pattern design

Everything about Sudoku that doesn't fit in one of the other sections

pattern design

Postby urhegyi » Thu Aug 05, 2021 6:48 am

I designed a new pattern to create some puzzles in the SE 7.X rating.
I can't explain why but after generating 2000 of them it seems to produce a lot of high rated ones and not an only 7.X.
Bad luck?
Code: Select all
1.....4...9..52.7....7..6.......3..8.8..9..2.6..8..5...6...5.1...84..3..9...6.... ED=8.4/8.4/2.6
8.....3...4..51.2....7..4.......5..4.6..8..1.9..3..2...2...4.8...61..9..7...6.... ED=8.5/8.5/2.6
7.....9...5..24.1....3..8.......9..4.3..7..8.6..5..2...1...3.7...68..4..2...5.... ED=8.9/8.9/2.6
7.....4...2..97.1....8..9.......1..6.7..8..4.4..3..5...5...6.8...17..3..9...2.... ED=9.2/9.2/8.4
2.....1...9..13.8....7..9.......7..2.4..6..1.8..5..4...3...4.6...96..5..7...8.... ED=8.4/8.3/7.2
1.....7...5..79.2....6..8.......7..3.2..3..1.3..4..6...9...3.8...12..4..6...5.... ED=8.8/6.7/6.7
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Re: pattern design

Postby Hajime » Thu Aug 05, 2021 7:51 am

It seems to me that you are ready for the "interactive gaming".
http://forum.enjoysudoku.com/interactive-games-f8.html
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Location: Netherlands

Re: pattern design

Postby JPF » Thu Aug 05, 2021 8:14 am

Here are some ED=7.x
Hidden Text: Show
Code: Select all
1.....2...3..45.6....7..5.......6..1.7..8..3.8..3..4...9...4.7...28..3..6...9....  ED=7.9/7.9/3.4
1.....2...3..45.6....7..5.......1..2.6..3..7.2..4..8...2...9.8...76..1..3...5....  ED=7.9/7.3/6.7
1.....2...3..42.5....6..3.......1..6.2..3..7.5..8..9...8...5.9...59..1..6...8....  ED=7.9/7.3/6.7
1.....2...3..45.6....7..8.......6..2.5..1..3.8..5..7...6...4.7...49..3..9...3....  ED=7.9/7.3/6.7
1.....2...3..45.6....2..3.......1..2.5..7..8.3..5..7...8...4.1...46..9..7...9....  ED=7.8/7.8/7.8
1.....2...3..45.6....2..7.......8..2.5..6..7.7..5..1...8...4.1...49..3..9...3....  ED=7.8/7.8/7.8
1.....2...3..14.5....2..6.......7..2.6..5..3.8..4..9...7...1.8...98..3..6...3....  ED=7.8/7.8/7.8
1.....2...3..14.5....2..3.......6..2.4..5..7.3..4..8...6...1.8...83..7..9...7....  ED=7.8/7.8/7.8
1.....2...3..45.6....2..7.......8..2.5..6..1.8..5..9...7...4.8...49..3..6...3....  ED=7.8/7.8/7.8
1.....2...3..45.6....2..3.......7..2.6..8..3.9..5..4...7...4.1...86..9..5...3....  ED=7.8/7.8/7.8
1.....2...3..42.5....6..4.......5..2.7..3..6.8..7..9...1...7.9...84..1..3...8....  ED=7.8/7.8/7.8
1.....2...3..45.6....7..8.......6..2.5..3..7.9..5..4...2...8.4...96..1..3...9....  ED=7.8/7.8/7.8
1.....2...3..14.5....2..3.......6..2.4..5..7.8..4..9...6...1.8...98..7..3...7....  ED=7.8/7.8/7.8
1.....2...3..42.1....5..4.......4..2.6..3..5.7..6..8...1...6.9...78..1..3...7....  ED=7.8/7.8/7.8
1.....2...3..24.5....1..6.......7..8.4..3..9.6..9..4...5...9.4...12..8..3...8....  ED=7.8/7.8/7.8
1.....2...3..45.6....1..3.......6..7.5..2..8.9..8..5...4...8.5...14..9..2...7....  ED=7.8/7.8/7.8
1.....2...3..24.5....1..6.......3..7.4..7..8.6..8..4...2...8.4...19..8..9...5....  ED=7.8/7.8/7.8
1.....2...3..45.6....1..7.......6..8.2..3..9.7..9..5...7...9.5...14..9..3...8....  ED=7.8/7.8/7.8
1.....2...3..24.5....1..6.......5..7.4..3..8.6..8..4...9...8.4...12..8..3...7....  ED=7.8/7.8/7.8
1.....2...3..45.6....1..3.......3..7.5..7..8.9..8..5...2...8.5...14..9..4...6....  ED=7.8/7.8/7.8
1.....2...3..45.6....1..7.......3..8.5..2..9.7..6..5...4...9.5...14..9..3...8....  ED=7.8/7.8/7.8
1.....2...3..24.5....1..6.......7..8.4..5..9.6..9..4...2...9.4...12..9..7...8....  ED=7.8/7.8/7.8
1.....2...3..24.5....1..6.......7..8.4..3..9.6..9..4...2...9.4...12..9..7...8....  ED=7.8/7.8/7.8
1.....2...3..24.5....1..6.......7..8.4..3..7.6..9..4...5...9.4...12..8..3...8....  ED=7.8/7.8/7.8
1.....2...3..12.4....5..6.......7..8.9..3..2.8..9..1...1...4.7...87..5..3...6....  ED=7.7/7.7/7.6
1.....2...3..14.5....6..4.......7..8.9..3..4.8..9..1...1...5.7...87..6..4...2....  ED=7.7/7.7/7.6
1.....2...3..41.5....6..1.......5..1.6..3..2.3..7..4...8...9.6...23..7..5...8....  ED=7.6/7.6/7.1
1.....2...3..41.5....6..1.......5..1.6..3..2.3..7..4...8...4.6...23..7..5...8....  ED=7.6/7.6/7.1
1.....2...3..45.6....2..7.......6..2.8..3..1.5..9..4...6...8.2...43..9..8...7....  ED=7.6/7.6/6.7
1.....2...3..41.5....2..6.......5..2.7..3..8.9..8..4...5...7.2...43..8..7...6....  ED=7.6/7.6/6.7
1.....2...3..45.6....2..7.......6..2.8..1..3.7..5..9...6...4.2...48..3..5...3....  ED=7.6/7.6/6.7
1.....2...3..45.6....2..7.......6..2.8..9..3.7..5..1...6...4.2...48..3..5...3....  ED=7.6/7.6/6.7
1.....2...3..12.4....5..6.......7..2.1..3..5.8..9..7...4...5.6...87..9..3...8....  ED=7.6/7.6/3.8
1.....2...3..45.6....2..7.......6..2.7..1..3.8..5..9...8...4.1...49..3..6...3....  ED=7.6/7.6/3.4
1.....2...3..45.6....7..5.......8..2.4..3..7.9..4..8...6...2.8...98..1..3...9....  ED=7.5/7.5/7.2
1.....2...3..45.6....7..5.......7..2.4..3..7.8..4..9...6...2.9...86..1..3...8....  ED=7.5/7.5/7.2
1.....2...3..45.6....7..4.......6..1.7..3..4.8..9..5...8...2.7...23..9..3...8....  ED=7.5/7.5/4.2
1.....2...3..45.6....3..4.......2..1.6..7..8.9..4..6...5...8.2...89..3..7...3....  ED=7.5/7.5/3.4
1.....2...3..12.4....5..6.......6..2.7..3..5.8..1..9...2...5.6...59..7..3...8....  ED=7.5/7.5/3.4
1.....2...3..45.6....2..3.......6..5.2..1..7.6..8..9...6...7.4...19..8..3...8....  ED=7.5/7.5/2.6
1.....2...3..42.5....6..4.......6..5.1..5..7.8..4..1...2...7.3...82..9..3...9....  ED=7.5/7.5/2.6
1.....2...3..45.6....2..3.......6..5.2..1..7.6..8..9...6...7.4...79..8..3...8....  ED=7.5/7.5/2.6
1.....2...3..45.6....2..7.......6..5.2..1..8.6..9..3...6...8.4...13..9..7...9....  ED=7.5/7.5/2.6
1.....2...3..41.5....6..4.......2..7.6..3..4.7..8..9...1...5.6...23..8..9...7....  ED=7.5/7.3/6.7
1.....2...3..45.6....7..5.......6..5.7..3..2.8..9..4...8...1.7...13..9..6...8....  ED=7.4/7.4/7.3
1.....2...2..34.5....6..3.......7..6.5..8..2.7..9..4...6...5.1...43..9..2...7....  ED=7.4/7.4/7.2
1.....2...3..42.1....5..6.......5..7.4..3..2.8..4..9...2...7.6...61..7..3...8....  ED=7.4/7.4/7.2
1.....2...3..42.5....6..7.......5..1.8..3..2.9..4..5...2...6.7...75..8..3...9....  ED=7.4/7.4/7.1
1.....2...3..45.6....7..5.......8..2.4..3..7.5..4..6...2...9.8...76..1..3...5....  ED=7.4/7.4/7.1
1.....2...3..45.6....3..7.......7..8.4..6..2.5..4..9...7...2.1...18..5..6...3....  ED=7.4/7.4/7.1
1.....2...3..45.6....7..5.......6..5.7..3..1.3..8..4...4...1.7...23..8..6...9....  ED=7.4/7.4/6.7
1.....2...3..41.5....2..6.......7..6.8..5..9.6..8..4...5...8.7...83..1..4...9....  ED=7.4/7.4/6.7
1.....2...3..41.5....2..6.......7..2.8..5..3.6..3..4...5...8.7...81..3..4...9....  ED=7.4/7.4/6.7
1.....2...3..41.5....2..6.......7..8.9..5..3.6..3..4...5...9.2...91..3..4...8....  ED=7.4/7.4/6.7
1.....2...3..45.6....2..7.......8..2.5..9..3.7..5..8...8...9.1...46..3..9...3....  ED=7.3/7.3/7.3
1.....2...3..24.5....6..4.......5..1.6..3..2.7..8..9...7...1.6...23..8..4...7....  ED=7.3/7.3/7.3
1.....2...2..34.5....6..3.......7..8.5..6..2.2..9..4...6...5.1...43..9..8...7....  ED=7.3/7.3/7.3
1.....2...3..45.6....2..7.......8..2.5..9..3.7..5..9...8...9.1...46..3..9...3....  ED=7.3/7.3/7.3
1.....2...3..45.6....1..7.......2..8.4..6..2.9..4..3...5...7.1...78..9..6...3....  ED=7.3/7.3/7.2
1.....2...3..42.5....6..7.......6..7.5..3..2.8..4..9...2...7.9...95..1..3...8....  ED=7.3/7.3/7.2
1.....2...3..45.6....1..5.......7..2.8..3..1.6..4..8...2...9.8...96..7..3...5....  ED=7.3/7.3/7.2
1.....2...3..42.1....5..6.......4..7.8..3..2.9..8..1...2...8.6...91..4..3...9....  ED=7.3/7.3/7.2
1.....2...3..45.6....1..7.......7..8.4..6..7.9..4..3...5...2.1...28..9..6...3....  ED=7.3/7.3/7.2
1.....2...3..42.5....6..7.......5..6.8..3..2.9..4..5...2...7.8...85..1..3...9....  ED=7.3/7.3/7.2
1.....2...3..41.5....3..6.......6..7.4..5..6.8..4..1...1...2.9...27..8..5...3....  ED=7.2/7.2/7.2
1.....2...3..41.5....3..6.......2..7.4..5..2.8..4..1...1...6.9...67..8..5...3....  ED=7.2/7.2/7.2
1.....2...3..12.4....5..6.......4..6.1..3..2.7..1..8...2...6.5...84..9..3...7....  ED=7.2/7.2/7.2
1.....2...3..42.5....5..3.......6..1.4..7..2.8..4..9...2...1.3...39..6..7...8....  ED=7.2/7.2/7.2
1.....2...3..42.5....6..7.......5..7.4..3..2.8..4..9...2...7.1...19..5..3...6....  ED=7.2/7.2/7.2
1.....2...3..41.5....6..7.......7..8.4..5..7.9..4..1...9...2.6...28..9..5...3....  ED=7.2/7.2/7.2
1.....2...3..24.5....3..6.......1..6.4..5..1.6..7..3...8...7.9...39..4..2...8....  ED=7.2/7.2/7.2
1.....2...3..41.5....6..7.......2..8.4..5..2.9..4..1...9...7.6...78..9..5...3....  ED=7.2/7.2/7.2
1.....2...3..45.6....2..7.......1..8.4..6..2.9..4..5...8...7.1...78..9..6...3....  ED=7.2/7.2/7.2
1.....2...3..14.5....3..6.......6..7.1..5..6.8..1..4...4...2.9...37..8..5...3....  ED=7.2/7.2/7.2
1.....2...3..24.5....3..6.......7..6.1..5..8.9..2..1...4...8.6...89..3..6...3....  ED=7.1/7.1/7.1
1.....2...3..14.5....6..3.......1..7.5..7..8.9..3..5...4...8.2...89..6..2...6....  ED=7.1/7.1/7.1
1.....2...3..41.5....6..3.......4..5.7..5..8.9..3..7...1...8.2...49..6..2...6....  ED=7.1/7.1/7.1
1.....2...3..42.5....6..4.......7..2.8..3..6.5..4..1...7...1.8...67..9..3...5....  ED=7.1/7.1/7.1
1.....2...3..45.6....3..7.......6..1.8..9..4.7..8..3...6...1.9...26..4..8...5....  ED=7.1/7.1/7.1
1.....2...3..45.6....3..4.......7..2.1..6..8.9..4..1...5...8.2...79..3..2...3....  ED=7.1/7.1/7.1
1.....2...3..45.6....3..4.......7..2.1..6..8.9..4..1...5...8.2...89..3..2...3....  ED=7.1/7.1/7.1
1.....2...3..24.5....3..6.......7..6.1..5..8.9..2..1...4...8.6...79..3..6...3....  ED=7.1/7.1/7.1
1.....2...3..24.5....6..4.......7..8.6..3..2.3..9..7...1...8.6...24..5..6...1....  ED=7.1/7.1/7.1
1.....2...3..24.5....3..6.......5..1.7..8..2.6..7..9...5...9.8...25..4..9...3....  ED=7.1/7.1/7.1
1.....2...3..42.5....6..4.......3..5.1..5..7.6..4..1...2...7.6...78..3..8...9....  ED=7.0/7.0/7.0
1.....2...3..42.5....6..4.......3..5.1..5..7.8..4..1...2...7.6...78..3..6...9....  ED=7.0/7.0/7.0
1.....2...3..45.6....7..4.......3..6.1..6..8.6..4..9...5...8.2...89..3..2...7....  ED=7.0/7.0/7.0
1.....2...3..45.6....1..4.......3..6.1..6..7.8..4..9...5...7.2...79..3..2...8....  ED=7.0/7.0/7.0
1.....2...3..41.5....2..6.......7..6.8..5..3.6..3..4...5...8.7...81..3..4...9....  ED=7.0/7.0/6.7
1.....2...3..45.6....2..7.......1..7.8..6..2.7..3..4...6...8.1...85..3..4...9....  ED=7.0/7.0/6.7
1.....2...3..45.6....2..7.......8..7.9..6..2.7..3..4...6...9.1...95..8..4...8....  ED=7.0/7.0/6.7
1.....2...3..45.6....2..7.......2..7.8..6..3.7..3..4...6...8.9...85..3..4...1....  ED=7.0/7.0/6.7
1.....2...3..24.5....6..4.......1..2.5..3..6.4..7..8...2...9.8...85..1..3...4....  ED=7.0/7.0/6.7
1.....2...3..45.6....6..4.......3..7.1..7..8.7..4..9...5...8.2...89..3..2...6....  ED=7.0/7.0/3.4

JPF
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Re: pattern design

Postby denis_berthier » Thu Aug 05, 2021 9:01 am

urhegyi wrote:I designed a new pattern to create some puzzles in the SE 7.X rating.
I can't explain why but after generating 2000 of them it seems to produce a lot of high rated ones and not an only 7.X.
Bad luck?


To better see the pattern:
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 . ! . . . !
     +-------+-------+-------+


I tried with gsf's generator. In 1000 minimals, I get:
Code: Select all
72  1.x
141 2.x
35  3.x
55  4.x
6   5.x
97  6.x
352 7.x
198 8.x
44  9.x


Compared to random grids with no a priori pattern, the mean is very high. But it is known that some dose of (broken) symmetry tends to increase the mean rating.
Apart from this, I can see no reason why a pattern should generate puzzles only in the 7.x range. I wouldn't call it bad luck if it has higher ratings.
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Posts: 3166
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Location: Paris

Re: pattern design

Postby JPF » Mon Aug 09, 2021 4:18 pm

Apart from this, I can see no reason why a pattern should generate puzzles only in the 7.x range.

This pattern:
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|
+-----+-----+-----+

contains only 7 non isomorphic valid puzzles, found by blue.
All ratings are 7.2 x:
Code: Select all
1.2...3.4.5.....1.6.7...8.2...1.2.......5.......3.6...2.1...4.8.4.....3.8.5...6.9   ED=7.2/2.6/2.6
1.2...3.4.5.....1.6.7...8.2...1.2.......5.......3.6...2.1...4.8.4.....3.8.5...9.6   ED=7.2/2.6/2.6
1.2...3.4.5.....1.6.7...8.2...1.2.......5.......3.7...5.8...7.9.4.....3.2.1...4.8   ED=7.2/2.6/2.6
1.2...3.4.5.....1.6.7...8.2...1.2.......5.......3.7...5.8...9.7.4.....3.2.1...4.8   ED=7.2/2.6/2.6
1.2...3.4.5.....6.6.7...2.8...1.2.......5.......3.9...5.9...8.7.4.....3.2.8...4.9   ED=7.2/2.3/2.3
1.2...3.4.5.....6.6.7...8.2...1.2.......5.......3.9...5.8...9.7.4.....3.2.9...4.8   ED=7.2/2.3/2.3
1.2...3.4.3.....2.5.4...6.7...3.6.......1.......2.5...8.6...9.3.5.....8.9.3...4.2   ED=7.2/2.6/2.6

btw, it seems unwise to use gsf's program to establish the rating distribution of valid puzzles compatible with a given pattern.
We have to be sure that the generation of these puzzles is carried out without bias.
Personally, I am not aware of the methodology used by gsf.

JPF
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Re: pattern design

Postby denis_berthier » Mon Aug 09, 2021 6:28 pm

JPF wrote:
Apart from this, I can see no reason why a pattern should generate puzzles only in the 7.x range.

This pattern:
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|
+-----+-----+-----+

contains only 7 non isomorphic valid puzzles, found by blue.
All ratings are 7.2 x:

Yes, but that's purely factual. After browsing the reference, I can see no general reason why it should be so. It's just the result of systematic computations. Nice pattern and result, though.
Generally speaking, there are no criteria that'd allow anyone to tell in advance that all the puzzles for some pattern are in some given range.

JPF wrote:btw, it seems unwise to use gsf's program to establish the rating distribution of valid puzzles compatible with a given pattern.
We have to be sure that the generation of these puzzles is carried out without bias.
Personally, I am not aware of the methodology used by gsf.

I never mentioned the real distribution for urhregyi's pattern. I informally compared the puzzles generated for it with those for other patterns, using gsf's generator in all cases (i.e. with the same bias in all cases). I don't think all this is worth any more formal analysis and I don't need it to be intimately certain that the unbiased mean rating for puzzles with this pattern is much higher than the general unbiased mean rating.
denis_berthier
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