coloin wrote:7 more patterns ¬
Confirm 7 new 6plus27 patterns. Good job! Total number of konown 6plus27 at the moment - 223.
Please send your patterns as puzzles only, without attaching pattern form.
Serg
Anticorner maximal invalid patterns
Re: Anticorner maximal invalid patterns
by Serg » Sat Aug 05, 2023 9:35 pm
Hi, coloin!
Confirm 7 new 6plus27 patterns. Good job! Total number of konown 6plus27 at the moment - 223.
Please send your patterns as puzzles only, without attaching pattern form.
Serg
Confirm 7 new 6plus27 patterns. Good job! Total number of konown 6plus27 at the moment - 223.
Please send your patterns as puzzles only, without attaching pattern form.
Serg
- Serg
- 2018 Supporter
- Posts: 890
- Joined: 01 June 2010
- Location: Russia
Re: Anticorner maximal invalid patterns
by blue » Sun Aug 06, 2023 12:19 pm
92 more ...
Hidden Text: Show
- blue
- Posts: 1045
- Joined: 11 March 2013
Re: Anticorner maximal invalid patterns
by coloin » Sun Aug 06, 2023 2:40 pm
blue wrote: 92 more
Very good !!
I had randomly generated 13 more - but all were in that last batch of 92 ...
Im tempted to think you somehow added 6 clues to all the 3-corner classes !!
- coloin
- Posts: 2494
- Joined: 05 May 2005
- Location: Devon
Re: Anticorner maximal invalid patterns
by JPF » Sun Aug 06, 2023 3:09 pm
Blue,impressive results!
Is your search exhaustive, or is there still room for other solutions found more or less randomly?
JPF
Is your search exhaustive, or is there still room for other solutions found more or less randomly?
JPF
- JPF
- 2017 Supporter
- Posts: 6139
- Joined: 06 December 2005
- Location: Paris, France
Re: Anticorner maximal invalid patterns
by Serg » Sun Aug 06, 2023 3:13 pm
Hi, Blue!
I confirm new 92 6plus27 patterns. Great work! I was somewhat wrong saying that my initial 6plus27 patterns list (117 patterns) is close to full
.
Here is updated 6plus27 patterns list with 315 patterns. (All patterns have Anticorner Minlex Form, permitted VPTs providing B6, B8 and B9 boxes full.)
Serg
blue wrote:92 more ...
I confirm new 92 6plus27 patterns. Great work! I was somewhat wrong saying that my initial 6plus27 patterns list (117 patterns) is close to full
.Here is updated 6plus27 patterns list with 315 patterns. (All patterns have Anticorner Minlex Form, permitted VPTs providing B6, B8 and B9 boxes full.)
Hidden Text: Show
Serg
- Serg
- 2018 Supporter
- Posts: 890
- Joined: 01 June 2010
- Location: Russia
Re: Anticorner maximal invalid patterns
by blue » Sun Aug 06, 2023 4:24 pm
JPF wrote:Is your search exhaustive, or is there still room for other solutions found more or less randomly?
There's still room.
I got a list of puzzles covering 311 shapes, using {-1,+1}/{-2,+1} on (27+7)'s.
It was missing 4 shapes for sure, and probably more.
- blue
- Posts: 1045
- Joined: 11 March 2013
Re: Anticorner maximal invalid patterns
by Serg » Sun Aug 06, 2023 10:42 pm
Hi!
Here is the next portion of maximal invalid anticorner patterns - 23 patterns.
the same in line form:
Serg
Here is the next portion of maximal invalid anticorner patterns - 23 patterns.
- Code: Select all
X7 X8 X9
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . .|. . .| |. . .|. . .|. . .|
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . x|. x .| |. . .|. . x|. x .| |. . .|. . x|. x .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . x|. . .|x x x|
|. . .|. x .|x x x| |. . x|. . .|x x x| |. . x|. . .|x x x|
|. . x|. . .|x x x| |. x .|. . .|x x x| |. . x|. . .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . x|x x x|x x x| |. . x|x x x|x x x| |. . .|x x x|x x x|
|. x .|x x x|x x x| |. x .|x x x|x x x| |x x x|x x x|x x x|
|. x .|x x x|x x x| |x . .|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X10 X11 X12
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . .|. . .| |. . .|. . .|. . .|
|. . .|. . .|. x x| |. . .|. . .|. x x| |. . .|. . .|. x x|
|. . .|. . x|x . .| |. . .|. . x|x . .| |. . .|. . x|x . .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . x|. . .|x x x| |. . x|. . .|x x x| |. . x|. . .|x x x|
|. . x|. . .|x x x| |. x .|. . .|x x x| |. x .|. . .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. x .|x x x|x x x| |. . x|x x x|x x x| |. . x|x x x|x x x|
|x . .|x x x|x x x| |. x .|x x x|x x x| |x . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X13 X14 X15
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . .|. . .| |. . .|. . .|. . .|
|. . .|. . .|. x x| |. . .|. . .|. x x| |. . .|. . .|. x x|
|. . .|. x x|. . .| |. . .|. x x|. . .| |. . .|. x x|x . .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . x|. . .|x x x| |. . x|. . .|x x x| |. . x|. . .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . x|x x x|x x x| |. . x|x x x|x x x| |. . .|x x x|x x x|
|. . x|x x x|x x x| |. x .|x x x|x x x| |. . x|x x x|x x x|
|x x x|x x x|x x x| |x . .|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X16 X17 X18
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . .|. . .| |. . .|. . .|. . .|
|. . .|. . .|x x x| |. . .|. . x|. . x| |. . .|. . x|. . x|
|. . .|. x x|. . .| |. . .|. x .|. x .| |. . .|. x .|. x .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . x|. . .|x x x| |. . x|. . .|x x x| |. . x|. . .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. x .|x x x|x x x|
|. . x|x x x|x x x| |x x x|x x x|x x x| |x . .|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X19 X20 X21
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . x|. x x| |. . .|. . x|. x x| |. . .|. . x|. x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . x|. . .|x x x| |. . x|. . .|x x x| |. . x|. . .|x x x|
|. . x|. . .|x x x| |. . x|. . .|x x x| |. x .|. . .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . x|x x x|x x x| |. . x|x x x|x x x|
|x x x|x x x|x x x| |. x .|x x x|x x x| |. . x|x x x|x x x|
|x x x|x x x|x x x| |x . .|x x x|x x x| |x . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X22 X23 X24
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . x|x x x| |. . .|. . x|x x x| |. . .|. . x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . .|. . .|x x x| |. . x|. . .|x x x| |. . x|. . .|x x x|
|. . x|. x .|x x x| |. . x|. . .|x x x| |. x .|. . .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . x|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. x .|x x x|x x x| |. x .|x x x|x x x| |x x x|x x x|x x x|
|x . .|x x x|x x x| |x . .|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X25 X26 X27
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|. x .| |. . .|. . .|. x .| |. . .|. . .|. x x|
|. . .|. . x|x . .| |. . .|. . x|x . .| |. . .|. . x|. . x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . x|. . .|x x x| |. . x|. . .|x x x| |. . x|. . .|x x x|
|. . x|. . .|x x x| |. x .|. . .|x x x| |. x .|. . .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. x .|x x x|x x x| |. . x|x x x|x x x| |x x x|x x x|x x x|
|x . .|x x x|x x x| |x . .|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X28 X29
+-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|. x x| |. . .|. . x|. . .|
|. . .|. x x|. . x| |. . .|. x .|. x .|
+-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x|
|. . .|. . .|x x x| |. . .|. . .|x x x|
|. . x|. . .|x x x| |. . x|. . .|x x x|
+-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+
the same in line form:
Hidden Text: Show
Serg
- Serg
- 2018 Supporter
- Posts: 890
- Joined: 01 June 2010
- Location: Russia
Re: Anticorner maximal invalid patterns
by coloin » Mon Aug 07, 2023 12:41 pm
Good progress ...
As i am sure you will show in future posts... 2 clues in band 1, means that ? 7 more clues are necessarey in B457, eg
So 3 clues in band 1 / shute 1 would appear to be obligatory to allow 6 clues in total to solve ...
Out of a good few unlikely patterns looked at, this pattern ...
has not been shown to have a valid puzzle
As i am sure you will show in future posts... 2 clues in band 1, means that ? 7 more clues are necessarey in B457, eg
- Code: Select all
+---+---+---+
|...|...|...|
|...|..4|...|
|..5|...|...|
+---+---+---+
|...|...|123|
|.1.|.7.|456|
|.6.|.5.|789|
+---+---+---+
|2..|391|875|
|3..|846|912|
|8..|527|634|
+---+---+---+
So 3 clues in band 1 / shute 1 would appear to be obligatory to allow 6 clues in total to solve ...
Out of a good few unlikely patterns looked at, this pattern ...
- Code: Select all
+---+---+---+
|...|...|...|
|.67|...|...|
|...|1..|...|
+---+---+---+
|..2|...|789|
|...|..9|451|
|9..|...|632|
+---+---+---+
|...|764|398|
|...|813|275|
|...|952|146|
+---+---+---+
has not been shown to have a valid puzzle
- coloin
- Posts: 2494
- Joined: 05 May 2005
- Location: Devon
Re: Anticorner maximal invalid patterns
by Serg » Mon Aug 07, 2023 7:13 pm
Hi, coloin!
I've done these checks on my valid anticorner patterns "base" (3769 patterns).
So, both your conjectures are still alive.
My solver says "More than 1 solutions" for this puzzle
Serg
coloin wrote:As i am sure you will show in future posts... 2 clues in band 1, means that ? 7 more clues are necessarey in B457, eg
- Code: Select all
+---+---+---+
|...|...|...|
|...|..4|...|
|..5|...|...|
+---+---+---+
|...|...|123|
|.1.|.7.|456|
|.6.|.5.|789|
+---+---+---+
|2..|391|875|
|3..|846|912|
|8..|527|634|
+---+---+---+
So 3 clues in band 1 / shute 1 would appear to be obligatory to allow 6 clues in total to solve ...
I've done these checks on my valid anticorner patterns "base" (3769 patterns).
- Code: Select all
Number of clues in B457/B235 boxes, when band1/stack1 contains 2 clues
7 375
8 233
Number of clues in band1/stack1 for 6 clues in anticorner area case
3 112
4 187
5 16
So, both your conjectures are still alive.
coloin wrote:Out of a good few unlikely patterns looked at, this pattern ...
- Code: Select all
+---+---+---+
|...|...|...|
|.67|...|...|
|...|1..|...|
+---+---+---+
|..2|...|789|
|...|..9|451|
|9..|...|632|
+---+---+---+
|...|764|398|
|...|813|275|
|...|952|146|
+---+---+---+
has not been shown to have a valid puzzle
My solver says "More than 1 solutions" for this puzzle
Serg
- Serg
- 2018 Supporter
- Posts: 890
- Joined: 01 June 2010
- Location: Russia
Re: Anticorner maximal invalid patterns
by Serg » Mon Aug 07, 2023 8:50 pm
Hi!
Here is part 3 of new maximal invalid anticorner patterns.
The same in Line Form.
Serg
Here is part 3 of new maximal invalid anticorner patterns.
- Code: Select all
X30 X31 X32
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . .|. . .| |. . .|. . .|. . .|
|. . .|. . .|. . x| |. . .|. . x|. . .| |. . .|. . x|. . .|
|. . x|. . .|. x .| |. . x|. x .|. . .| |. . x|. x .|. . .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. x x|x x x| |. . .|. x x|x x x| |. . .|x . x|x x x|
|. . .|. x x|x x x| |. . .|. x x|x x x| |. . .|x . x|x x x|
|. . .|. x x|x x x| |. . .|. x x|x x x| |. . .|x . x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. x .|x x x|x x x| |. x .|x x x|x x x| |. x .|x x x|x x x|
|. x .|x x x|x x x| |. x .|x x x|x x x| |. x .|x x x|x x x|
|x . .|x x x|x x x| |x . .|x x x|x x x| |x . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X33 X34 X35
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . .|. . .| |. . .|. . .|. . .|
|. . .|. . x|. . .| |. . .|. . x|. . x| |. . .|. . x|. . x|
|. . x|. x .|. . .| |. . x|. . .|. . .| |. . x|. . .|. . .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x .|x x x| |. . .|. x x|x x x| |. . .|x x .|x x x|
|. . .|x x .|x x x| |. . .|. x x|x x x| |. . .|x x .|x x x|
|. . .|x x .|x x x| |. . .|. x x|x x x| |. . .|x x .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. x .|x x x|x x x| |. x .|x x x|x x x| |. x .|x x x|x x x|
|. x .|x x x|x x x| |. x .|x x x|x x x| |. x .|x x x|x x x|
|x . .|x x x|x x x| |x . .|x x x|x x x| |x . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X36 X37 X38
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. x .|
|. . x|. . .|. . x| |. . x|. . .|. . x| |. . .|. . x|x . .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . x|x x x| |. . .|. x x|x x x| |. . .|. . .|x x x|
|. . .|x x .|x x x| |. . .|. x x|x x x| |. . .|. . .|x x x|
|. . .|x x .|x x x| |. . .|. x x|x x x| |. . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. x .|x x x|x x x| |. x .|x x x|x x x| |. . .|x x x|x x x|
|. x .|x x x|x x x| |. x .|x x x|x x x| |x x x|x x x|x x x|
|x . .|x x x|x x x| |x . .|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X39 X40 X41
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|. x .| |. . .|. . .|. x .| |. . .|. . .|. x .|
|. . .|. . x|x . .| |. . .|. . x|x . .| |. . .|. . x|x . .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . .|. . x|x x x| |. . .|. x .|x x x| |x x x|. . .|x x x|
|. . .|x x .|x x x| |. . .|x . x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x| |. . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X42 X43 X44
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|. x .| |. . .|. . .|x x .| |. . .|. . .|x x .|
|. . .|. . x|x . .| |. . .|. . x|. . .| |. . .|. . x|. . .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . x|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . .|. x .|x x x| |. . .|. . .|x x x| |. . .|. . x|x x x|
|. . .|x . .|x x x| |. . .|x x x|x x x| |. . .|x x .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X45 X46 X47
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|x x .| |. . .|. . .|x x .| |. . .|. . .|x x .|
|. . .|. . x|. . .| |. . .|. . x|. . .| |. . .|. . x|. . .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . x|x x x|
|. . .|. x .|x x x| |x x x|. . .|x x x| |. . .|. x .|x x x|
|. . .|x . x|x x x| |x x x|x x x|x x x| |. . .|x . .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |. . .|x x x|x x x| |x x x|x x x|x x x|
|x x x|x x x|x x x| |. . .|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X48 X49
+-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|x x .| |. . .|. . .|x x .|
|. . x|. . .|. . .| |. . x|. . .|. . .|
+-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |x x x|. . .|x x x|
+-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+
The same in Line Form.
Hidden Text: Show
Serg
- Serg
- 2018 Supporter
- Posts: 890
- Joined: 01 June 2010
- Location: Russia
Re: Anticorner maximal invalid patterns
by coloin » Tue Aug 08, 2023 8:24 pm
Indeed the pattern I used does not have valid puzzles
if I had used your templates for the crossing bands I would have known why
if I had used your templates for the crossing bands I would have known why
- Code: Select all
+---+---+---+ |---+---+---+
|...|...|...| |...|...|...|
|.67|...|...| |.67|...|...|
|...|1..|...| |...|1..|...|
+---+---+---+ +---+---+---+
|..2|...|789| |..2|341|789|
|...|..9|451| -> |...|629|451|
|9..|...|632| |9..|578|632|
+---+---+---+ +---+---+---+
|...|764|398| |...|764|398|
|...|813|275| |...|813|275|
|...|952|146| |...|952|146|
+---+---+---+ +---+---+---+ no valid puzzles with this near maximal pattern
- coloin
- Posts: 2494
- Joined: 05 May 2005
- Location: Devon
Re: Anticorner maximal invalid patterns
by coloin » Wed Aug 09, 2023 8:45 pm
A prerequisite for valid 6plus27 patterns would appear to be 2,3,4 or 5 clues in box 1
At least 3 clues in band 1 and stack 1
Either 0 or 1 clue in box 5
The patterns [315 in total found so far] will be either have
5 clues in B12347 [ one of 36 patterns] and 1 clue in B5 [103/315 valid found]
or
6 clues in B12347 and an empty B5 [ includes the 36 patterns plus 1 clue in B12347 and maybe other patterns ] [212/315 valid found]
At least 3 clues in band 1 and stack 1
Either 0 or 1 clue in box 5
The patterns [315 in total found so far] will be either have
5 clues in B12347 [ one of 36 patterns] and 1 clue in B5 [103/315 valid found]
or
6 clues in B12347 and an empty B5 [ includes the 36 patterns plus 1 clue in B12347 and maybe other patterns ] [212/315 valid found]
Last edited by coloin on Thu Aug 24, 2023 3:54 pm, edited 1 time in total.
- coloin
- Posts: 2494
- Joined: 05 May 2005
- Location: Devon
Re: Anticorner maximal invalid patterns
by Serg » Wed Aug 09, 2023 11:31 pm
Hi, coloin!
You can see a counterexample with 1 clue in B1 box in my post (in this thread).
"5 clues in B1 box" is impossible. (I checked all templates with 5 clues in B1 box and filled B5689 boxes - all need at least 2 clues in B5 box to produce valid pattern.) Hence 1-4 clues in B1 box were already observed among 6plus27 valid patterns.
No counterexamples were observed yet.
This is true.
Serg
coloin wrote:A prerequisite for valid 6plus27 patterns would appear to be 2,3,4 or 5 clues in box 1
You can see a counterexample with 1 clue in B1 box in my post (in this thread).
"5 clues in B1 box" is impossible. (I checked all templates with 5 clues in B1 box and filled B5689 boxes - all need at least 2 clues in B5 box to produce valid pattern.) Hence 1-4 clues in B1 box were already observed among 6plus27 valid patterns.
coloin wrote:At least 3 clues in band 1 and stack 1
No counterexamples were observed yet.
coloin wrote:Either 0 or 1 clue in box 5
The patterns will be either have
5 clues in B12347 [ one of 36 patterns] and 1 clue in B5 [212/315 valid found]
or
6 clues in B12347 and an empty B5 [ includes the 36 patterns plus 1 clue in B12347 and maybe other patterns ] [103/315 valid found]
This is true.
Serg
- Serg
- 2018 Supporter
- Posts: 890
- Joined: 01 June 2010
- Location: Russia
Re: Anticorner maximal invalid patterns
by Serg » Thu Aug 10, 2023 4:55 pm
Hi, coloin!
More general statement can be proved.
Definition. Crossing of pattern is pair of some band and some stack of Sudoku solution grid.
Fact1. Any band (stack) of valid pattern must have not less than 2 clues.
Fact2. Any crossing of valid pattern must have not less than 5 clues.
Statement. Any crossing of valid pattern must have not less than 3 clues in its band or in its stack.
Proof. Any crossing of valid pattern has not less than 2 clues in its band or in its stack (Fact1). Assume a crossing has exactly 2 clues in his band. In this case a crossing must have at least 3 clues in its stack (Fact2). So, any crossing of valid pattern can not have exactly 2 clues in its band and in its stack simultaneously. The statement is proved.
Serg
coloin wrote:A prerequisite for valid 6plus27 patterns would appear to be ...
At least 3 clues in band 1 and stack 1
More general statement can be proved.
Definition. Crossing of pattern is pair of some band and some stack of Sudoku solution grid.
Fact1. Any band (stack) of valid pattern must have not less than 2 clues.
Fact2. Any crossing of valid pattern must have not less than 5 clues.
Statement. Any crossing of valid pattern must have not less than 3 clues in its band or in its stack.
Proof. Any crossing of valid pattern has not less than 2 clues in its band or in its stack (Fact1). Assume a crossing has exactly 2 clues in his band. In this case a crossing must have at least 3 clues in its stack (Fact2). So, any crossing of valid pattern can not have exactly 2 clues in its band and in its stack simultaneously. The statement is proved.
Serg
- Serg
- 2018 Supporter
- Posts: 890
- Joined: 01 June 2010
- Location: Russia
Re: Anticorner maximal invalid patterns
by Serg » Thu Aug 10, 2023 5:00 pm
Hi!
Next 11 anticorner maximal invalid patterns are available.
The same in Line Form.
Serg
Next 11 anticorner maximal invalid patterns are available.
- Code: Select all
X50 X51 X52
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . .|. . .| |. . .|. . .|. . .|
|. . x|. . .|. . .| |. . x|. . .|. . .| |. . x|. . .|. . .|
|. x .|. . .|. . x| |. x .|. . .|. . x| |. x .|. . .|. . x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. . .|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |x x x|x x x|x x x|
|. . .|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x| |. . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X53 X54 X55
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . .|. . .| |. . .|. . .|. . .|
|. . x|. . .|. . .| |. . x|. . .|. . .| |. . x|. . .|. . .|
|. x .|. . .|. . x| |. x .|. . .|. . x| |. x .|. . .|. . x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |x . .|. . .|x x x|
|. . .|x x x|x x x| |x x x|. . .|x x x| |x . .|x x x|x x x|
|x x x|. . .|x x x| |x x x|x x x|x x x| |x . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |x . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |x . .|x x x|x x x|
|x x x|x x x|x x x| |. . .|x x x|x x x| |x . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X56 X57 X58
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|. . x| |. . .|. . .|. x .| |. . .|. . .|. x .|
|. . x|. . .|. . x| |. . .|. . x|x . .| |. . .|. . x|x . .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . x|x x x| |. . .|. . .|x x x| |. . .|x x x|x x x|
|. . .|. . x|x x x| |. . .|. . .|x x x| |x x x|. . .|x x x|
|. . .|x x .|x x x| |. . .|. x x|x x x| |x x x|. . .|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. x .|x x x|x x x| |. . x|x x x|x x x| |. . .|x x x|x x x|
|. x .|x x x|x x x| |. x .|x x x|x x x| |. . .|x x x|x x x|
|x . .|x x x|x x x| |x x x|x x x|x x x| |. . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
X59 X60
+-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . x|
|. . .|. . .|x x .| |. . x|. . .|. . .|
|. . .|. . x|. . .| |. x .|. . .|. . .|
+-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|. . .|x x x|
|x x x|. . .|x x x| |x . .|x x x|x x x|
|x x x|. . .|x x x| |x . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+
The same in Line Form.
Hidden Text: Show
Serg
- Serg
- 2018 Supporter
- Posts: 890
- Joined: 01 June 2010
- Location: Russia
