Diagonal Patterns in the "Patterns Game"

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Diagonal Patterns in the "Patterns Game"

Postby coloin » Thu Feb 17, 2011 12:22 am

This puzzle has a diagonal pattern in every box [27 clues]
Code: Select all
+---+---+---+
|..1|..2|..3|
|.3.|.8.|.9.|
|5..|4..|8..|
+---+---+---+
|..5|..1|..7|
|.4.|.7.|.8.|
|1..|6..|4..|
+---+---+---+
|..6|..3|..8|
|.7.|.2.|.6.|
|9..|8..|3..|
+---+---+---+

Many of the patterns in the patterns game[which produce puzzles with ED > 9.2 ] have 3 clues diagonally placed in a box

So if all the boxes have the diagonal pattern then minlex versions of the puzzles all have similar B12347
Code: Select all
+---+---+---+
|..1|..2|..3|
|.3.|.8.|.9.|
|5..|4..|8..|
+---+---+---+
|..5|...|...|
|.4.|...|...|
|1..|...|...|
+---+---+---+
|..6|...|...|
|.7.|...|...|
|9..|...|...|
+---+---+---+


Here are some 27 clue "all diagonal" patterns - there may well be a few more

Code: Select all
001002003020030040400500100006001007080060090200900800008003004050080070300200500
001002003020030010400500600002005007080090040700600900005080090040200500900003008
001002003020010040300500600002006001040030070500800400004200800030060007900003020
001002003020030040300500600002007008030010060600300700007100400080060010100004009
001002003020010040300400500002006004040030200700100080006009007050070900100200060
001002003020010040300500100004006002070100080100020300009005004040090050200400700
001002003020030040300500600002003004070600500800070090003006001090200300700050060
001002003020010040500600100002004001070800900600050030007006500080070006400900070
001002003020030040300500600003007080050040001800900700009008050070060004100400900
001002003020030040500600700002005060050040100800300009007004030090080005400900200
001002003020030040300500600003007100050010020200800009008060400040005007600900010
001002003020010040500600700002060080030007400900300007004070030010008200700100009
001002003020010040500600100002040070060003800400500002009080200010007006300900050
001002003020010040500600700002080600030004009600100050004200300060050090800009006
001002003020030040500100600004010700060400080200009006006900100090020008300005070
001002003020030040400500100003600007060007080100050200006003010070900004900040300
001002003020040050300600700002100080070006002400090600006070090030009001900500800
001002003020010040300500600007300060030007100400020008008700200040005030100080009
001002003020030040500600700002800090080040100400007006003004070090200600700050009
001002003020010040300500600002100700050007008900040050003008004010090070800600300
001002003020010040300500200003600400070005080600040009009004007040700600200030050
001002003020010040300500600005100200040070001200008030009600070060040300800007004
001002003020010040500600100004500700080060030100007005007800400030050090400009006

There are 6 ways to complete a diagonal and 4 boxes to complete.

How many of these all diagonal patterns with 21+ clues can be made by isomorphic swapping to have symmetry [S2 and above] which qualifies it for the game ?

And here is a few - from the non-minimal puzzles above
Code: Select all
.....1.2.....2...1..75..6....6..2..8.9..3..4.5..6..1....3..42..9...6...5.6.8...9. #    11 FN C25.m/S2.d
..1..3....2..4..3.4..1..5....6..7..1.8..9..6.2..8..9....8..4..3.5..7..8....5..2.. #   758 FNP C25.m/S4.da/M1.3.30
..1..3..2.2.....3.4..1..5....6..7..1.8..9..6.2..8..9....8..4..3.5.....8.3..5..2.. #  1078 FNP C25.m/S2.p/M1.2.54
..1.2.3...2...3..44..5...1..5...8.....8.3.4.....2...5..8...6..92..9...8...6.1.7.. #  1160 FNP C25.m/S2.p/M1.4.27
..1.3...2.2...4.3.5..7..6....7.....4.9..5..8.4.....9....2..6..5.5.1...4.8...9.3.. #   293 FNP C25.m/S2.p/M1.6.1
..21...3......2..45...3....6..3..4....5..7..8.4..6..9....9...7.7....46...3..2...5 #   500 FNP C24.m/S2.d/M1.14.2
..28....9.8...4.1.4...7.6...2...3..4....2....5..6...7...3.4...7.9.2...6.7....59.. #   415 FNP C25.m/S2.p/M1.10.4
.1.3..2..2...5..4......7..63..1..9...6.....7...9..8..57..2......2..8...1..4..6.9. #   378 FNP C24.m/S4.da/M1.10.6
.2...1.3.1...2.......3....6..1..2..7.7..5..8.4..9..5.......3.4.9...1.7....68....3 #   729 FNP C24.m/S2.d/M1.2.52
.3...1.2.4...2......75..6....6..2..8.9..3..4.5..6..1....3..42..9...6...5...8...9. #   469 FNP C25.m/S2.d/M1.18.5
.6...7..18..9...6...2.8.9...1......2..4.1.5..2......3...3.5.2...8...4..35..7...8. #   720 FNP C25.m/S4.da/M1.5.11
1..2..3....2..1..4.3..5..1.4..6..2....7.....8.1...2.3.9..5..4....4..9..5.2..4..7. #   194 FNP C26.m/S2.d/M1.3.27
1..2..3...2..1..4...5..6...4....5..7.8..6..3...17..5..7....8..4.3..5..9....9..6.. #   515 FNP C25.m/S2.d/M1.22.5
1..3.......2.....3.4..1..5.6..7..1....8..9..6....8..9....4..3....5..7..8.3..5..2. #  1824 FNP C23.m/S2.d/M1.2.26
2...1...3..3..2....5.4..1....6..8.9.1...6...7.9.2..8....8..5.7....3..5..3...8...4 #   845 FNP C25.m/S4.da/M1.6.10
2..1...3...3..2..4.5....6..7..3..1.......5..2.8..2..9...68..4..5....4.7..9..6.... #   519 FNP C24.m/S2.d/M1.20.3
3..2....1..1..3.2..6..5.4..7..5....2..4..9.8..9..6......9.....5.5..2....8..3..9.. #   780 FNP C24.m/S2.d/M1.4.35


C
coloin
 
Posts: 1539
Joined: 05 May 2005

Re: Diagonal Patterns in the "Patterns Game"

Postby ronk » Thu Feb 17, 2011 10:52 am

coloin wrote:Here are some 27 clue "all diagonal" patterns - there may well be a few more

Code: Select all
001002003020030040400500100006001007080060090200900800008003004050080070300200500
001002003020030010400500600002005007080090040700600900005080090040200500900003008
001002003020010040300500600002006001040030070500800400004200800030060007900003020
001002003020030040300500600002007008030010060600300700007100400080060010100004009
001002003020010040300400500002006004040030200700100080006009007050070900100200060
001002003020010040300500100004006002070100080100020300009005004040090050200400700
001002003020030040300500600002003004070600500800070090003006001090200300700050060
001002003020010040500600100002004001070800900600050030007006500080070006400900070
001002003020030040300500600003007080050040001800900700009008050070060004100400900
001002003020030040500600700002005060050040100800300009007004030090080005400900200
001002003020030040300500600003007100050010020200800009008060400040005007600900010
001002003020010040500600700002060080030007400900300007004070030010008200700100009
001002003020010040500600100002040070060003800400500002009080200010007006300900050
001002003020010040500600700002080600030004009600100050004200300060050090800009006
001002003020030040500100600004010700060400080200009006006900100090020008300005070
001002003020030040400500100003600007060007080100050200006003010070900004900040300
001002003020040050300600700002100080070006002400090600006070090030009001900500800
001002003020010040300500600007300060030007100400020008008700200040005030100080009
001002003020030040500600700002800090080040100400007006003004070090200600700050009
001002003020010040300500600002100700050007008900040050003008004010090070800600300
001002003020010040300500200003600400070005080600040009009004007040700600200030050
001002003020010040300500600005100200040070001200008030009600070060040300800007004
001002003020010040500600100004500700080060030100007005007800400030050090400009006

When the 23 patterns are canonicalized .. gsf-solver -f%#xc infile.dat ... there exist only 10 essentially different patterns.

Code: Select all
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X.
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X...X.X...X.X.X..X..X..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X...X.X.X...X.X....XX..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X..X..X...XX..X..X....X
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X..X..X.X....XX....XX..
..X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X..X.X...X.X.X..X..X....X.X.
..X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X....X.X.X...X.X...X.X....X..X
ronk
2012 Supporter
 
Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Thu Mar 03, 2011 12:09 am

Thanks ronk for alerting me to an error

I did a bit more searching found only - 15 in total.

Code: Select all
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X.
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X..X..X.X.X...X.X...X.X..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X..X.X..X.X....XX...X.X..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X...X.X...X.X.X..X..X..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X...X.X.X...X.X....XX..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X..X..X...XX..X..X....X
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X..X..X.X....XX....XX..
..X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X..X.X...X.X.X...X.X....XX..
..X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X..X.X...X.X.X..X..X....X.X.
..X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X....X.X...X.X...XX..X..X...X.
..X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X....X.X...X.X.X..X..X....X.X.
..X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X....X.X.X...X.X...X.X....X..X


Here is a representative of each. Interestingly only one pattern cant be made symetrical with the 27 clues.
Code: Select all
..1..2..3.2..1..4.5..6..1....2..4..1.5..6..7.7..2..3....7..5..8.8..7..9.9..3..2.. #   C27/S4.da/M1.16.3   
2...4...6..4..2.3..7.8..1....24...1.1...3...2.3...54....5..9.7..1.6..2..6...7...9 #   C27.M/S4.da/M1.31.2
..2..3.1..3..1.2..5..6....4..5..7.2..9..4.8..6..9....7.8..9..5.2..5..4....3..8..9 #   C27/S2.d/M1.33.1   
..1.2.3...2...1..43..5...6...42...8.9...3...2.3...67...4...3..75..8...4...2.6.1.. #   C27.M/S2.p/M1.13.4 
1....2..3.9..4..1...73..5....21....9.6..2..5.9....56....3..41...7..8..2.2..6....8 #   C27.M/S4.da/M1.11.6
2...3.1....14...2..5...6..3.6.2..4..3...5..7...7..3..65..8..7...9..1..4...6..2..9 #   C27/S2.d           
.2..7...84..6..9....5..4.7..1.2..3..2...1...4..3..5.6..9.5..6....1..7..37...3..5. #   C27.M/S4.da/M1.16.1
1..3..2...2..4..1...3..6..52...8..7..7.5..3....9..1..67...9.5...4.1....8..8..2.6. #   C27/S2.d           
..2.1.3...1...2.4.5..3....2..5..7.8.6...3...4.4.6..9..7....4..6.3.2...5...4.9.7.. #   C27.M/S4.da         
..1..2..3.2..1..4.3..5..6....51..2...4..7...12....8.3...96...7..6..4.3..8....7..4 #   C27 [asymmetric]   
..1..3..2.2..4..3.4..6..5....23...1..4...57..5...9...8..6.8..7..9.1..6..7....2..1 #   C27/S2.d           
2..1....3..1..2.4..5..3.6..5..7...9...6.8.2...8...4..1..7.6..8..6.4..1..3....7..5 #   C27/S4.da           
2...3.1....14...2..5...6..3.6.2..4..3....4.7...7.8...65..8..7...9..1..4...6..2..9 #   C27/S2.d           
6....2.7...8.1...5.9.5..3....2..1..3.1..2..4.5..3..2....4..8.9.1...9.8...3.4....7 #   C27.M/S4.da         
..1.2...3.2...34..5..1...6...4..1.7.2...9...6.6.4..8...9...2..8..69...1.3...5.7.. #   C27.M/S4.da


Not sure if there are more patterns or not

C
coloin
 
Posts: 1539
Joined: 05 May 2005

Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Tue May 17, 2011 10:58 am

From these 15 27 clue templates I removed 3 clues and found 8099 different 24 clue templates.

Of these only 18 had an empty box

Code: Select all
.....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X..
.....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X.
.....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X..X.X.X..X..X...X..X.
.....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X
.....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X..
.....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X.X..X.X..X..X...X...X
.....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X.X..X..X.X..X..X....X..X
.....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X.X.X...X.X....XX....X.X.
.....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X..X..X.X.X...X.X...X.X..
.....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X..X.X..X.X....XX...X.X..
.....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X..X.X..X.X..X..X...X...X
.....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X.X..X..X...XX..X..X....X
.....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X.X..X..X.X....XX....XX..
.....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X.X.X...X...X..XX..X...X.
.....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X.X.X...X...X.X.X..X....X
.....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X.X.X...X.X...X.X....X..X
.....X..X....X..X....X..X....X..X.X..X..X.X..X..X....X..X.X...X.X.X...X.X....XX..
.....X..X....X..X....X..X....X..X.X..X..X.X..X..X....X..X.X.X...X.X....XX....X.X.


C
coloin
 
Posts: 1539
Joined: 05 May 2005

Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Wed Nov 09, 2011 4:35 pm

been thinking about the 27-puzzles with all "diagonal" patterns.

im still surprised about only 15 ED patterns.

I had sort of assumed that the more total ED puzzles a pattern had the bigger the range in the ratings.

Removing clues from a 27-puzzle - might make a puzzle be formable from another of the 15 ED 27-patterns.

Except this can only happen when you remove 2 clues from a box.

Therefore there may well be more puzzles if a pattern has one box with only one clue.

I might look at patterns with 25 clues with 2 clues removed from one box

C
coloin
 
Posts: 1539
Joined: 05 May 2005

Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Wed Nov 23, 2011 3:19 pm

Going back to the 15 ED patterns with all 27 clues in a potentially diagonal pattern.

I am wondering what the incidence is of these patterns.

Essentially there are 6 ways to have a "diagonal" pattern in a box - trivially this is 6^9 patterns

Given that B1B2B3B4B7 can always be fixed - there are at most 6^4 [/2] ways to complete B5B6B8B9

Can anyone show what the incidence of the 15 ED patterns ?

Can anyone estimate the approx total number of puzzles in the 15 ED patterns ?

C
coloin
 
Posts: 1539
Joined: 05 May 2005

Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Sun Dec 13, 2015 1:48 pm

Regarding the diagonal patterns .... and hard puzzles..... Maybe the obvious answer is the correct one.

Given that a set pattern has n puzzles, and some patterns will have more puzzles than others , although by nature symmetrical patterns will have less ed puzzles.

Do diagonal patterns have less puzzles with ED x/x/1.2 than other patterns with a box with 3 clues in a non-diagonal pattern ?

Or do diagonal patterns just have more puzzles than other non-diagonal patterns ?

C
coloin
 
Posts: 1539
Joined: 05 May 2005

Re: Diagonal Patterns in the "Patterns Game"

Postby champagne » Sun Dec 13, 2015 4:47 pm

So far I start a search for hardest in the n clues space starting from seeds of size n-1 rating 10.0 and more

Starting from your 15 ED for 26 or 27 clues never searched (as far as I know) could be another way to launch a new 'n'
champagne
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Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Thu Dec 17, 2015 9:36 pm

From the 15 ED Patterns with a representative puzzle.
Removing 3 clues from them - gave 43571 puzzles/pseudopuzzles .....
Of which 3455 could be morphed to be symmetrical .....
Of which 567 had an essentially different pattern.
Those with a box distribution of 222333333 will come from a unique stem of the 15.
Those with other distributions may share a stem
- here are the 567 [24 clue] minlex patterns - which can be made symmetrical
Code: Select all
...........X..X..X.X..X..X...X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X..
...........X..X..X.X..X..X...X..X..X.X..X.X..X..X...X...X..XX...X..X..X.X..X....X
...........X..X..X.X..X..X...X..X..X.X..X.X..X..X...X...XX....X.X..X..X.X....XX..
...........X..X..X.X..X..X...X..X.X..X..X...XX..X..X....X..X.X..X..X...XX..X..X..
...........X..X..X.X..X..X...X..X.X..X..X...XX..X..X....X.X...X.X...X.X.X..X..X..
...........X..X..X.X..X..X...X..X.X..X.X....XX...X.X....X.X..X..X.X....XX....XX..
...........X..X..X.X..X..X...X..X.X..X.X....XX...X.X....X.X.X...X...X.X.X..X....X
...........X..X..X.X..X..X...X..X.X..X.X....XX...X.X....XX..X...X..X...XX....X.X.
...........X..X..X.X..X..X...X..XX...X.X....XX...X..X...X..XX...X.X....XX...X..X.
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coloin
 
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Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Mon Dec 21, 2015 3:27 pm

And further removing of clues

23 clues - 1488 ED patterns which can be made symmetrical
Code: Select all
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.....X..X..X....X..X..X.X....XX......X..X.X..X....X.X...XX....X.X..X.X..X....X...

22 clues - 2772 ED patterns which can be made symmetrical
Code: Select all
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coloin
 
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Re: Diagonal Patterns in the "Patterns Game"

Postby m_b_metcalf » Mon Dec 21, 2015 4:43 pm

Coloin,
Are you planning to submit thousands of patterns to the Patterns Game?

Mike
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m_b_metcalf
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Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Mon Dec 21, 2015 9:55 pm

not really - i just wondered how many patterns there were, and perhaps how many had been used ......
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Postby Pat » Thu Jan 07, 2016 4:10 pm

coloin wrote:

    i just wondered---how many had been used

for a report of all 297 past patterns

    ( 31 early un-numbered,
    + 266 numbered games;
    game 267 not yet
    )
see post 248795.

diagonality information is not provided.
    your interest is in patterns having diagonality in all 9 boxes,
    whereas i'd like to count boxes having diagonality
    (e.g. 8 is still almost as good as 9).
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Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Sat Jan 09, 2016 10:26 pm

interesting slant
your pattern with 5 clues in one of the boxes made up to 29 clues
Code: Select all
+---+---+---+
|..1|2..|.3.|
|.7.|..4|5..|
|5..|.6.|..7|
+---+---+---+
|2..|7.6|.4.|
|..7|.3.|8..|
|.8.|5.2|..6|
+---+---+---+
|4..|.2.|..8|
|..6|9..|.5.|
|.9.|..3|1..|
+---+---+---+


with 5 clues in a box there are 3 ways to make it up to 5 and have 2 diagonal equivs in the box
at most there will be 3 * 9 * 15 patterns with clue box dist of 533333333
reductions for non symmetry and isomorphs.
could do it easily - is this what you are thinking ?

patterns like yours with 25 clues would have clue box dist of 533332222
removing a clue from a box with 3 clues retains the original pattern stem.
of these some would be symmetrical in some way
C
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Postby Pat » Sun Jan 10, 2016 3:00 pm

Pat (2008.Nov.6) wrote:

  • in # 49,
    with only 20 cells given
    and poor diagonality ( only 3 boxes ),
    highest rating = 9.1/2.6/2.6
    ( and players un-happy for lack of "diamonds" )
    results

  • in # 57,
    also only 20 givens
    but full diagonality ( all 9 boxes ),
    highest rating = 10.4/6.7/6.7
    results

could be interesting to re-visit these two
with better software (and stronger computers)
# 49 wrote:
Code: Select all
. . . . . . O O .
. . . O O . . . .
. . O . . . O O .
. O . . . . . . O
. O . . O . . . O
. . . . . O . . .
O . O . . . O . .
O . O . . . . . .
. . . O O . . . .

# 57 wrote:
Code: Select all
. . O O . . . . .
. O . . . O O . .
O . . . . . . O .
O . . O . . . O .
. . . . O . . . .
. O . . . O . . O
. O . . . . . . O
. . O O . . . . .
. . . . . O O . .

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