5.27.5...4.9.......68

[denis_berthier]

Those too, I have as all in T3.
I applied a random relabeling to each of the puzzles.
Would you check whether they still come out as "T4" ?

Some of them become T3. I must investigate the reason why this happens. The abstract rules are obviously invariant. I have coded them in Clips in a way that should be invariant. There must be a subtle bug somewhere in the code.

[blue]

Ahh, progress
Good news.

[P.O.]

my results for cbg-000 are the same as blue with 0tp, which corresponds to the initialization for me, summing level 0 and level 1

Code: Select all

0tp: 11119
2tp:  1916
3tp:  6984
4tp:  1339
5tp:    17 : (109 2897 4671 5035 8146 9663 9977 10426 13514 13651 13841 14849
              15434 18340 18494 18843 19025)


my results for the 134 puzzles in te3:

Code: Select all

4tp:  18
5tp: 115
6tp:   1 : (26)