The New Sudoku Players' Forum

[champagne]

No reason to have a correlation here, nut no reason to deny the possibility to have one.

As I have to improve the process to scan millions of solution grids (filtering the tridagon finder output to clean most of the low ratings), a big task, I'll do the test. Keeping all rating over 11.5 for example should not pass some hundreds of solution grids.

[denis_berthier]

.
Maybe a simpler question.
Suppose you filter all the complete solution grids in several stages:
- first stage: does it have a solution tridagon? From my calculations, we already know that ~50% will pass this stage and that, in the T&E(3) domain, we'll miss ~15-20% grids that may have minimal puzzles with a non-degenerate tridagon;
- second stage for a grid having passed the first: does it have at least one minimal puzzle with a non-degenerate tridagon. At this point already, it seems we don't know the answer about the proportion that pass the test (at least, I'ven't seen any answer).
- third stage for a grid having passed the second one: does it have at least one minimal puzzle with a non-degenerate tridagon AND sufficiently hard (e.g. at least in T&E(2) or with at least SER 11.x - choose x as you like). Here also, it seems we have no answer - because the answer is intractable.

Anything to add about the above 3 points?

[Edit]: do you have an easy way of extracting a complete grid by its number in the full list of 5472730538 non-iso ones? If so, I can provide a list of 1,000 or 10,000 random digits in the [1 5472730538] range, so that we can have a fully random set of complete grids for further computations.
.
.

[champagne]

Most of the answer to your point are given with many details in this thread
http://forum.enjoysudoku.com/non-degenerated-tridagon-puzzles-direct-search-t45331.html

Your example gave a very small number of minimal puzzles <= 27 clues. In many cases, I got many more.

One remark : a solution grid can have several "magic square" here an example for the grid rank 132808

267983154938415762541726398123564879789231546456897213612379485895142637374658921;132808
514839276672154983938267514123978465789645132456312798367421859291586347845793621;132808
367895124291374685845612397789123546123456879456789213938541762672938451514267938;132808
214958637865743921937126485123897546456231879789564213541389762398672154672415398;132808

I started the test on your previous idea.
I took in my data base of potential hardest all the rating >= 10.2

This gave me 26653 different solution grids and I did not see one matching mith's file.
I expect to have next hour the list of possible magic squares , likely in the range 20000/40000

If these starts are as rich as usual, I'll have to process them by chunks of 1000/2000 starts

[denis_berthier]

Most of the answer to your point are given with many details in this thread
http://forum.enjoysudoku.com/non-degenerated-tridagon-puzzles-direct-search-t45331.html

I had a quick look. Not the slightest suggestion that 50% of the grids have a "solution tridagon".
So my main question remains. How is this pre-filter supposed to help the search for tridagons (except by reducing it by a factor ~2 wrt to all the grids)?

[champagne]

Most of the answer to your point are given with many details in this thread
http://forum.enjoysudoku.com/non-degenerated-tridagon-puzzles-direct-search-t45331.html

I had a quick look. Not the slightest suggestion that 50% of the grids have a "solution tridagon".
So my main question remains. How is this pre-filter supposed to help the search for tridagons (except by reducing it by a factor ~2 wrt to all the grids)?

This "prefilter" is never used in my process.
Each solution grid is first searched to produce the possible starts morphing the solution grid to have the "magic square" in the canonical form in boxes 5689.

This is not at all a critical part of the code. Here, it took 25 mn to process the 26653 solution grids to get 18574 starts.
I did not check how many solution grids are in this file.

The main process has been started and as I feared, some chunks of 1000 starts are producing output files over 10 GB. (max current is 15 GB not yet closed.
(1GB as output of the finder for a chunk of 1000 starts is ~12 000 puzzles in average per start)

[denis_berthier]

This "prefilter" is never used in my process.
Each solution grid is first searched to produce the possible starts morphing the solution grid to have the "magic square" in the canonical form in boxes 5689.
This is not at all a critical part of the code. Here, it took 25 mn to process the 26653 solution grids to get 18574 starts.
I did not check how many solution grids are in this file.

From "26653 solution grids" to "18574 starts". If that's not a pre-filter, I don't know how to call it. You may have several "starts"/"magic squares"/"solution tridagons" per grid, but you have fewer grids at the end than at the start - fortunately.

But I agree that it's not the critical part - unfortunately.
.

[blue]

.
Maybe a simpler question.
Suppose you filter all the complete solution grids in several stages:
- first stage: does it have a solution tridagon? From my calculations, we already know that ~50% will pass this stage and that, in the T&E(3) domain, we'll miss ~15-20% grids that may have minimal puzzles with a non-degenerate tridagon;
- second stage for a grid having passed the first: does it have at least one minimal puzzle with a non-degenerate tridagon. At this point already, it seems we don't know the answer about the proportion that pass the test (at least, I'ven't seen any answer).
- third stage for a grid having passed the second one: does it have at least one minimal puzzle with a non-degenerate tridagon AND sufficiently hard (e.g. at least in T&E(2) or with at least SER 11.x - choose x as you like). Here also, it seems we have no answer - because the answer is intractable.

Anything to add about the above 3 points?

One remark : a solution grid can have several "magic square" here an example for the grid rank 132808

267983154938415762541726398123564879789231546456897213612379485895142637374658921;132808
514839276672154983938267514123978465789645132456312798367421859291586347845793621;132808
367895124291374685845612397789123546123456879456789213938541762672938451514267938;132808
214958637865743921937126485123897546456231879789564213541389762398672154672415398;132808

To answer the "second stage" question ...

Here is an example of a "maximal" puzzle with a non-degenerate tridagon with one true guardian.

Code: Select all

+----------------+---------------+-------------+
| 4     5    123 | 123  6    7   | 123  8    9 |
| 8     123  7   | 9    123  4   | 123  5    6 |
| 1239  123  6   | 5    8    123 | 4    123  7 |
+----------------+---------------+-------------+
| 123   4    5   | 123  7    9   | 6    123  8 |
| 7     123  8   | 6    123  5   | 9    123  4 |
| 6     9    123 | 8    4    123 | 123  7    5 |
+----------------+---------------+-------------+
| 12    8    9   | 12   5    6   | 7    4    3 |
| 23    6    4   | 7    23   8   | 5    9    1 |
| 5     7    13  | 4    9    13  | 8    6    2 |
+----------------+---------------+-------------+

There are 2,968,332,766 puzzles like that, on 1,807,371,808 solution grids.
Any minimal puzzle with a non-degenerate tridagon with one true guardian, is (isomorphic to) a minimized version of one of the "maximals".

Aside: Displaying the "maximal" puzzle above, as a pencilmark diagram, was a little misleading.
Most of the puzzles have a one or two naked singles for tridagon digits, in boxes 3,6,7 or 8.
I had to go through a few of them before I found one that was suitable.

---

Trivia: 18 of the grids, have 24 maximal puzzles. None have more than 24.
The breakdown by "puzzles per grid", looks like this:

Code: Select all

 Np |      Grids |    Puzzles
----+------------+-----------
 24 |         18 |        432
 22 |          7 |        154
 21 |          1 |         21
 20 |        210 |       4200
 19 |         12 |        228
 18 |        184 |       3312
 17 |         85 |       1445
 16 |        595 |       9520
 15 |        463 |       6945
 14 |       1929 |      27006
 13 |       4061 |      52793
 12 |      12593 |     151116
 11 |      27669 |     304359
 10 |      80662 |     806620
  9 |     240572 |    2165148
  8 |     762245 |    6097960
  7 |    2070808 |   14495656
  6 |    7473886 |   44843316
  5 |   22319557 |  111597785
  4 |   71818891 |  287275564
  3 |  135488290 |  406464870
  2 |  526955246 | 1053910492
  1 | 1040113824 | 1040113824
----+------------+-----------
    | 1807371808 | 2968332766


Here are the puzzles for one of the "24-puzzle" grids:

Code: Select all

.234.678.4.678..2378..234.623...76.8.6483..728.72643..3.2978.646783452...4.612837 (159)
.234.678.4.678..2378..234.623...7648.6483..728.72.43..3.2.7856467834.291.4.6.2837 (159)
.234.678.4.678..2378..234.623...7648.6483.9728.72643153.2.78.6467.34.2...4.6.2837 (159)
.234.678.4.678..2378..234.6231..764856483..728972643..3.2.78.6467834.2...4.6.283. (159)
.2345.7.945.7.9.237.9.2345.23.59..4.5.4.3.972.972.43.53.297.564.7.345291945..2837 (168)
.2345.7.945.7.9.237.9.2345.23.597.4.5.4.3..72.972.43.53.29785.4.7.34529.945612.37 (168)
.2345.7.945.7.9.237.9.2345.23.597.4.5.4831972.972643.53.297.5.4.7.34529.94...2.37 (168)
.2345.7.945.7.9.237.9.2345.231597.4.564.3.9728972.43.53.297.5.4.7.3.529.945..2.37 (168)
1.3.5678..5678.1.378.1.3.56.315.76.856.83..7.8.7.6.31531..785646783.5291..561.837 (249)
1.3.5678..5678.1.378.1.3.56.315.76.856.831.7.8.7.6..1531.97856.678345..1..5612837 (249)
1.3.5678..5678.1.378.1.3.56.315.764856.8319728.7.6.31531..7856.6.83.5..1..561.837 (249)
1.3.5678..5678.1.378.1.3.562315.76.8564831.7.897.6.31531..7856.6783.5..1..561..37 (249)
1.345..8945..891.3.891.345..3159..485.48.19..89...431531.9.8564..8345291945.1.837 (267)
1.345..8945..891.3.891.345..3159..485.48319..89...43.531.9785.4..8345.9194561283. (267)
1.345..8945..891.3.891.345..31597.485.48319..89.26431531.9.85.4..8345.919.5.1.83. (267)
1.345..8945..891.3.891.345.23159..485648319..897..431531.9.85.4..834..91945.1.83. (267)
12..567.9.567.912.7.912..562.15.76..56...1972.9726..15.1297.56467...52919.5612837 (348)
12..567.9.567.912.7.912..562.15976..56...19.2.9726..15.1297856.67.3452919.5612..7 (348)
12..567.9.567.912.7.912..562.15976..56.831972.97264.15.1297.56.67...5.919.5612..7 (348)
12..567.9.567.912.7.912..562.159764856...1972.9726.315.1297.56.67...52919.56.2..7 (348)
12.4.6.894.6.8912..8912.4.62.1.9..48.648.19.289.264.1..12978.646.834529194.6128.. (357)
12.4.6.894.6.8912..8912.4.62.1.9.648.648.19.289.26..1..129.85646.8.4.29194.612837 (357)
12.4.6.894.6.8912..8912.4.62.1.9.648.648.197289.264315.129.8.646.8.4.29194.61.8.. (357)
12.4.6.894.6.8912..8912.4.62.1597648.648319.289.264.1..129.8.646.8.4.29.94.6128.. (357)

[denis_berthier]

To answer the "second stage" question ...
[...]
There are 2,968,332,766 puzzles like that, on 1,807,371,808 solution grids.
Any minimal puzzle with a non-degenerate tridagon with one true guardian, is (isomorphic to) a minimized version of one of the "maximals".

It's a step forward but still far from an answer to the 2nd question.
The hardest step in it remains: find a minimal puzzle with a non-degenerate tridagon. As you noted, most "maximal" puzzles in the 24 example are solved with singles, before any tridagon can appear.
This suggests one has to put more stringent conditions (I.e. passing stage 2 may still be of little practical interest in the search of hard puzzles having a tridagon).
.

[champagne]

There are 2,968,332,766 puzzles like that, on 1,807,371,808 solution grids.
Any minimal puzzle with a non-degenerate tridagon with one true guardian, is (isomorphic to) a minimized version of one of the "maximals".

Hi blue,

If I got it, 1,807,371,808 out of the 5 472 730 538 can deliver non-degenerate tridagon with one true guardian. It is about 1/3 of the solution grids, but I know that a potential start is not enough to produce such puzzles.

BTW, I have a bug in the starts builder, some of my starts don't have the expected square.
And I would agree that adding the appropriate clues, any such puzzle ends in one of your maximal list.

unhappily, as a first reaction, I don't see how this cant help to find hardest such puzzles. The Graal would be another "loki".

In the current test, the "non-degenerate tridagon" finder will produce about 300 GB of grids with <=27 clues, in about 30 hours.
But just filtering the results by the T&E(1) filter is 6/7 times longer and the final rating is worst.
The first results don't show better ratings than in other tests for these solution grids having puzzles with high ratings

[blue]

unhappily, as a first reaction, I don't see how this cant help to find hardest such puzzles. The Graal would be another "loki".

No it won't help.
I ran the numbers shortly after you started the other thread: http://forum.enjoysudoku.com/non-degenerated-tridagon-puzzles-direct-search-t45331.html
I was curious about how many "starts" there are, and on how many solution grids, and about what percentage of the whole, is represented in mith's big list.

EDIT Asssuming that a tridagon pattern in the solution is the following

Code: Select all

..x x..
.x. .x.
x.. ..x

x.. x--
.x. -x-
..x --.

where the last digit on the pattern in the last box is anywhere but not in the last cell

Nothing to add to this,
this is by far the most common final status in mith's file

I counted these too:

Code: Select all

..x x..
.x. .x.
x.. ..x

x.. x--
.x. -.-
..x --x

mith's list has 2,113,220 puzzles of the first type, over 28026 "starts", and 1,629,623 puzzles of the 2nd type, over 19937 "starts".
FWIW: By big list, has 2,146,660,838 "starts" of the first type (on 1,508,823,488 solution grids), and 821,671,928 of the 2nd type (on 744,278,570 solution grids).
The grid that I listed 24 puzzles/"starts" for, has 17 of first type, and 7 of the 2nd.

[champagne]

Code: Select all

..x x..
.x. .x.
x.. ..x

x.. x--
.x. -x-
..x --.

I counted these too:

Code: Select all

..x x..
.x. .x.
x.. ..x

x.. x--
.x. -.-
..x --x

You are right as usual. the 2 patterns are not isomorphic.
In fact, when I have the right pattern in the boxes 1,2,3, I test the permutations on the main diagonal in box 3 to reach 2 digits in the main diagonal in box 4, so I should catch both, but I have to check.

I also made a test to see which bands could produce the boxes 1,2 pattern

Code: Select all

..x x..
.x. .x.
x.. ..x

I was surprised to see that many bands have no such pattern (band 0 has 18 starts). As this is not in the critical area, I did not do more.

[champagne]

Some results for grids having less then 32 clues after a first set of rules, this is an attempt to find good starts limiting the full rating to grids with a good potential for the T&E(3) field.
As far as I can see, this is very similar to other tests, some good seeds, but the best in the range 11.0 11.2.
I started the rating of all grids passing T&E(1), but this is a longer task

Hidden Text: Show

Code: Select all

 
.94.8....3..1.........5..8....56..13...8.76.5....3187...7.15.3....6.87.....37.56.;10.9/10.3/2.6
.94.8...63..1.........5..8....56..13...8.76.5....3187...7.15.3....6.87.....37.56.;10.9/10.3/2.6
.94......3..1.........5..8....56..13...8.76.5....3187..67.15.3....6.87.1...37.56.;10.9/10.3/3.4
.94.8....3..1.........5..8....56..13...8.76.5....3187...7.15.3....6.87.1...37.56.;10.9/10.3/3.4
..2.......1.....8..9....7.....62..47...4.38.6..4.8723.....46.787..3.26.4..687.3..;10.9/10.4/2.6
.94.8....3..1.........5..8....56..13...8.76.5..6.3187...7.15.3....6.87.....37.56.;10.9/10.4/2.6
.94.8....3..1.6.......5..8....56..13...8.76.5....3187...7.15.3....6.87.....37.56.;10.9/10.4/2.6
.7.........6.....28......5....97..23...3.24.5.2..4579.....53....3.2.45.94..79.23.;10.9/10.5/10.0
........1143...5....81......8.21..65.569.81.2..1...89.....92.....25.19.6...68.2..;10.9/10.5/2.8
....79...2..........8.......5.79..31.3.1.59.6....6357.9...37.6..6.9.13.7...65.19.;10.9/10.6/8.9
9....5.....8...6.5..4.........79..313..5.19.6..9.6357.....37......1.63.77..95.16.;10.9/10.8/10.4
....9...1.73............8..2..15..68.186.92.5....2891.....65......2.1..6.5698.12.;10.9/10.9/10.1
.....5.6...8.1.....2....3..7..69..15...1.39.7....5763...5.61.73...7.9..6...53.19.;10.9/10.9/10.2
..3..4....5..9....6.........1.27..497.24.91.5....1572.....42......9.75.4.7.15.29.;10.9/10.9/10.5
..1....4..5...49..8......2....79..32...4.57.9..9.3245..2..59.7....3.72.....24.39.;10.9/10.9/2.6
.63....2.21.........52........32..97...9.75.4..9.5423...4.32.79...7.54.2...49....;10.9/10.9/2.6
.9........78...4..6........5..23..97.3.9.75.4....5423.....79.23.2.4.37.5...52..4.;10.9/10.9/2.6
.9461..7..1...........5...1...78..56...1..3.7....3.18...5.61..8...8.37.5..857.61.;10.9/10.9/2.6
29..67............5.4.........72..511..6.57.8....1826.....56.177..1.28.5...87....;10.9/10.9/2.6
.6.............2..71...4.....398..548..4.53.2....3298.....58.2.5..2.94.8...34.59.;10.9/10.9/2.8
.6..9.............71...4.....398..548..4.53.2....3298.....58.2....2.94.8.8.34.59.;10.9/10.9/2.8
........1.43.6.5....8.......8921..65.5....1.2..1.5689.....92.....25.19.69..68.2..;10.9/10.9/3.4
5.......4...8.3....9.........348..62...2.73.8..8.3647.....68.4....7.42.64..32.78.;10.9/10.9/3.4
6..7..4....1.....3.9..........87..64.643.28.77.....23...6.87.4....4.37.6...62.38.;10.9/10.9/3.4
8.6...4....3.4.5...4......9..279..45..94.53.2....2397.....74......5.92.4...23.7..;10.9/10.9/3.4
9...1......8.....5..46.......679..313..5.19.6....6357...1.37......1.6...7.395.16.;10.9/10.9/3.4
9...1......8.....5..46......5.79..313..5.19.6....6357...1.37......1.6...7.395.16.;10.9/10.9/3.4
..7.....114....5....81......8.21..65.569.81.2..1...89.....92.....25.19.6...68.2..;10.9/9.3/2.6
..5...7.2....78....71.......6432..87...8.76.4....6432...8.42...4..7.3...3..68....;11.0/10.2/2.6
.3....2...67...........5......89..121..5.48.9....2145...4.52.81.1.9.8..4..8...92.;11.0/10.2/3.4
.3....2...672..........5......89..121..5.48.9....2145...4.52.81.1.9.8..4..8...92.;11.0/10.2/3.4
.31...2...67...........5......89..121..5.48.9....2145...4.52.81.1.9.8..4......92.;11.0/10.3/2.6
4......7...9...2....1.........87..26...2.34.7....4683.....27.6..6.3.47.2.2.68.34.;11.0/10.4/3.4
....6.7..3.4.......9..........65..21..62.19.7.2..9765...2.15.6....7.61.2...92.57.;11.0/10.5/10.4
......2...9...4...6.1.........83..54.5.4.29.8..8.5932..8..45.32...9.84.55..32....;11.0/10.5/2.6
19..............2.36.8.7......46..32...7.86.4....3278.....84.73..43.62.8...27.4..;11.0/10.5/2.6
.........63.1.......5.2.7.....91..74...7.52.1..1.4259.4...91..21..5.49.7...27....;11.0/10.7/3.4
37...1...............9....2...12..54...4.58.9....9821...5.49.28..85.24.12..81..9.;11.0/11.0/10.2
..5.2..3..21.....46...........54..98.8.2.34.5....8932.....52.43...4.8..9...39.85.;11.0/11.0/10.3
..3..4....5..9....6.........1.27..497..4.91.5....1572.....42.7....9.75.4.7.15.29.;11.0/11.0/10.4
9..........8...6.5..4...7...5.79..313..5.19.6....6357.....37......1.63.77..95.16.;11.0/11.0/10.4
9....5.....8...6.5..4.........79..313..5.19.6....6357.....37.5....1.63.77..95.16.;11.0/11.0/10.4
....1.....3.6.....54....2.....28..36..31.78.2....6317.37..26.8....8.1.....873.62.;11.0/11.0/2.6
...1.....47..8.....6..........54..89...8.91.3.8..1345.....38..13..9.15.8..845.93.;11.0/11.0/2.6
..1....3.2.4.8.....7.9........89..45...4.53.2....3289.5...49.23...2.85.4...35.9..;11.0/11.0/2.6
..1....3.8.6..4......7........54..23...3.27.9....7945..9..53.42...9.73.5..542.9..;11.0/11.0/2.6
..3..4....5.......7......6.26.41..38..13.82.6......14.....41.83...2.36.1...68..2.;11.0/11.0/2.6
..3.64....5.......7........26.41..38..13.82.6....2614.....41.83...2.36.1...68..2.;11.0/11.0/2.6
..6......3..4......5...1.....219..858..5.42.9.9..8241.....45.21...9.8..4...21.89.;11.0/11.0/2.6
..7.2.9.....7.....8.3.1.7.....95..16.6.1.72.9.1..6257.....96.2....2.1......57.19.;11.0/11.0/2.6
..9.3..5......9..186..5.3.9..491..75...7.54.3....4319..5..91.3......4..7....7..1.;11.0/11.0/2.6
..965....1.........4.........279..53...3.62.7....2596..5..73.9..3.5.97.6...26.53.;11.0/11.0/2.6
.1....3.2..........672..9....9....2354.3.27.9....7945.....25.34...9.42.7...73..9.;11.0/11.0/2.6
.31...2...67...........5......89..121..5.48.9....2145..94.52.81.1.9.8..4......92.;11.0/11.0/2.6
.6.......8.46..........1...6..79..25...1.69.7.9..2516...2.69.51..95.7.....621.7..;11.0/11.0/2.6
.63....2..1.........52........32..97...9.75.4..9.5423...4.32.79...7.54.2...49....;11.0/11.0/2.6
.63....2..1.........52........32..97...9.75.4..9.5423...4.32.79...7.54.2.2.49....;11.0/11.0/2.6
.63....2..1....9....52........32..97...9.75.4..9.5423...4.32.79...7.54.2...49....;11.0/11.0/2.6
.63..9.2..1....9....5.........32..97...9.75.4..9.5423...4.32.79...7.54.2...49....;11.0/11.0/2.6
.7.......8........3..6.7.1....19..52.9.7.51.6....6297.....79.65...5.62.1..621..9.;11.0/11.0/2.6
.8.6.4...1..........5.........46..373..7.89.4.7..9386.....76.98..78.94.3.9.34....;11.0/11.0/2.6
19..............2..658........46..32...7.86.4....3278.....84.73..43.62.8...27.4..;11.0/11.0/2.6
2..3...........1..9.8167......51..37..76.38.1....7856.....36......7.1...3.685.71.;11.0/11.0/2.6
4.62...7.......213............75...8..83.21.7....185..........23.28.57.1..712.38.;11.0/11.0/2.6
51.....4......6.....3........489..12.8.2.16.4....6498.....12.98.2.6.94.1...48.2..;11.0/11.0/2.6
8.3..........7.....4.......7..21..65..65.71.81...6827.....85..7...7.68.2...12.65.;11.0/11.0/2.6
8.36.........7.....4.......7..21..65..65.71.81...6827.....85..7...7.68.2...12.65.;11.0/11.0/2.6
..1...2.8.4.8....5.....5.....623..877..5.63.2.2..8765.....58.2....7.2..3...36..7.;11.0/11.0/2.8
9.4..5.7.......6...2..7..5...325..872..3.75.6....6832.7...32.65.....6..8....8..3.;11.0/11.0/2.8
..........62..93...1.52.......89..45...3.29.8....4523..4........892.45.33..95.48.;11.0/11.0/3.4
..91......2.......5....8..........153..5.68.44...8136..64.53..1...8.46.3.3.61.54.;11.0/11.0/3.4
.1.......3.4..2.....7.....6..965..21..62.19.7....9765.....15.6....7.61.2...92.57.;11.0/11.0/3.4
.2..8.....5.3.1...8.........8.7...94.794.81.3.....987.73..94....4.8.39.7..817....;11.0/11.0/3.4
.3....2...67...........5......89..121..5.48.9....2145..94.52.81.1.9.8..4..8...92.;11.0/11.0/3.4
.9.........8......2.13....4.8.23..46...8.73.2....6487...6.42......6.34.73..78.26.;11.0/11.0/3.4
.9.........8......2.13....4.8.23..46...8.73.2....6487..7..42......6.34.73..78.26.;11.0/11.0/3.4
.9.........8..6...2.1.....4.8.23..46...8.73.2....6487...6.42......6.34.73..78.26.;11.0/11.0/3.4
.9.4.......8......2.1.....4.8.23..46...8.73.2....6487...6.42......6.34.73..78.26.;11.0/11.0/3.4
.9.4.......8......2.1.....4.8.23..46...8.73.2....6487..7..42......6.34.73..78.26.;11.0/11.0/3.4
2..3...........1..9.81.7......51..37..76.38.1....7856.....36......7.1...3.685.71.;11.0/11.0/3.4
4......7...9...2....1......3..87..26...2.34.7....4683.....27.6..6.3.47.2.2.68.34.;11.0/11.0/3.4
9...1......8.....5..46........79..313..5.19.6....6357...1.37......1.6...7.395.16.;11.0/11.0/3.4
9...1......8.....5..46......5.79..313..5.19.6....6357.....37......1.6...7.395.16.;11.0/11.0/3.4
9...1......8.....5..46......5679..313..5.19.6....6357.....37......1.6...7.395.16.;11.0/11.0/3.4
.3....2...67...........5......89..121..5.48.9.8..2145...4.52.81...9.8..4...14.92.;11.0/11.0/7.1
.8.......6.......4..72.3.....379..457..5.42.3....3297.....57.39...4.9..2...32.45.;11.0/11.0/7.1
.3....2...67...........5......89..121..5.48.9....2145...4.52.81.1.9.8..4......92.;11.1/10.3/3.4
.3....2...672..........5......89..121..5.48.9....2145...4.52.81.1.9.8..4......92.;11.1/10.3/3.4
..7.....834..9...2..........2.98..54...4.52.1.5..2198.....14......2.98.59..85.1..;11.1/10.4/2.6
.17....9.34......2..........2.98..54.9.4.52.1.5..2198.....14..9...2.98.59..85....;11.1/10.4/2.6
.17....9.34......2..........2.98..54...4.52.1.5..2198.5...14..9...2.98.59..85....;11.1/10.5/2.6
4......8.......1...3.....6....98..15..52.18.68...5629.....28.5..2.5.96..5..61.92.;11.1/10.5/9.4
......7.53.4.......9.........965..21...2.19.71...9765.....15.6...57.61.2...92.57.;11.1/11.1/10.3
9..........8...6.5..4.......5.79..313..5.19.6....6357.....37......1.63.77..95.16.;11.1/11.1/10.4
9..........8...6.5..4.......5.79..313..5.19.6....6357.....37......1.63.77.395.16.;11.1/11.1/10.4
..3..4....5..9....6.........1.27..497..4.91.5....1572.....42......9.75.4.7.15.29.;11.1/11.1/10.5
..7......34..9...2..........2.98..54...4.52.1.5..2198.....14..9...2.98.59..85.1..;11.1/11.1/2.6
..7....9.34..9...2..........2.98..54...4.52.1.5..2198.....14..9...2.98.59..85.1..;11.1/11.1/2.6
..7.2.9.....7.....8.3...7.....95..16.6.1.72.9.1..6257.....96.2....2.1......57.19.;11.1/11.1/2.6
..8....7.37.......6...47......41..92.9.2.81.7....7984.....21..4...7.49.1...98.72.;11.1/11.1/2.6
.3.4...6......3....18...3.....27..96...9.42.3..2.3647..7..69...4..3.29.7...74.6..;11.1/11.1/2.6
.6.......8.46..........1......79..25...1.69.7.9..2516...2.69.511.95.7......21.7..;11.1/11.1/2.6
3.......79...5.......8.7....8.21..6512.5.67.8....7812...5.82.....17.52.6...16....;11.1/11.1/2.6
51.....4......6.....3.........89..12.8.2.16.4....6498.4...12.98.2.6.94.1...48.2..;11.1/11.1/2.6
.6.......8.46..........16.....79..25...1.69.7.9..2516.....69.51..95.72.6...21.7..;11.1/11.1/2.8
........21.3...4.5.......8.8..52....9.58.42.7..4.9785..9..52.7....7.95.....48.92.;11.1/11.1/3.4
.3....2...67...........5......89..121..5.48.9....2145..94.52.81.1.9.8..4......92.;11.1/11.1/3.4
.3....2...672..........5......89..121..5.48.9....2145..94.52.81.1.9.8..4......92.;11.1/11.1/3.4
.9.........8......2.13....4...23..46...8.73.2....6487..7..42......6.34.73..78.26.;11.1/11.1/3.4
.9.4.......8......2.1.....4...23..46...8.73.2....6487..7..42......6.34.73..78.26.;11.1/11.1/3.4
.9.4.......8......2.13....4...23..46...8.73.2....6487..7..42......6.34.73..78.26.;11.1/11.1/3.4
9..........8...6.5..4.......5.79..313..5.19.6....6357.....37......1.6...7.395.16.;11.1/11.1/3.4
.17....9.34......2..........2.98..54...4.52.1.5..2198.....14..9...2.98.59..85....;11.1/11.1/3.6
.17....9.34..9...2..........2.98..54...4.52.1.5..2198.....14..9...2.98.59..85....;11.1/11.1/3.6
.3....2...67...........5......89..121..5.48.9....2145...4.52.81...9.8..4...14.92.;11.1/11.1/7.1
.3....2...67...........5......89..121..5.48.9....2145..94.52.81...9.8..4...14.92.;11.1/11.1/7.1
.3....2...672..........5......89..121..5.48.9....2145...4.52.81...9.8..4...14.92.;11.1/11.1/7.1
..8....97.........6.1....3..2.45..79...7.93.2....2354.....47..3...2.59.44..39.72.;11.1/11.1/9.3

I'll do a test on all solution grids of mith's file to compare the results with this one, but this will likely take 2 weeks, maybe 3.

[denis_berthier]

.
all in T&E(2), with BxB = 3|4|5
.

[champagne]

We would have been very lucky to get the graal testing only 18 574 solution grids out of 1,807,371,808

But seen in another way, getting a rating >=11 is not so trivial.
We surely have here several starts for other groups of interesting grids, applying the processes used to build the "loki" family.