Diagonal Patterns in the "Patterns Game"

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Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Sun Jan 10, 2016 5:30 pm

Well ... they could be worth revisiting - as we are certainly ? x100 better than we were !
no 57
Code: Select all
+---+---+---+
|..1|7..|...|
|.2.|..1|6..|
|6..|...|.3.|
+---+---+---+
|2..|9..|.4.|
|...|.2.|...|
|.1.|..8|..7|
+---+---+---+
|.8.|...|..1|
|..7|4..|...|
|...|..5|2..|
+---+---+---+
comes from this 27 clue [ there appears to be only 15 ed 27 clue patterns]
+---+---+---+
|..1|7..|..2|
|.2.|..1|6..|
|6..|.9.|.3.|
+---+---+---+
|2..|9..|.4.|
|..9|.2.|8..|
|.1.|..8|..7|
+---+---+---+
|.8.|...|..1|
|..7|4..|.6.|
|3..|..5|2..|
+---+---+---+  the 3rd clue in the 2 clue boxes are forced


I am beginning to think that its all down to the sheer number of puzzles per pattern .... and the fact that singles are less likely with non horiz/vert clues in a individual box.
There will obviously be less puzzles with 20 clues than 25
C
coloin
 
Posts: 1637
Joined: 05 May 2005

Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Sun Jan 10, 2016 7:28 pm

Well .... I should perhaps have realized !

These 29 clue patterns, with 5 clues in one of the boxes - "arranged diagonally"- many will be isomorphic ....
Code: Select all
+---+---+---+
|..1|..3|..2|
|.2.|.4.|.1.|
|5..|1..|6..|
+---+---+---+
|..2|6.1|..4|
|.5.|.7.|.6.|
|7..|3.4|2..|
+---+---+---+
|..7|..8|..5|
|.8.|.9.|.7.|
|9..|2..|3..|
+---+---+---+

Here are 9 ED, an example and its minlex pattern - thats all I got !
Code: Select all
..1..3..2.2..4..1.5..1..6....26.1..4.5..7..6.7..3.42....7..8..5.8..9..7.9..2..3.. #    11 FN C29/S4.da       
..2..3.1..3..1.2..5..6....4..5..7.2..9..4.8..6..9....7.8..9.15.2..5..48...3..8..9 #    16 FNB C29/S2.d       
..1.2.3...2...1..43..5...6...42.5.8.9...3...2.3.1.67...4...3..75..8...4...2.6.1.. #     8 FN C29/S2.p         
1..2....3.9..4..1...7..35....28.1..9.6..2..5.9..5.46....34..1...7..8..2.2....6..8 #  1293 FNTWXY C29.M/S4.r   
..21....3.4..9..1.3....75..1..5.2..9.2..6..5...59.86....4..31...8..7..2.6..2....8 #  2212 FNBTHWY C29/S2.d   
1....2..3.9..4..1...73..5....21....9.6..2..5.9....56....3..41...7..8..262..6...98 #     8 FN C29/S2.d         
68..4...253.2..4....1..8.7..1...42..2...3...1..45...3..7.9..5....2..6.1.9...7...6 #    13 FN C29/S2.d         
..13..2...9..1..4.7....5..32..9....1.6..5..2...9..65..3....14...7..2..85..28...36 #     9 FN C29/S2.d         
..2..3.1..3..1.2..5..6....4..58.7.2..9..4.8..6..9.1..7.8..9..5.2..5..4....3..8..9 #    12 FN C29/S2.d         
                                                                                                             
..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..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.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...XXX....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.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..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X..X.XX.X.X...XXX...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..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...XXX..                             
..X..X..X.X..X..X.X..X..X....X..X..X.X..X.XX.X..X..XX...X.X...X.X.X...X.X....XX..                             

In a while I will remove clues from these and see how many patterns we have which are symmetrical 23 clues with box dist of 533222222

here are 13 ED patterns - with a symetrical pattern with a box with 5 clues - poss of interest -and thats all I got of these !
Code: Select all
+---+---+---+
|..1|..2|..3|
|.2.|.1.|.4.|
|5..|6..|1..|
+---+---+---+
|..2|.34|..1|
|.5.|.6.|.7.|
|7..|25.|3..|
+---+---+---+
|..7|..5|..8|
|.8.|.7.|.9.|
|9..|3..|2..|
+---+---+---+

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..XXX
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X..XXX..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.XX..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.X..X..X.X
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X.X..X.X..X..X..XXX..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....XX.X
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..XXX..X..XX...X.X...X.X.X...X.X....XX..
..X..X..X.X..X..X.X..X..X....X..X..X.X..X..XXX..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..XXX..X..XX...XX....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...XXX...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.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..XX..XX..XX.X....X
coloin
 
Posts: 1637
Joined: 05 May 2005

Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Mon Jan 11, 2016 7:15 pm

Code: Select all
+---+---+---+
|...|...|..7|
|.4.|.2.|.9.|
|..9|..8|3..|
+---+---+---+
|...|1.2|8..|
|.8.|.3.|.4.|
|..2|4.5|..6|
+---+---+---+
|..8|9..|...|
|.3.|.5.|.6.|
|5..|..6|..2|
+---+---+---+

This pattern .... with 533332222 ...there were 411 ED patterns which were symmetrical ...
probably patterns which might be fruitful would have these clues in boxes ....
Code: Select all
323
252
323
coloin
 
Posts: 1637
Joined: 05 May 2005

Postby Pat » Wed Jan 13, 2016 4:07 pm

coloin (2015.Dec.13) wrote:

    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 ?

coloin (2016.Jan.10) wrote:

    I am beginning to think that its all down to the sheer number of puzzles per pattern .... and the fact that singles are less likely with non horiz/vert clues in a individual box.

a small reduction in diagonality -- from 9 boxes to 8 -- makes a small difference, which is hard to prove;

but a drastic reduction -- from 9 boxes (game 57) to just 3 (game 49) -- makes a huge difference

    and with only 20 givens -- we may be able to generate all puzzles (for those 2 games) and thus get the proof:
    • # 57 has a "low" number of puzzles,
    • # 49 has a very low number of puzzles
    (based on one small experiment)
pause now?
to resume when game 268 ends
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Pat
 
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Re: Diagonal Patterns in the "Patterns Game"

Postby coloin » Mon Jan 18, 2016 12:52 pm

Box distribution with diagonal givens .....

533332222 - 411 ed symmetrical patterns
533322222 - 355 ed symmetrical patterns
533222222 - 817 ed symmetrical patterns

so we indeed wont be running out of patterns like this
Code: Select all
+---+---+---+
|...|...|..2|
|.1.|.4.|.5.|
|..3|..9|7..|
+---+---+---+
|...|1.2|3..|
|.5.|.3.|.6.|
|..9|4.5|...|
+---+---+---+
|..8|2..|4..|
|.7.|.1.|...|
|6..|...|..9|
+---+---+---+    533222222
coloin
 
Posts: 1637
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Postby Pat » Wed Feb 08, 2017 1:02 pm

m_b_metcalf (2017.Feb.1) wrote:

    This pattern is related to 258,
    which reached 11.3,
    but has a mini-diagonal less.

b9 disturbed,

does this make fewer puzzles ?

OR, with "same" number of puzzles,
does it make them easier ??
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Re: Diagonal Patterns in the "Patterns Game"

Postby tarek » Sat Feb 11, 2017 5:27 pm

I sense another hardest puzzle hunt here!!!

Tarek
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Postby Pat » Tue Jun 13, 2017 9:06 am

coloin (2015.Dec.13) wrote:do diagonal patterns
just have more puzzles
than other non-diagonal patterns ?
    coloin (2016.Jan.10) wrote:I am beginning to think that
    it's all down to the sheer number of puzzles per pattern ....
22 cells given --
  • 285 -- full diagonality
  • 287 -- poor diagonality
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high diagonality

Postby Pat » Fri Aug 18, 2017 9:09 am



      high diagonality
      ( only disturbed in one box )

    champagne's pattern # 288
    ( 23 cells given )
    ==> 11.3

    my pattern # 289
    ( 24 cells given )
    ==> ??
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re: high diagonality

Postby Pat » Sun Aug 20, 2017 2:57 pm

coloin,
pattern # 289 has turned out to be a riddle for you

with high diagonality,
i would've guessed we'd get some 10.* goodies

but finding 9.* here
seems as challenging as 10.* in many other patterns
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