The New Sudoku Players' Forum

[Paquita]

I have the statistics for the lateral versus the tridagon blocks for different BxB

B7B
Lateral blocks
3 3
4 326
5 957
6 2670
7 1104
8 61
9 4
11 1
Tridagon blocks
8 1
11 1
12 1
13 9
14 64
15 450
16 1422
17 1645
18 968
19 407
20 116
21 38
22 4
Stats
5,92684354272337
16,947717518533
B8B
Lateral blocks
4 260
5 934
6 2494
7 1013
8 109
9 9
10 1
Tridagon blocks
14 47
15 344
16 1311
17 1737
18 1017
19 313
20 40
21 9
22 1
23 1
Stats
5,96016597510373
16,9315352697095
B9B
Lateral blocks
2 1
3 39
4 477
5 2464
6 3480
7 1463
8 248
9 3
Tridagon blocks
14 184
15 715
16 1991
17 2159
18 1695
19 937
20 420
21 61
22 5
23 8
Stats
5,80782874617737
17,1434862385321
B10B
Lateral blocks
3 9
4 619
5 2119
6 1861
7 561
8 20
Tridagon blocks
14 4
15 166
16 656
17 1223
18 1364
19 1039
20 543
21 171
22 23
Stats
5,46367315475043
17,9385238003469
B11B
Lateral blocks
3 2
4 120
5 654
6 861
7 45
8 3
9 3
Tridagon blocks
15 79
16 401
17 711
18 356
19 101
20 34
21 6
Stats
5,50236966824645
17,0740521327014
B12B
Lateral blocks
5 115
6 551
7 351
8 28
9 2
Tridagon blocks
13 2
14 6
15 160
16 482
17 296
18 99
19 2
Stats
6,28462273161414
16,3075453677173
B13B
Lateral blocks
4 8
5 113
6 307
7 162
Tridagon blocks
14 14
15 106
16 213
17 199
18 42
19 2
20 14
Stats
6,05593220338983
16,3576271186441
B14B
Lateral blocks
4 3
5 1
6 7
7 4
Tridagon blocks
15 3
16 7
17 2
19 1
20 2
Stats
5,8
16,6666666666667

Here, the suggestion is that B10B is the most extreme. This result is according to the fact that the B10B requires the largest calculation time of all BxB. Maybe B10B is the hardest?

[denis_berthier]

.
Hi Paquita,
It's interesting to see that :
- there are many more (necessarily non-tridagon) clues in the tridagon blocks than in the lateral blocks,
- there is some slight difference depending on the BxB value, with a lowest value in the lateral blocks at B10B.

It is natural to ask the question, but I don't know if this explains the longer computation times (that you independently noticed previously) for the BxB classif at x=10 . Do you see a reason why it could explain it? Taken out of the whole puzzle context, it may make these blocks harder to solve. But the validity of such reasoning is debatable.

Did you compute the above numbers of clues for the minimals or the min-expands?
.

[denis_berthier]

.
Now that you have all the data, there's one more computation you could do: is there any correlation
- between the number of clues in the two type of blocks ?
- between the number of clues in one of those tow types and the BxB classif for high x ?

(Once you have the data in separate files, CSP-Rules has the functions to do such calculations.)
.

[Paquita]

Denis,
This was calculated on the minimals. Previously I showed that the difference in clues between tridagon and lateral blocks is larger in the expands.

I am not sure what you mean with your question.
For all the high BxB I also wrote down "Stats" that is the average number of clues for the tridagon and lateral blocks, for that BxB.
Maybe you can use that to compute the correlation?

[Paquita]

Champagne collected 14451700 TH puzzles
of which 4.6 M are from mith (say that is the amount of T&E3)
so about 9851700 TH, T&E2 puzzles
high BxB are 26696, so 0.27%
We already know that the high BxB puzzles have SER/skfr rates of ED = 11.0 and above
We can also see now that for the higher ED rates the probability increases that a puzzles is high BxB

49 11.9
36 high BxB = 73%

5 : 7
6 : 6
7 : 13
8 : 2
10: 21

3156 11.8
1350 high = 42%

7 : 12
8 : 15
9 : 519
10 : 245
11 : 507
12 : 52


204745 11.7
14138 high= 6.9%

7 : 2753
8 : 2411
9 : 3660
10 : 3547
11 : 707
12 : 655
13 : 352
14 : 2


661294 11.6
9402 high= 1.4%

7 : 1447
8 : 2057
9 : 3810
10 : 1105
11 : 211
12 : 350
13 : 270
14 : 10


442784 11.5
187 high = 0.4%
7 : 70
8 : 34
9 : 75
10 : 0
11 : 0
12 : 4
13 : 0
14 : 0

[denis_berthier]

.
Stats about a super-collection assembled from totally different sources, each of them assembled according to largely undefined methods, don't mean much.

so about 9851700 TH, T&E2 puzzles
high BxB are 26696, so 0.27%

0.27% of largely biased collection.

We already know that the high BxB puzzles have SER/skfr rates of ED = 11.0 and above

I'm not sure of this; but anyway the point is, the converse is false. As I've shown very long ago, the correlation between SER and BxB is weak.
.

[Paquita]

I am not saying there is a direct relation between BxB and SER or that the one could be translated into the other.
Both represent very different ways to solve a puzzle.
I am merely showing that a puzzle that rates high on one system, has a good chance that it shows high on the other system as well.
Where of course there are many more high SER than high BxB TH puzzles.
All BxB puzzles have a high SER rate, but not all high SER rated puzzles have a high BxB rate. However, the higher the SER rate, the more the chance that it has a high BxB rate

[denis_berthier]

Hi Paquita,

For all the high BxB I also wrote down "Stats" that is the average number of clues for the tridagon and lateral blocks, for that BxB.
Maybe you can use that to compute the correlation?

One can't compute correlations using only the mean values. One needs the full data sequences. As you already have them, I thought you could easily do the computations, using the elementary stat functions in CSP-Rules (the only requirement is to have the values in separate files).

Example: you have a file containing nb-clues-trid and a file containing nb-clues-lateral. Then you can compute the correlation as:

Code: Select all

(correlation-coefficient
     nb-clues-trid
     nb-clues-lateral
     <nb-clues-trid-file>
     <nb-clues-lateral-file>
     <common file length>
)

.

[Paquita]

Hi Denis

Yes I get a result from CSP rules. Do you want one overall correlation or by BxB? I could not find the command to redirect the output to a file in CSP.
I calculated it for B7B :

E(nb-clues-trid) = 5.92523911770447
E(nb-clues-lateral) = 16.9515908647277
Sigma(nb-clues-trid) = 0.842735034800345
Sigma(nb-clues-lateral) = 1.27116050165731
correlation-coefficient(nb-clues-trid, nb-clues-lateral) = -0.327903368774359
regression nb-clues-lateral = a * nb-clues-trid + b
a = -0.494601260816318
b = 19.8822216029825

[denis_berthier]

I could not find the command to redirect the output to a file in CSP.

Such results don't need to be redirected to a file.

Yes I get a result from CSP rules. Do you want one overall correlation or by BxB?

I think it would be more interesting globally.

I calculated it for B7B :
E(nb-clues-trid) = 5.92523911770447
E(nb-clues-lateral) = 16.9515908647277...
correlation-coefficient(nb-clues-trid, nb-clues-lateral) = -0.327903368774359

Are you sure you didn't mix up the two files? The means should be exchanged.
Correlation is negative, as expected. But too small to be meaningful.

Other correlations you could check are with the total nb of clues:
nb-clues-total vs nb-clues-trid (this should be high)
nb-clues-total vs nb-clues-lateral
.

[hendrik_monard]

414 solutions of the puzzles in de list(s) published by paquita on February 22nd are new. 85 of them are solutions of puzzles from Champagne's list.
These 414 new solutions, bringing the total number of solutions of puzzles with x >= 7 to 2473, have been added to the list of solutions available here:
https://drive.google.com/file/d/1gLUBdAcdF9ntMiS_bc7Z_AEAu7XfhOnQ/view?usp=drive_link
.

[hendrik_monard]

After some twinning based operations performed on puzzles from the lists recently published by paquita, another 55 new solutions appeared.

Hidden Text: Show

Code: Select all

.234..78.45.7...237.82..5.42.....87.38...2.45......3.25..8.....8..591.......27458   7
12..567...5678.1..7.81.25..21.5......8762....6...........8..23487.....51......8..   7
12..567...5678.1..7.81.25..2.....894......2.....27..51...6.....5..81....68..27...   7
..3.567.9..67.9.32..923.56.....65.9.....7.......3.2.75..5....2.69.5.3...84.....5.   7
12..567...5678.1..7.81.25..21.5......8762....6...........2...34.72....51...8..2..   7
.234..78.45.7...237.82..5.42.....87.38...2.45......3.25..891...8..5.........27458   7
..34...89....8923...93.21.4.......4.564...92..38294...31.84..92...9.3.1.....21...   7
...4.6.8.45.1.9........3.4.24.9..51...15...929.52..4.8.14.9285.59.....2.8.2..5...   7
1...567.9...1.9.366..37.15..1659.37........65...6..9.13.1...5...84......9..7.....   8
...4.678.....8.2.6...72..45......57.3........9.5.7......48.762...6.42.58..256.4.7   8
...4.678.4..18..366...731.4.6.347...3.9......7.5.....3...8.1.......34..1.1476.3.8   8
.23.56..945...9...6.9......29.53..4.3.56.4.9..46.92.3..32...9.4.....5.2......31.8   8
12..56..9.571.9..66.927...12.....8.7......4.2...76291.5.2.1769....9.5...9..62....   8
1...56......18....68.7.2..52.65.8...51..27.6..7861.......871.2.7.....3..8.....97.   8
12..567...5678.1..7.81.25...8156....57.2.8...6...17......82....8.....23........4.   8
....5..89...18.23.......1.52.4......395...8.2.6...........9.32.8..53..919..2.15.8   9
...45.7.9...1.9..3.....751.2.........48.....5.3..45....1..94.57.9.37.4.1.7.5.139.   9
...45.7.9...1.9..3.....751.2.........48.....5.3..45....9..74.51.1.39.4.7.7.5.139.   9
1.3.5678..57.8....68...........1.9..516....73.......2137.8.1..5.61.75.....5.3...7   9
1.3.5678..57.8....68...........1.9..516....73.......2137...1..58.5.3...7.61.75...   9
12...67...571.92..6.927.1....6....73....6792...5...64...1.2.....62.95.1......1..2   9
1.3..67.9.57..9.3669...315...5.41.......9731...183.....19.6.57...6...9.....9...6.   9
12..56.89.5....2.6......15.28.5...9..619..5.8.......12...8.5921.1.294.....2.7....   9
1.3..678..57....3686...71.5.357...186.8.....771....5.....9.....5816.3.......4....   9
1.3..678..57....3668...31.5..6...3.8.186...577.....61.....2.......9........3.5871   9
12..567...5718.2..8.67.25...6....89.......6.3...62..75.7.8.5....1826........1....   9
1.3..67.9.57..9.3669...75......45......8.1...51697....73........6579.1.39.1.....7   9
1.3456...4.7......69....4.....61.54....5.38.......4...3..8.5.645...413.8...36.15.   9
..3.56....5718....68.7.3..5..16.8...83..71.6..7653..........4.....817..3.......9.   10
..3.56....5718....68.7.3..5..16.8...83..17.6..7653..........4.....871..3.......9.   10
1......8..5....2.66.9...15......4......6..81..1.83.....615..92.59.2...688.29..5.1   10
1.....7.9.571.9..669.7.315......4......8.........613755...1..6.73....51...1...9..   10
..3.567.9..71.9.36..937.51....96..71.....39......17..5..6....5..4.......8.1......   10
.23...7..45....2.3..8....4.23...4.788.5..34.2.74..853......5..7....9.......6.2...   10
..3.567.9..71.9.36..637.51.2.........85........9.1........9...7....3569......1.53   10
.23...7..45....2.3..8.....52.4..35.887...4.32.35..847......5..7....9.......6.2...   10
.2.45..89.5..8923..9.3.24.5.3.....4.7.........81.........9.58.4...82.39......3.5.   10
.2....78.4.7...2.668.....54.7.3.5.......9.........4..5.48..2.6756...842.7.2...5.8   10
.2..56...45......6..8.........63...1....15.72...2.736..3..621.7...3.165..1.57..23   10
12..567...5.1.92..6.927.5......97....7.5.1...91.62...7.6......8......64.....62175   11
1...56.8....18..3.86.7...5.......47.....7...2.78...3155.1.3....78.61...3.36......   11
....5..89...18.2.3......1..2.4.......6.......895...3213..2.591.5..89..329...318.5   11
1..45.7.94..7.913.7...13.54...9.53.7...1..49.........53.2.......6.......941...573   11
12..567...5718.2..8.67.21........64.678...5.1...6..8.3..2......5.12.....78.56..12   11
12.4.67.....18....8...72...2......43...2648.7......52..8164..7.64..27...7.28.1.6.   11
...45..89.5..8932..8.3.24.5....3..988..92.54.......2.33.8...954.41.9....79.......   11
12..567...5678.1..7.81.2...21.5......8762....6.5............8.487.....51...8..23.   11
12..567...5678.1..7.81.2...2.....89.......2.4...27..51...6.5...5..81....68..27...   11
..3.567.9..67.9.32...23.56.....65.9....97.......3.2.75.42....5.69.523...8.5....2.   11
12..567...5678.1..7.81.2...21.5......8762....6.5.........8..2.4872....51...2..83.   11
.234..78.45.7...237.8...5.42.....87.38.....45......3.25..8.1...8..59........27458   11
.234..78.45.7...237.8...5.42.....87.38.....45......3.25..89....8..5.1.......27458   11
1..45.7.94..7.913.7...13.45...9.53.7...1..49..........3.2.......6.......941....73   11
...45..89.5..89..3.8.3.2.5....89..34...2.4.......35.2.53.948...74........96......   11
.2..56......78.123...2.1...24...837..8.....4.....4.8..37.....188.41..2.7.128..43.   12

These puzzles and their (new) solutions will be added to the database (see link in my previous message)

[denis_berthier]

.
Hi Hendrik

Nice to see you here again.
Good to see the list continues growing.
Have you checked how many grids are common with the T&E(3) solution grids? I guess the percentage remains very low.
.

[Paquita]

E(nb-clues-trid) = 17.1603237342368
E(nb-clues-lateral) = 5.79288537549406
Sigma(nb-clues-trid) = 1.3594124850027
Sigma(nb-clues-lateral) = 0.879626037782845
correlation-coefficient(nb-clues-trid, nb-clues-lateral) = -0.476705178234256
regression nb-clues-lateral = a * nb-clues-trid + b
a = -0.308458464040022
b = 11.0861324769863

E(nb-clues-total) = 27.9090156220591
E(nb-clues-trid) = 17.1603237342368
Sigma(nb-clues-total) = 1.06196304523874
Sigma(nb-clues-trid) = 1.3594124850027
correlation-coefficient(nb-clues-total, nb-clues-trid) = 0.541545191206916
regression nb-clues-trid = a * nb-clues-total + b
a = 0.693228730905942
b = -2.18700774627736

E(nb-clues-total) = 27.9090156220591
E(nb-clues-lateral) = 5.79288537549406
Sigma(nb-clues-total) = 1.06196304523874
Sigma(nb-clues-lateral) = 0.879626037782845
correlation-coefficient(nb-clues-total, nb-clues-lateral) = 0.506707719130801
regression nb-clues-lateral = a * nb-clues-total + b
a = 0.0419706980663164
b = 4.62152450749251


The average total clues number is high

[denis_berthier]

E(nb-clues-trid) = 17.1603237342368
E(nb-clues-lateral) = 5.79288537549406
correlation-coefficient(nb-clues-trid, nb-clues-lateral) = -0.476705178234256

E(nb-clues-total) = 27.9090156220591
E(nb-clues-trid) = 17.1603237342368
correlation-coefficient(nb-clues-total, nb-clues-trid) = 0.541545191206916

E(nb-clues-total) = 27.9090156220591
E(nb-clues-lateral) = 5.79288537549406
correlation-coefficient(nb-clues-total, nb-clues-lateral) = 0.506707719130801

The average total clues number is high

Yes. Minimal puzzles in T&E(3) or in T&E(2) with high BxB tend to have more clues (at the start) than the mean number for all minimals. I had stats about that in Table 3.1 of [HCCS2, 2024].
That's why I asked about the last two calculations.
Both correlations are positive and almost equal, which means that extra clues have no preference for falling on either the tridagon or the lateral cells.
I expected a higher value for correlation-coefficient(nb-clues-total, nb-clues-trid). But it seems there's no meaningful correlation.
I had no expectation for correlation-coefficient(nb-clues-total, nb-clues-lateral).

Note that (- 27.91 17.16 5.79 ) = 4.96 clues in the mean in the block opposite the tridagon (less than in a tridagon block but much more than in a lateral block).
This suggests a higher part of the extra clues might tend to fall in the opposite block. You could check if this is true by doing a last correlation calculation: nb-clues-total vs nb-clues-oppos.
(This supposes you create a new file for the nb-clues-oppos.)
.