The New Sudoku Players' Forum

[champagne]

When I started to be interested by the” tridagon” search, the vicinity search in the “loki” family seemed to reach the limits.
see http://forum.enjoysudoku.com/t-e-3-puzzles-split-from-hardest-sudokus-thread-t40514-75.html

IMO the main reason was the specificity of the pattern.
Here is the “loki” puzzle morphed to minlex solution grid.

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1.3.5......71.9...69.37......1..3..75.96.73.....51.......96..........4....5...86.  loki npuz=1
123456789457189236698372145241893657589627314736514928314968572862735491975241863 sol returned
|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|
| 1         248       3        | 248       5         2468     | 2679      24789     24689    |
| 248       2458      7        | 1         248       9        | 256       23458     234568   |
| 6         9         248      | 3         7         248      | 125       12458     12458    |
|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|
| 248       2468      1        | 248       2489      3        | 2569      24589     7        |
| 5         248       9        | 6         248       7        | 3         1248      1248     |
| 23478     234678    2468     | 5         1         248      | 269       2489      24689    |
|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|
| 23478     123478    248      | 9         6         12458    | 1257      12357     1235     |
| 23789     123678    268      | 278       238       1258     | 4         123579    12359    |
| 23479     12347     5        | 247       234       124      | 8         6         1239     |
|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|++++++++++++++++++++++++++++++|


The pattern is in boxes 1246 for the digits 248.
Although I did not check the status in mith’s file, it seems to me very hard to get out of these 2 properties with a vicinity search.

Curious to see what could happen, I started a direct scan for “non degenerated tridagon puzzles” in solution grids.

See http://forum.enjoysudoku.com/non-degenerated-tridagon-puzzles-direct-search-t45331.html

The idea was to get seeds to find new starts.
The scan on the first 36 million solution grids gave plenty of high ratings, but only one skfr 11.8, the rating of “loki”.
After a first vicinity step on the highest ratings, more 11.8 showed up, located in 8 solution grids.
The last in the list is the 11.8 coming out of the direct scan already named “kuto”

In the list, the puzzle is followed by
The skfr rating
The solution grid rank
The puzzle bit field in the solution grid
The 3 digits of the pattern
The 4 boxes of the pattern

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.234.67..4.678....78..23...2.4.3....37.8......68.....4............248.......6..91;11.8;  2549642;kf3pe2BmW007G6   159 1245
12.4.6...4.6.89.....912..........53...8...........1.7..42......6.1..294.89....6..;11.8;  3540130;he6S0O40K6eS31   357 1278
1.3.567...567..1..78...3..........4.3.......2...83.5..57.6.8...6..31......1.75...;11.8;  7071200;rn9Z0G14Bh83q0   249 1278
....5.7.9...7.912....12..6521.69......4.....6.3.....9....96......1.72.5..7.5.1...;11.8; 11699945;G5TOU34KGOWMg0   348 2389
1...567.9...7.912.....2..652..9.......8.....6..4........569........729...7.5.1...;11.8; 19822582;n5TGE14a0S0Eg0   348 2389
12...67...5...91..7.9....652..83...........725...9....6......91.1.......97....25.;11.8; 25912993;ZHC5E30E21M033   348 1379
.2.4.67...........789........53..87..38....92.7......5..2.7.95.....3.2.8.9.....3.;11.8; 30384643;g107WP6MWK3g22   146 4679
.23...7.945......27.9.3.54.2......9439...5.....7...3.5...8....7..4.2.......6.....;11.8;537529786;6TWLBmZWe8a280   168 1346


Here I see nearly no chance to have bridges between these starts, except for the 2 solution grids sharing same digits and same boxes.
The 348 1379 could also bridge with 348 2389 in a kind of double TH

I have started the vicinity search on “kuto”.
To see what happen, I’ll do a separate vicinity on each of these solution grids, mixing only the 3 having the digits348

[blue]

Here I see nearly no chance to have bridges between these starts, except for the 2 solution grids sharing same digits and same boxes.
The 348 1379 could also bridge with 348 2389 in a kind of double TH

If you transformed all of the puzzles to use the same 3 digits, and same 4 boxes, it would be easier to see a chance for bridges.
For two puzzles that (at a minimum) use the same digits and boxes, there are still transformation options available, that can bring one puzzle closer to the other.

[champagne]

Here I see nearly no chance to have bridges between these starts, except for the 2 solution grids sharing same digits and same boxes.
The 348 1379 could also bridge with 348 2389 in a kind of double TH

If you transformed all of the puzzles to use the same 3 digits, and same 4 boxes, it would be easier to see a chance for bridges.
For two puzzles that (at a minimum) use the same digits and boxes, there are still transformation options available, that can bring one puzzle closer to the other.

Hi blue,

I am not clear at all on the chances to have here disjoint or quasi disjoint families.

Some facts:
I produced millions of puzzles rating skfr >=10.5 with no hit in mith's file, but this without the TE3 constraint.
This with as primary seed only "non degenerated tridagon" puzzles of the solution grids 1 to 36M
Mith's file has 4.6 M puzzles all T&E3 in 60K solution grids. It's highly probable that many puzzles with a high rating not T&E3 have been seen but not stored.

I don't have the T&E3 filter, But I could have done an analysis of mith's file to see what are the properties of the 60000 solution grids hit in mith's file (digits and boxes in minlex canonical morph). We already know that a big part of them have no tridagon pattern in the solution grid.

My feeling was that expressing all puzzles in minlex mode would help. The reason can be that this is the canonical morph used to avoid redundancy.
Your proposal is completely different and I can understand why.

I confess that where I am, I see nothing better than to start the vicinity on each family and to see if a bridge appears

[eleven]

Had a rather quick look, if i can solve these puzzles manually, only one resisted with skfr 9.2

The first two leave a remote triple after placing the tridagon forced number.

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.234.67..4.678....78..23...2.4.3....37.8......68.....4............248.......6..91

Hidden Text: Show

Code: Select all

+----------------------------+------------------------------+----------------------------+
|  *159      2        3      |   4       *159      6        | 7        158      589      |
|   4       *159      6      |   7        8       *159      | 12359    1235     2359     |
|   7        8       *159    |  *159      2        3        | 14569    1456     569      |
+----------------------------+------------------------------+----------------------------+
|   2       *159      4      |   6        3        159+7    | 1589     1578     5789     |
|   3        7       *159    |   8       *159      4        | 12569    1256     2569     |
|  *159      6        8      |  *159      1579     2        | 1359     1357     4        |
+----------------------------+------------------------------+----------------------------+
|   568      345      257    |   1359     1579     1579     | 234568   2345678  235678   |
|   1569     1359     1579   |   2        4        8        | 356      3567     3567     |
|   58       345      257    |   35       6        57       | 23458    9        1        |
+----------------------------+------------------------------+----------------------------+

Tridagon => r4c6=7

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+----------------------+----------------------+----------------------+
| 159    2      3      | 4      159    6      | 7      158    589    |
| 4     *159    6      | 7      8     *19     | 159    23     23     |
| 7      8      159    | 159    2      3      | 14569  1456   569    |
+----------------------+----------------------+----------------------+
| 2     *159    4      | 6      3      7      | 1589   158    589    |
| 3      7      159    | 8      159    4      | 1569   1256   2569   |
| 159    6      8      | 159    159    2      | 3      7      4      |
+----------------------+----------------------+----------------------+
| 56     3-5     2     | 19     7      19     | 4568   34568  3568   |
| 1569   139-5  159    | 2      4      8      | 56     356    7      |
| 8      4      7      | 3      6      5      | 2      9      1      |
+----------------------+----------------------+----------------------+

Remote triple 159 => 5r24c2 - 5r78c2

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+----------------------+----------------------+----------------------+
| 159    2      3      | 4      159    6      | 7      158    589    |
| 4     *159    6      | 7      8     *19     |b15-9   2      3      |
| 7      8      159    | 159    2      3      | 14569  1456   569    |
+----------------------+----------------------+----------------------+
| 2    a*15-9   4      | 6      3      7      |°1589  °158   °589    |
| 3      7      159    | 8      159    4      |°1569   15-6   2      |
| 159    6      8      | 159    159    2      | 3      7      4      |
+----------------------+----------------------+----------------------+
| 56     3      2      | 19     7      19     | 4568   4568   568    |
| 1569   19     159    | 2      4      8      | 56     3      7      |
| 8      4      7      | 3      6      5      | 2      9      1      |
+----------------------+----------------------+----------------------+

RT: br2c7 must be the same as ar4c2, and go to r5c8 => -9r2c7,r4c2, -6r5c8, stte

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12.4.6...4.6.89.....912..........53...8...........1.7..42......6.1..294.89....6..

Hidden Text: Show

Tridagon => 8r7c6

Code: Select all

+----------------------+----------------------+----------------------+
|  1      2      357   | 4      357    6      | 37     8      9      |
|  4      357    6     | 357    8      9      | 1237   125    12357  |
| *357    8      9     | 1      2    d*35     | 347    6     a45-37  |
+----------------------+----------------------+----------------------+
|  29     16     4     | 8      69     7      | 5      3      126    |
| d235-7  167-35 8     | 26     345    35     | 124    9      1246   |
| d2359   6-35  e35    | 269    345    1      | 8      7      246    |
+----------------------+----------------------+----------------------+
|b*357    4      2     | 69     69     8      |°137   °15    °1357   |
|  6      357    1     | 357    357    2      | 9      4      8      |
|  8      9      357   | 357    1      4      | 6     c25    °2357   |
+----------------------+----------------------+----------------------+

RT: 7r37c1 - 7r5c1, and either 4r3c9 or a3c9 must go to br7c1 and (see box 9) cr9c8 => -37r3c9
35r3c6 must go to r56c1 and make a pair with r6c3 => -35r56c2
Solves with kite, skyscraper and x-wing

The next one kept being hard for me (skfr r9.2)

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1.3.567...567..1..78...3..........4.3.......2...83.5..57.6.8...6..31......1.75...

Hidden Text: Show

tridagon => 8r9c1

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+-------------------+-------------------+-------------------+
| 1     249   3     | 249   5     6     | 7     289   489   |
| 249   5     6     | 7     8     249   | 1     239   349   |
| 7     8     249   | 1     249   3     | 2469  2569  4569  |
+-------------------+-------------------+-------------------+
| 29    1269  58    | 259   269   17    | 3     4     78    |
| 3     1469  58    | 459   469   17    | 69    78    2     |
| 249   2469  7     | 8     3     249   | 5     169   169   |
+-------------------+-------------------+-------------------+
| 5     7     249   | 6     249   8     | 249   13    13    |
| 6     249   249   | 3     1     249   | 8     57    57    |
| 8     3     1     | 249   7     5     | 2469  269   469   |
+-------------------+-------------------+-------------------+

The next 4 are easy to solve with the tridagon placements and common advanced techniques

I liked to solve the last one (though there should be quicker ways).

Code: Select all

.23...7.945......27.9.3.54.2......9439...5.....7...3.5...8....7..4.2.......6.....

Hidden Text: Show

Code: Select all

+----------------------+----------------------+----------------------+
| 168    2      3      | 4      5      68     | 7      168    9      |
| 4      5     *168    | 7      689    689    |*168    3      2      |
| 7      68     9      | 1      3      2      | 5      4      68     |
+----------------------+----------------------+----------------------+
| 2      168    5      | 3      1678   1678   | 68-1   9      4      |
| 3      9     *168    | 2      4      5      |*168    7     *168    |
| 168    4      7      | 9      168    168    | 3      2      5      |
+----------------------+----------------------+----------------------+
| 59     136    126    | 8      19     1349   | 24     156    7      |
| 168    13678  4      | 5      2      137    | 9      168    1368   |
| 59     1378   128    | 6      179    13479  | 24     158    138    |
+----------------------+----------------------+----------------------+

skyscraper 1 r25 => -1r4c7

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+--------------------+----------------------+------------------------+
| 168    2      3    | 4      5    @*68     |   7      168    9      |
| 4      5     @68+1 | 7    @*68+9  a689    |  *68+1   3      2      |
| 7      68     9    | 1      3      2      |   5      4      68     |
+--------------------+----------------------+------------------------+
| 2      168    5    | 3      1678 @*68+17  | @*68     9      4      |
| 3      9     @68   | 2      4      5      |  @68+1   7      168    |
| 168    4      7    | 9      168    168    |   3      2      5      |
+--------------------+----------------------+------------------------+
| 59     136    126  | 8      19     1349   |   24     156    7      |
| 168    13678  4    | 5      2      137    |   9      168    1368   |
| 59     1378   128  | 6      179    13479  |   24     158    138    |
+--------------------+----------------------+------------------------+

5-cell oddagon 68 on *-marked cells, guardians 9r2c5, 1r2c7 and 17r4c6
7-cell oddagon 68 on @-marked cells, guardians 9r2c5, 1r2c3 and 17r4c6
So because 1r2c7 and 1r2c3 exclude one another, we get 9r2c5 or 17r4c6
9r2c5 - (9=68)r2c6 - (6|8=17)r124c6
=> -68r4c6

Code: Select all

+----------------------+----------------------+----------------------+
| 168    2      3      | 4      5      68     | 7      168    9      |
| 4      5      168    | 7      689    689    | 168    3      2      |
| 7     a68     9      | 1      3      2      | 5      4      68     |
+----------------------+----------------------+----------------------+
| 2     a168    5      | 3      1678  b17     | 68     9      4      |
| 3      9      68     | 2      4      5      | 168    7      168    |
| 168    4      7      | 9      168    168    | 3      2      5      |
+----------------------+----------------------+----------------------+
| 59     136    126    | 8      19     1349   | 24     156    7      |
| 168   d139-68 4      | 5      2     c137    | 9      168    1368   |
| 59     1378   128    | 6      179    13479  | 24     158    138    |
+----------------------+----------------------+----------------------+

(68=1)r34c2 - (1=7)r4c6 - r8c6 = 7r8c2

Code: Select all

+----------------------+----------------------+-----------------------+
| *68+1   2      3     | 4      5     *68     |  7      168    9      |
|  4      5      168   | 7     *689   *689    | *68+1   3      2      |
|  7     *68     9     | 1      3      2      |  5      4      68     |
+----------------------+----------------------+-----------------------+
|  2     *68+1   5     | 3      1678   17     | *68     9      4      |
|  3      9      68    | 2      4      5      |  168    7      168    |
|  68-1   4      7     | 9      168    168    |  3      2      5      |
+----------------------+----------------------+-----------------------+
|  59     136    126   | 8      19     1349   |  24     156    7      |
|  168    137    4     | 5      2      137    |  9      168    1368   |
|  59     1378   128   | 6      179    13479  |  24     158    138    |
+----------------------+----------------------+-----------------------+

8-cell oddagon 68 in *-cells, guardians 1r1c1, r2c7, r4c2
1r2c7 - r2c3 = 1r1c1
=> -1r6c1

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+---------------------+-------------------+-------------------+
|   168   2     3     | 4     5     68    | 7     168   9     |
|   4     5     168   | 7     689   689   | 168   3     2     |
|   7    *68    9     | 1     3     2     | 5     4   b*68    |
+---------------------+-------------------+-------------------+
|   2     1     5     | 3     68    7     | 68    9     4     |
|   3     9    *68    | 2     4     5     | 168   7    *68+1  |
|  *68    4     7     | 9     168   168   | 3     2     5     |
+---------------------+-------------------+-------------------+
|   59   *36    126   | 8     19    1349  | 24    156   7     |
| a*68+1  7     4     | 5     2    a13    | 9     168  b1368  |
|   59   *38    128   | 6     7     1349  | 24    158   138   |
+---------------------+-------------------+-------------------+

8-cell oddagon 68, extra candidates 1r8c1,r5c9
13r8c16 - (1|3=68)r35c9 - (6|8=1)r5c9 => 1r5c9

Code: Select all

+-------------------+-------------------+-------------------+
| 1     2     3     | 4     5     68    | 7     68    9     |
| 4     5     68    | 7     689   689   | 1     3     2     |
| 7    *68    9     | 1     3     2     | 5     4    *68    |
+-------------------+-------------------+-------------------+
| 2     1     5     | 3     68    7     | 68    9     4     |
| 3     9     68    | 2     4     5     | 68    7     1     |
| 68    4     7     | 9     168   168   | 3     2     5     |
+-------------------+-------------------+-------------------+
| 59   *36    12    | 8     19    1349  | 24    156   7     |
|*68    7     4     | 5     2     13    | 9     168  *68+3  |
| 59   *38    12    | 6     7     149   | 24    15    38    |
+-------------------+-------------------+-------------------+

6-cell oddagon 68 => r8c9=3, stte

[coloin]

Im wondering if we can home in on the vicinity search

Im sure blue can provide the absolute numbers .....

It might be possible to categorize each of these puzzles according to the 3 boxes of the tridagon pattern...

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+---+---+---+     +---+---+---+    +---+---+---+
|xx2|1xx|...|     |xx2|1xx|...|    |xx2|1xx|...|
|x3x|x2x|...|     |x3x|x2x|...|    |x3x|x2x|...|
|1xx|xx3|...|     |1xx|xx3|...|    |1xx|xx3|...|
+---+---+---+     +---+---+---+    +---+---+---+
|3xx|...|...|     |3xx|...|...|    |3xx|...|...|
|x2x|...|...|     |x2x|...|...|    |x2x|...|...|
|xx1|...|...|     |xx1|...|...|    |xx1|...|...|
+---+---+---+     +---+---+---+    +---+---+---+
|...|...|...|     |...|...|...|    |...|...|...|
|...|...|...|     |...|...|...|    |...|...|.2.|
|...|...|...|     |...|...|.21|    |...|...|..1|
+---+---+---+     +---+---+---+ or +---+---+---+   tridagon pattern in B124

Code: Select all

                                                                             
+---+---+---+                                                                   
|672|145|...|                                                                   
|839|627|...|                                                                   
|145|893|...|                                                                   
+---+---+---+                                                                   
|397|...|...|                                                                   
|426|...|...|                                                                   
|581|...|...|                                                                   
+---+---+---+                                                                   
|...|...|...|                                                                   
|...|...|...|                                                                   
|...|...|...|                                                                   
+---+---+---+     > 1000 of these ED   

Code: Select all

                                                                                 
+---+---+---+                                                                   
|..2|145|...|                                                                   
|.3.|627|...|                                                                   
|1..|893|...|                                                                   
+---+---+---+                                                                   
|345|...|...|                                                                   
|928|...|...|                                                                   
|761|...|...|                                                                   
+---+---+---+                                                                   
|...|...|...|                                                                   
|...|...|...|                                                                   
|...|...|...|                                                                   
+---+---+---+     > 140 of these   

Hidden Text: Show

Code: Select all

..2145....3.627...1..893...397......826......541.................................
..2145....3.627...1..893...348......529......761.................................
..2145....3.627...1..893...348......729......561.................................
..2145....3.627...1..893...349......728......561.................................
..2145....3.627...1..893...349......725......861.................................
..2145....3.627...1..893...365......428......791.................................
..2145....3.627...1..893...365......729......841.................................
..2145....3.627...1..893...368......425......791.................................
..2145....3.627...1..893...368......529......741.................................
..2145....3.627...1..893...378......426......591.................................
..2145....3.627...1..893...395......428......761.................................
..2145....3.627...1..893...395......728......461.................................
..2145....3.627...1..893...396......425......871.................................
..2145....3.627...1..893...398......425......761.................................
..2145....3.627...1..893...346......729......851.................................
..2145....3.627...1..893...349......826......751.................................
..2145....3.627...1..893...356......428......791.................................
..2145....3.627...1..893...356......829......741.................................
..2145....3.627...1..893...358......426......791.................................
..2145....3.627...1..893...358......429......761.................................
..2145....3.627...1..893...359......728......461.................................
..2145....3.627...1..893...359......826......741.................................
..2145....3.627...1..893...359......428......761.................................
..2145....3.627...1..893...396......728......451.................................
..2145....3.627...1..893...396......827......451.................................
..2145....3.627...1..893...397......426......851.................................
..2145....3.627...1..893...398......426......751.................................
..2145....3.627...1..893...349......825......761.................................
..2145....3.627...1..893...349......526......781.................................
..2145....3.627...1..893...364......729......581.................................
..2145....3.627...1..893...364......925......781.................................
..2145....3.627...1..893...364......529......781.................................
..2145....3.627...1..893...364......529......871.................................
..2145....3.627...1..893...364......825......971.................................
..2145....3.627...1..893...364......925......871.................................
..2145....3.627...1..893...365......724......981.................................
..2145....3.627...1..893...365......924......781.................................
..2145....3.627...1..893...365......924......871.................................
..2145....3.627...1..893...369......724......581.................................
..2145....3.627...1..893...369......524......781.................................
..2145....3.627...1..893...369......524......871.................................
..2145....3.627...1..893...374......529......861.................................
..2145....3.627...1..893...376......924......581.................................
..2145....3.627...1..893...379......524......861.................................
..2145....3.627...1..893...384......529......761.................................
..2145....3.627...1..893...384......925......761.................................
..2145....3.627...1..893...385......924......761.................................
..2145....3.627...1..893...389......524......761.................................
..2145....3.627...1..893...347......529......861.................................
..2145....3.627...1..893...347......926......581.................................
..2145....3.627...1..893...354......729......861.................................
..2145....3.627...1..893...354......829......761.................................
..2145....3.627...1..893...354......926......781.................................
..2145....3.627...1..893...359......824......761.................................
..2145....3.627...1..893...364......827......951.................................
..2145....3.627...1..893...349......528......761.................................
..2145....3.627...1..893...365......429......781.................................
..2145....3.627...1..893...369......425......781.................................
..2145....3.627...1..893...376......429......581.................................
..2145....3.627...1..893...385......429......761.................................
..2145....3.627...1..893...356......429......781.................................
..2145....3.627...1..893...359......426......781.................................
..2145....3.627...1..893...389......426......751.................................
..2145....3.627...1..893...364......725......981.................................
..2145....3.627...1..893...375......924......861.................................
..2145....3.627...1..893...386......524......971.................................
..2145....3.627...1..893...349......527......861.................................
..2145....3.627...1..893...357......824......961.................................
..2145....3.627...1..893...357......924......861.................................
..2145....3.627...1..893...386......724......951.................................
..2145....3.627...1..893...386......425......971.................................
..2145....3.627...1..893...386......529......471.................................
..2145....3.627...1..893...386......427......951.................................
..2145....3.627...1..893...378......524......691.................................
..2145....3.627...1..893...346......527......891.................................
..2145....3.627...1..893...347......526......891.................................
..2145....3.627...1..893...357......624......891.................................
..2145....3.627...1..893...357......926......841.................................
..2145....3.627...1..893...397......824......651.................................
..2145....3.627...1..893...379......628......541.................................
..2145....3.627...1..893...347......629......851.................................
..2145....3.627...1..893...347......829......651.................................
..2145....3.627...1..893...349......827......651.................................
..2145....3.627...1..893...356......429......871.................................
..2145....3.627...1..893...358......429......671.................................
..2145....3.627...1..893...358......629......471.................................
..2145....3.627...1..893...349......527......681.................................
..2145....3.627...1..893...367......524......981.................................
..2145....3.627...1..893...354......829......671.................................
..2145....3.627...1..893...357......924......681.................................
..2145....3.627...1..893...359......624......871.................................
..2145....3.627...1..893...379......624......851.................................
..2145....3.627...1..893...384......627......951.................................
..2145....3.627...1..893...368......429......571.................................
..2145....3.627...1..893...357......429......681.................................
..2145....3.627...1..893...386......429......571.................................
..2145....3.627...1..893...389......627......451.................................
..2145....3.627...1..893...398......726......541.................................
..2145....3.627...1..893...348......629......751.................................
..2145....3.627...1..893...349......628......751.................................
..2145....3.627...1..893...358......629......741.................................
..2145....3.627...1..893...397......426......581.................................

but only [ at least] 16 ED of these B2B4 combinations..

Code: Select all

+---+---+---+
|...|.45|...|
|...|6.7|...|
|...|89.|...|
+---+---+---+
|.45|...|...|
|9.8|...|...|
|76.|...|...|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+


Hidden Text: Show

Code: Select all

....45......6.7......89.....45......9.8......76..................................
....45......6.7......89.....45......7.8......96..................................
....45......6.7......89.....45......8.6......79..................................
....45......6.7......89.....45......8.6......97..................................
....45......6.7......89.....45......9.6......87..................................
....45......6.7......89.....46......9.5......87..................................
....45......6.7......89.....46......7.8......59..................................
....45......6.7......89.....78......9.6......54..................................
....45......6.7......89.....94......7.5......86..................................
....45......6.7......89.....94......8.6......57..................................
....45......6.7......89.....95......7.4......86..................................
....45......6.7......89.....96......7.8......54..................................
....45......6.7......89.....46......8.7......95..................................
....45......6.7......89.....56......8.4......79..................................
....45......6.7......89.....75......9.4......86..................................
....45......6.7......89.....98......7.6......54..................................


[blue]

Hi Champagne,

My feeling was that expressing all puzzles in minlex mode would help. The reason can be that this is the canonical morph used to avoid redundancy.

That's the right idea.

Your proposal is completely different and I can understand why.

I'm not proposing anything different, I was only hinting at this:

Suppose that starting from canonical form for puzzle A, and making "vicintity" changes that keep the tridagon digits and boxes unchanged, you can get to puzzle B: A -> C1 -> C2 -> ... -> Cn -> B.
If you canonicalize C1,C2,...,Cn and B, you're likely (?) to get puzzles with tridagons that use a wide variety of digits and boxes.

[ You can still get from A to canonical(C1), from canonical(C1) to canonical(C2), and so on, and eventually to canonical(B)
It's just that the each step invoives re-canonicalizing after the "(small) vicintity" change. ]

I confess that where I am, I see nothing better than to start the vicinity on each family and to see if a bridge appears

Thar sounds right.

[blue]

Im wondering if we can home in on the vicinity search

Im sure blue can provide the absolute numbers .....

Sorry , but I can't see your suggestions as helping with a vicinty search.
They might lead to a more intuitive canonical form for the (saved) puzzles, but I can't see it changing what needs to happen in the search.

[champagne]

I was only hinting at this:

Suppose that starting from canonical form for puzzle A, and making "vicintity" changes that keep the tridagon digits and boxes unchanged, you can get to puzzle B: A -> C1 -> C2 -> ... -> Cn -> B.
If you canonicalize C1,C2,...,Cn and B, you're likely (?) to get puzzles with tridagons that use a wide variety of digits and boxes.

I don't have the T&E3 filter, But I could have done an analysis of mith's file to see what are the properties of the 60000 solution grids hit in mith's file (digits and boxes in minlex canonical morph). We already know that a big part of them have no tridagon pattern in the solution grid.

I think that this is the same idea.

As far as we know, Mith's file is the result of tens of vicinity cycles but may be using other seeds that just "loki". A good example to see what can happen.

But I have currently no code to do it. I never worked so far on the solving path of the tridagon.

I have a limited time to spend on this topic. I have in priority to control the flow of runs and to check carefully many things.
I hope to have time to write and test the missing code next month.

And I am happy to see that we share the same vision on the way to make progress to-day on the "family" issue.

[champagne]

Had a rather quick look, if i can solve these puzzles manually, only one resisted with skfr 9.2

Hi eleven,

Good to have from time to time a solver view.
After only one vicinity step, these puzzle should still be very close to a "pure tridagon at start", so relatively easy to solve with the set of "rules" implemented on the tridagon pattern.

"marek stefanik" analysis of the hard puzzles coming out of the direct scan showed mainly easy puzzles except for some having several guardians in the "forbidden" cell for the 3 digits.

I have more 11.8, but I kept only one for each potential family; The other are in the vicinity thread

[marek stefanik]

I liked to solve the last one (though there should be quicker ways).

There are, indeed, quicker ways.

Hidden Text: Show

After TH => –168r6c8:

Code: Select all

,-----------------,----------------,----------------,
|A#168 2      3   | 4  5    *68    | 7  A#168  9    |
| 4    5     #168 | 7  689   689   |#168  3    2    |
| 7  B#68     9   | 1  3     2     | 5    4  B#68   |
:-----------------+----------------+----------------:
| 2  B#1–68   5   | 3  1678  7–168 |#168  9    4    |
| 3    9     #168 | 2  4     5     |E168  7   #168  |
|A#168 4      7   | 9 *168  *168   | 3  I#2    5    |
:-----------------+----------------+----------------:
| 59   136    126 | 8  19    1349  | 24  *156  7    |
|*168  13678  4   | 5  2     137   | 9   *168  3–168|
| 59   1378   128 | 6  179   13479 | 24  *158  138  |
'-----------------'----------------'----------------'

TH 168# with a single internal (2r6c8) at the rectangle => A and B are remote triples
hidden single 1B in r4c2
With the external in r5c7, each of 168 is forced in r16 once into b25 and in c18 once into b79.
168r16\c6b5A => –168r4c6
168c18\r8b9A => –168r8c9, stte

only one resisted with skfr 9.2

My solution for the hard one is not exactly pretty, but I was at least able to make it presentable (hopefully).

Hidden Text: Show

After TH => –249r9c1:

Code: Select all

,----------------,---------------,------------------,
| 1    249   3   | 249  5    6   | 7     289   489  |
| 249  5     6   | 7    8    249 | 1     239   349  |
| 7    8     249 | 1    249  3   | 2469  2569  4569 |
:----------------+---------------+------------------:
| 29   1269  58  | 259  269  17  | 3     4     78   |
| 3    1469  58  | 459  469  17  | 69    78    2    |
| 249  2469  7   | 8    3    249 | 5     169   169  |
:----------------+---------------+------------------:
| 5    7     249 | 6    249  8   | 249   13    13   |
| 6    249   249 | 3    1    249 | 8     57    57   |
| 8    3     1   | 249  7    5   | 2469  269   469  |
'----------------'---------------'------------------'

Look at b6p2356. 24 are placed diagonally in a 2x2 block with 78.

Imagine there were for example 28 pairs in c89 and r45:

Code: Select all

+------------------+----
| 3     4     7–8  | 28
| 69    7–8  #2    | 8–2
| 5     169   169  |
+------------------+----
|       28    8–2  |

The 2 forces the 8s in both pairs to eliminate both 8 candidates in the box.
Likewise, there cannot be 48 pairs.
This configuration appears somewhat frequently in TH puzzles and is key to solving many of them.

My first step uses a convoluted version of this, so here is an easier example from later in the solve:

Code: Select all

,----------------,---------------,------------------,
| 1    249   3   | 249  5    6   | 7    #8+29  #8+49|
| 249  5     6   | 7    8    249 | 1     239   349  |
| 7    8     249 | 1    249  3   | 2469  2569  4569 |
:----------------+---------------+------------------:
| 29   1269 #58  |#5+29 269  17  | 3    #4    #78   |
| 3    1469 #58  |#5+49 469  17  | 69   #78   #2    |
| 249  2469  7   | 8    3    249 | 5     169   169  |
:----------------+---------------+------------------:
| 5    7     249 | 6    249  8   | 249   13    13   |
| 6    249   249 | 3    1    249 | 8     57    57   |
| 8    3     1   | 249  7    5   | 2469  269   469  |
'----------------'---------------'------------------'

We are close to a 28/48 pair in r1c89 and a virtual 28/48 pair in r45c34.
Suppose that the 2|4|9 in r1c89 and in r45c4 are the same.
If they are 2s or 4s, we break 8b6 as before.
Therefore, they must be 9s.

Finally, let's get on with the solution:

Code: Select all

,----------------,---------------,------------------,
| 1   #249   3   |x249  5    6   | 7     289   489  |
|x249  5     6   | 7    8   #249 | 1     239   349  |
| 7    8     249 | 1    249  3   |x2469  56+29 56+49|
:----------------+---------------+------------------:
| 29  x1+269 58  | 259  269  17  | 3     4     78   |
| 3   x1+469 58  | 459  469  17  | 6+9   78    2    |
| 249  6+249 7   | 8    3   x249 | 5     169   169  |
:----------------+---------------+------------------:
| 5    7     249 | 6    249  8   | 249   13    13   |
| 6   #249   249 | 3    1   #249 | 8     57    57   |
| 8    3     1   | 249  7    5   | 2469 x6+29 x6+49 |
'----------------'---------------'------------------'

Suppose there is a digit x from 24 in r45c2. r45c2 is then an x1 pair.
xr6 takes r6c6, then remote pair (#) on the remaining 249 digits forces xr1c4, xr2c1.
6b4 takes r6c2, 6b6 takes r5c7.
In r3, we get 56c89 and xc7. We get an x6 pair in r9c89.
Now, r45c26 is a virtual x(1)7 pair, r938c89 is a virtual x(65)7 pair.
Following the above examples with 8s, either choice of x results in 7 being eliminated from b6.
Therefore –2r4c2, –4r5c2. 4b4\r6 => –4r6c6

Code: Select all

,----------------,---------------,------------------,
| 1   *249   3   | 249  5    6   | 7     289   489  |
|#249  5     6   | 7    8    249 | 1     239   349  |
| 7    8    @249 | 1    249  3   | 2469  2569  4569 |
:----------------+---------------+------------------:
| 29   169   58  |*259 @269  17  | 3     4     78   |
| 3    169   58  |*459 @469  17  | 69    78    2    |
| 249  2469  7   | 8    3   #249 | 5     169   169  |
:----------------+---------------+------------------:
| 5    7     249 | 6    249  8   | 249   13    13   |
| 6    249   249 | 3    1    249 | 8     57    57   |
| 8    3     1   | 249  7    5   | 2469  269   469  |
'----------------'---------------'------------------'

Suppose now that r2c1 and r6c6 (#) contain the same digit.
If it's 2 or 4, it cannot be placed in b4.
If it's 9, 24 in c1 and r6 must both take the intersection.
Either way, we reach a contradiction.

Note that b12 have one of 249 in each minirow and b25 have one of 249 in each minicolumn.
Each minicolumn in b5 has a matching minirow in b1 in the sense that they see the same 249 cell in b2.
Either each minicolumn contains the same 2|4|9 as its matching minirow, or each minicolumn contains a different 2|4|9 from its matching minirow.
Proof: Suppose that's not the case.
Then there must be one matching pair with the digit x and two non-matching pairs with the digits y and z.
Then x must take both b2 cells seen by the non-matching pairs, i.e. contra.

Since r6c6 and r2c1 have different values, also the 2|4|9 in r45c4 is different from the 2|4|9 in r1c2 and thus it appears in r1c89.

Code: Select all

,----------------,---------------,------------------,
| 1    249   3   | 249  5    6   | 7    #8+29  #8+49|
| 249  5     6   | 7    8    249 | 1     239   349  |
| 7    8     249 | 1    249  3   | 2469  2569  4569 |
:----------------+---------------+------------------:
| 29   1269 #58  |#5+29 269  17  | 3    #4    #78   |
| 3    1469 #58  |#5+49 469  17  | 69   #78   #2    |
| 249  2469  7   | 8    3    249 | 5     169   169  |
:----------------+---------------+------------------:
| 5    7     249 | 6    249  8   | 249   13    13   |
| 6    249   249 | 3    1    249 | 8     57    57   |
| 8    3     1   | 249  7    5   | 2469  269   469  |
'----------------'---------------'------------------'

As we've seen before, if it's 2 or 4, we break 8b6.
Therefore, it's 9. 6.8 skfr

Code: Select all

,--------------,------------,---------------,
| 1   24   3   | 24  5   6  | 7    C89 aB89 |
| 49  5    6   | 7   8   49 | 1     2   3   |
| 7   8    29  | 1   29  3  | 46    56  456 |
:--------------+------------+---------------:
| 2   19   58  | 59  6   17 | 3     4   78  |
| 3   16–9 58  |b59  4   17 |c69    78  2   |
| 49  469  7   | 8   3   2  | 5     1 dA69  |
:--------------+------------+---------------:
| 5   7    49  | 6   29  8  | 24    3   1   |
| 6   29   249 | 3   1   49 | 8     57  57  |
| 8   3    1   | 24  7   5  | 2469 D69  4–69|
'--------------'------------'---------------'

Now, if the 9 doesn't take one of r1c9 and r5c4, it breaks the same way 2 did.
9r1c9 == 9r5c4 – 9r5c7 = 9r6c9 – loop => –9r5c2, –9r9c9
(6=9)r6c9 – 9r1c9 = 9r1c8 – (9=6)r9c8 => –6r9c9, stte

"marek stefanik" analysis of the hard puzzles coming out of the direct scan showed mainly easy puzzles

Some of them were actually about on par with this one, albeit a small minority. But yes, only two of them were even harder (hopefully I didn't miss any).
5....1....3.8......4..6.....2.....984.....1.2..9...46...4.86.2181.2.49.6...19....;11.3/11.3/3.6
..1....8.9..4....6.5.....4.7..32..64...6.48.7..4.8723.....36.78...7.24.3...84.6..;11.3/11.3/2.6

I'll get into the vicinity thread at some point, I've tried a few puzzles from it which were reposted in the direct search thread and they were really difficult (not sure I actually solved any).

[coloin]

....... I can't see your suggestions as helping with a vicinty search.
They might lead to a more intuitive canonical form for the (saved) puzzles, but I can't see it changing what needs to happen in the search.

Yes the full 6 clues in the box will occur more often in expanded puzzles... and less likely to occur in the minimal puzzle. My vicinity search has been with minimal puzzles only .
I will investigate one of the 16 patterns....and see how the puzzles look
A vicinity search keeping the clue pattern xxxxxx111 or xxxxxx110 would increase yield if it could be implemented easily.

[champagne]

more on last post of blue

Hi Champagne,

My feeling was that expressing all puzzles in minlex mode would help. The reason can be that this is the canonical morph used to avoid redundancy.

That's the right idea.

I had here a problem with mith's file, built on a T&E3 filter and not in minlex morph.

I started to move it to canonical and to rate it using skfr. This will be over end of this week, with an expected oddity.
As noticed by blue, many puzzles have a UR in the solving path. The skfr rating can go down to ER 4.5 with skfr.
As such puzzles are easy to solve for manual players, I stick to the use of skfr as rating tool, including uniqueness rules.

At the end, many puzzles with a rating below 10.5 will be discarded, but we know that in this family we can have missing puzzles not T&R3 with a high rating.

Depending on the analysis of the results, I have in mind to redo some vicinity in this family, may be with several "seeds" to see if they show up.

Hi Champagne,

I confess that where I am, I see nothing better than to start the vicinity on each family and to see if a bridge appears

That sounds right.

I have prepared six families out of the first step of vicinity. I'll open a separate thread for each of them.

I drafted a very simple code to find the digits and the boxes of the tridagon threat in the solving path. It seems to work well. I'll start the check on mith's file after the re rating of the file

[champagne]

I am making slow progress with the current revision of mith's file
First results show many puzzles with a rating below 10.5, the cutoff in my work.

I have now my standard way to store and report on the results.

Here is a puzzle stored for redundancy checks and report

.234.67..4.678....78..23...2.4.3....37.8......68.....4............248.......6..91;118; 2549642;kf3pe2BmW007G6;159;9

.234.67..4.678....78..23...2.4.3....37.8......68.....4............248.......6..91; "puzzle in minlex morph of the solution grid"
118; "skfr rating where 10.8 is 108"
2549642; "solution grid rank"
kf3pe2BmW007G6; " 81 bits field of the puzzle in the solution grid "
159; " three digits assumed to be the tridagon signature"
9 " diagonal box 1-9 not in the magic square of the tridagon square"

This will be the content of the files to download in the future from my google drive.
The first file will be mith's file shrinked to skfr >=10.5 and morphed to canonical

[coloin]

Thats pretty good

I looked at your dll thread to see what the commands were to go from a minimal/minexpand puzzle to "2549642;kf3pe2BmW007G6" for example
Perhaps you could outline what the command is using sktvcat ?

Ive been converting minimal puzzles to min-expanded puzzles [ with a consistant "gsf -E" function]
This seems to reduce the file size by a factor x5 - x10 without loss of accuracy.

Identifying the other puzzles in the same solution grid also reduces redundancy in getting new puzzles. Most of the time all the minimal puzzles diverge from a single max-expand.
This means all the minimals with at least the rating of the max-expand are found relatively easily.

A while back I cleaned up all of miths puzzles. in minlex grid format and min-expanded..... here

[champagne]

Hi coloin,
The code doing it is still in dirty mode on my side. I did not see so far enough interest to put it in a DLL, but the main points are in the thread
http://forum.enjoysudoku.com/proposal-for-a-canonical-puzzle-t45209.html

The minimal name is a 19 bytes sequence of characters, but I find easier in my work to keep it in the 2 components

solution grid rank
81 bits field pattern of the puzzle in the solution grid.

The 64 charaters chain used to show the 6 bits field in printable form is

Code: Select all

const char* bit6 = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz{}";
//                  1234567890123456789012345678901234567890123456789012345678901234


This is a sequence keeping the "sort" potential using classical tools.

Starting from any puzzle, to reach the final name, several steps are needed

A) Check that this is a valid puzzle (brute force)
B) Get the minimal solution grids and the auto morphs (DLL)
Get the rank (DLL)
C) Morph the puzzle to the smallest lexical using the auto morphs of the solution grid
D) convert the puzzle to the bit field


Nothing hard with the current DLLs, but needs a new DLL with the main functions to have it easy to use.

My current code for this task is the following

Code: Select all

      if (sgo.vx[4] == 1) {
         if (SkbfCheckValidityQuick(ze) != 1) {            
            cout << ze  << " invalid puzzle "  << endl;
            continue;
         }
         SkbsGetMin(vv, smin);
         uint64_t r = SkvcatGetRankFromSolMin(smin);
         cout << "r=" << r << endl;
         GRIDPERM wgperm;
         char* pbase = ptpgc->t[0];
         wgperm.Import19(vv, pbase);
         wgperm.MorphPuzzle(ze, zem);
         for (int i = 1; i < ptpgc->nt; i++) {// check auto morph get the smallest
            wgperm.Import19(vv, ptpgc->t[i]);
            wgperm.MorphPuzzle(ze, zem2);
            register int x = 0;
            for (; x < 81; x++)if (zem[x] != zem2[x])break;
            if (x < 81 && zem2[x] == '.') memcpy(zem, zem2, 81);            
         }
         char zbit[15]; zbit[14] = 0;
         PuzzleInBitField(zem, zbit);
         Fout_p_R_Bin(zes, r, zbit);

      }