The New Sudoku Players' Forum

[coloin]

Useful Filter ......

FWIW
out of 802 ed patterns [ 48000 puzzles]
there were 10 double diagonal patterns with valid puzzles

Code: Select all

.......1......2.34..5.6.......3...2...1...7...4...1.......5.6..23.8......1....... #   687 FNBP C18.m/S4.da/M1.3.14
.......1......1.23..4.5.........6.4...7...5...3.2.........4.8..92.6......1....... #    13 FN C18.m/S4.da
.....1.2........31..4.2.......5....6..7...4..2....3.......7.8..91........3.9..... #   180 FNBP C18.m/S4.da/M1.16.1
.....1.2..2......3..4.5.......3....1..6...4..5....2.......6.7..8......5..1.4..... #   498 FNBP C18.m/S4.da/M1.29.5
.....1.....2....3..1...45.......61.4.........2.78.......52...8..8....6.....3..... #   189 FNBP C18.m/S4.da/M1.15.2
...12......34......56......74.......1.......6.......38......15......34......96... #    11 FN C18.m/S4.da
1......2......3..4....54.........16...1...7...82.........21....7..6......3......9 #    17 FNB C18.m/S4.da
1.....2.......3.......45..6......74...4...1...56......2..17.......3.......5.....8 #    20 FNB C18.m/S4.da
12....3..3....4........5..6......17...........65......2..1........7....4..8....95 #     9 FN C18.m/S4.da
1......2........34..5.1.......2.6.....7...5.....3.4.......8.7..82........4......1 #   331 FNBP C18.m/S4.da/M1.26.6


[Afmob]

A small update on my computation: About 1,300 patterns have been analyzed which led to 23 patterns having valid 18 clue DD symmetric puzzles. What's interesting is that there are some patterns which have a lot of essentially different puzzles (Top 3: 221, 103 and 98 puzzles). You will get the final results tomorrow.

[Afmob]

Alright, I've got 48 patterns with a total of 1,357 valid puzzles. As announced there are some patterns with a lot of different puzzles (Top 3: 221, 179 and 122 puzzles).

[Serg]

Hi, Afmob!

Alright, I've got 48 patterns with a total of 1,357 valid puzzles. As announced there are some patterns with a lot of different puzzles (Top 3: 221, 179 and 122 puzzles).

Great work! Congratulations to all participants of this search project! I was sure that double diagonal 18-clue puzzles were impossible when this search was started - there were too low (2580) possible patterns. But we can see that diagonal shape is much more efficient than vertical shape. One could see that there exist 121 e-d vertical symmetric 18-clue patterns having valid puzzles from 700,000 possible e-d patterns and 48 e-d double diagonal symmetric 18-clue patterns having valid puzzles from 2580 possible e-d patterns.

Next thing wondering me is the speed of search. One week only was necessary to go from idea of this search to final results.

You can see filtering by maximal patterns in this case was not very efficient. Maybe it would be useful to have "complementary" maximal patterns list having 9 clues in B3, B6, B7, B8 and B9 boxes (4 "free" boxes).

Serg

[Serg]

Hi!
I'd like to comment once more results of exhaustive search for 18-clue double diagonal puzzles, reported now by Afmob.

It turns out, 18-clue double diagonal puzzles are the most symmetric type of 18-clue puzzles, because 18-clue full symmetric puzzles cannot be constructed (number of clues in the puzzles having 4 symmetry axes (vertical, horizontal, diagonal and antidiagonal) is given by formula n = 4k or n = 4k + 1), 18-clue puzzles having 90-degree rotational symmetry cannot be constructed too, 18-clue puzzles having vertical and horizontal symmetries were not found.

Serg

[coloin]

Indeed well done Afmob.
Strange that some patterns have so many puzzles .......

Possibly] [bound to be] there are diagonal patterns of 19 and 20 clues without puzzles which will spawn a good few 18-patterns,

I spent a little time trying to find a 22 clue d-symmetric pattern without puzzles - so far failed

This sort of pattern is possible

Code: Select all

+---+---+---+
|...|...|.45|
|...|...|..7|
|..2|..8|...|
+---+---+---+
|...|123|...|
|...|456|...|
|..6|789|...|
+---+---+---+
|...|...|769|
|4..|...|351|
|51.|...|824|
+---+---+---+

But in the 18-clue puzzles I looked at - 11 clues were needed plus 7 in B5B9.

Code: Select all

+---+---+---+
|...|...|.3.|
|.7.|...|.12|
|...|..5|...|
+---+---+---+
|...|.6.|...|
|...|31.|...|
|..5|..8|4..|
+---+---+---+
|...|..3|67.|
|82.|...|5..|
|.1.|...|...|
+---+---+---+

C

[Serg]

Hi, all!
I checked for minimality all found vertically and double diagonal symmetric 18-clue puzzles. All 411 vertically symmetric puzzles are minimal. 1353 (of 1357) double diagonal symmetric puzzles are minimal too, but 4 double diagonal symmetric puzzles are not minimal. Namely these puzzles:

Code: Select all

.......1......1.23..4.5.......6...4...7...5...3...2.......4.6..82.3......1.......
.......1.....1..23..4..5......5..4...3.....6...7..8......4..9..61..3.....2.......
.......1..2.....34....54........65....7...6....82........37....46.....8..5.......
.....1..2..3....4..4..5.........6..7..1...5..2..8.........3..1..6....3..9..4.....

Unfortunately 17-clue puzzles, made from these puzzles by deleting extra clue, are already known.

Serg

[coloin]

Aside from the 18s with one diagonal symmetry [many]
A morph of a recently found puzzle by me here has 180 rotational symmetry

Code: Select all

+---+---+---+
|54.|...|3..|
|...|...|...|
|...|..8|.76|
+---+---+---+
|127|...|...|
|...|...|...|
|...|...|435|
+---+---+---+
|41.|5..|...|
|...|...|...|
|..6|...|.98|
+---+---+---+

out of 102 18-puzzles with 2 clues in a band that i found - 13 had symmetry

Code: Select all

35....1................8.76127.....................43541.5................6....98 #   232 FNBTH C18.m/S2.p
53....1................8.76127.....................43541.5................6....98 #   234 FNBTH C18.m/S2.p
54....1................8.76127.....................43541.5................6....98 #    93 FNBH C18.m/S2.p
54....2................8.76127.....................43541.5................6....98 #    91 FNBH C18.m/S2.p
54....3................8.76127.....................43541.5................6....98 #    92 FNBH C18.m/S2.p    above
54....3................8.76127.....................45323.5................6....98 #   172 FNBTH C18.m/S2.p
54....3................8.76237.....................45141.5................6....98 #   156 FNBH C18.m/S2.p
54....3................8.76327.....................45141.5................6....98 #   156 FNBH C18.m/S2.p
54....3................9.76927.....................41581.5................6....97 #    23 FNB C18.m/S2.p
54....3................9.26927.....................41581.5................3....79 #   148 FNBH C18.m/S2.p
54....3................9.78927.....................41543.5................6....97 #   279 FNBTX C18.m/S2.p

......123.........4.5..6...317.....................268...1..4.9.........632...... #     9 FN C18.m/S2.p

1.........2....5....3..4.6.786.....................125.1.5..7....4....9.........3 #   153 FNBH C18.m/S2.p


I have edited to show that there are 11 of the one pattern and 2 other different patterns

C

[Serg]

Hi, coloin!

A morph of a recently found puzzle by me here has 180 rotational symmetry

Code: Select all

+---+---+---+
|54.|...|3..|
|...|...|...|
|...|..8|.76|
+---+---+---+
|127|...|...|
|...|...|...|
|...|...|435|
+---+---+---+
|41.|5..|...|
|...|...|...|
|..6|...|.98|
+---+---+---+

Well done! Now we have examples of all possible 18-clue valid puzzles' symmetries - vertical, double diagonal and 180 degree rotational. For two of them even exhaustive search was done.

Serg

[m_b_metcalf]

there were 10 double diagonal patterns with valid puzzles

Code: Select all

.......1......2.34..5.6.......3...2...1...7...4...1.......5.6..23.8......1....... #   687 FNBP C18.m/S4.da/M1.3.14
.......1......1.23..4.5.........6.4...7...5...3.2.........4.8..92.6......1....... #    13 FN C18.m/S4.da
.....1.2........31..4.2.......5....6..7...4..2....3.......7.8..91........3.9..... #   180 FNBP C18.m/S4.da/M1.16.1
.....1.2..2......3..4.5.......3....1..6...4..5....2.......6.7..8......5..1.4..... #   498 FNBP C18.m/S4.da/M1.29.5
.....1.....2....3..1...45.......61.4.........2.78.......52...8..8....6.....3..... #   189 FNBP C18.m/S4.da/M1.15.2
...12......34......56......74.......1.......6.......38......15......34......96... #    11 FN C18.m/S4.da
1......2......3..4....54.........16...1...7...82.........21....7..6......3......9 #    17 FNB C18.m/S4.da
1.....2.......3.......45..6......74...4...1...56......2..17.......3.......5.....8 #    20 FNB C18.m/S4.da
12....3..3....4........5..6......17...........65......2..1........7....4..8....95 #     9 FN C18.m/S4.da
1......2........34..5.1.......2.6.....7...5.....3.4.......8.7..82........4......1 #   331 FNBP C18.m/S4.da/M1.26.6


This is certainly an isomorph of one of these patterns, but has symmetry of givens too:

Code: Select all

 . 1 . . . . . . 2
 3 . . . . 4 . . .
 . . . . 5 . 6 . .
 . . . 2 . . . 4 .
 . . 5 . . . 7 . .
 . 6 . . . 8 . . .   18 clues
 . . 4 . 7 . . . .   Diagonal and anti-diagonal symmetry
 . . . 6 . . . . 1   And, symmetry of givens
 8 . . . . . . 3 .   ED=7.2/7.2/3.4

[eleven]

Nice.
In the 180 degree rotational symmetry the givens are symmetric with the number mappings (13),(2,8),(4,6),(5,7). So in the center r5c5 there must be a 9.

Now it can be solved with (2 opposite) swordfish and a small chain, or (i don't like to look for swordfish) you could use symmetry moves, e.g.

Code: Select all

+----------------------+----------------------+----------------------+
|d46-579 1      6789   | 3789   368    3679   | 34     5789   2      |
| 3      25789  26789  | 1789   1268   4      | 1589   15789  5789   |
|c2479  c24789  2789   | 13789  5      12379  | 6      1789  b34     |
+----------------------+----------------------+----------------------+
| 179    3789   13789  | 2      136    57     | 13589  4      35689  |
| 124    2348   5      | 134    9      136    | 7      1268   368    |
| 12479  6      12379  | 57     134    8      | 12359  1259   359    |
+----------------------+----------------------+----------------------+
| 16     2359   4      | 13589  7      12359  | 2589   25689  5689   |
| 2579   23579  2379   | 6      2348   2359   | 24589  25789  1      |
| 8      2579   16     | 1459   124    1259   | 2459   3    ea46-579 |
+----------------------+----------------------+----------------------+
4r9c9 = r3c9 - r3c12 = 4r1c1&6r9c9 => -579r1c1,r9c9

Singles/pairs then bring you here:

Code: Select all

+----------------------+----------------------+----------------------+
| 46     1      6789   | 3789   68-3   3679   |c34     5      2      |
| 3      5      26     | 189   b26     4      | 189    189    7      |
| 2479   2489   2789   | 13789  5      12379  | 6      189    34     |
+----------------------+----------------------+----------------------+
| 179    389    13789  | 2      136    57     | 13589  4      35689  |
| 124    2348   5      | 134    9      136    | 7      1268   368    |
| 12479  6      12379  | 57     134    8      | 12359  129    359    |
+----------------------+----------------------+----------------------+
| 16     239    4      | 13589  7      12359  | 2589   2689   5689   |
| 5      239    239    | 6     b48     239    |c48     7      1      |
| 8      7     d16     | 1459  a24-1   1259   | 2459   3      46     |
+----------------------+----------------------+----------------------+

2r9c5 = 2r2c5&8r8c5 - (8=3)r18c7&1r9c3 => -1r9c5,-3r1c5