The New Sudoku Players' Forum

[champagne]

It seems that the conjecture is dead.
However, where we are, it would be interesting to have the full list of 3+4+27 puzzles


12345678945718962368927314524............79................1..........54......... ED=1.5/1.2/1.2
12345678945718962368927314524............79................1..........52......... ED=1.5/1.2/1.2
12345678945718962368927314524............73................1..........54......... ED=1.5/1.2/1.2
12345678945718962368927314524............73................1..........52......... ED=1.5/1.2/1.2
12345678945718962368927315424............79................1..........48......... ED=1.5/1.2/1.2
12345678945718962368927315424............79................1..........45......... ED=1.5/1.2/1.2
12345678945718962368927315424............73................1..........48......... ED=1.5/1.2/1.2
12345678945718962368927315424............73................1..........45......... ED=1.5/1.2/1.2

[blue]

Very good
Congratulations.

How did you do it ?

[champagne]

Very good
Congratulations.

How did you do it ?

As I wrote earlier, I started a check of my ~ 66000 patterns made of the 1871 * columns permutations in stacks 2/3 against the 401 minlex bands of gsf's catalog;

I don't have the power that mladen can lock for a while, so it is a slow process.
This came this morning (likely during the night) in one of the 10 ongoing batches.

I am convinced that we have to learn from the exhaustive count, so this partial result should not stop what you are doing with mladen.

[champagne]

more in an ongoing run

12345678945718923669873251496...........7.8...............2...........91.........
12345678945718923669873251496...........7.8...............2...........61.........
12345678945718923669873251496...........7.3...............2...........91.........
12345678945718923669873251496...........7.3...............2...........61.........

EDIT these ones in a closed batch

12345678945718923669873251496..........8...7.................4.....95............
12345678945718923669873251496..........8...7.................4.....65............
12345678945718923669873251496..........3...7.................4.....95............
12345678945718923669873251496..........3...7.................4.....65............

[JPF]

Hi champagne,

interesting!

Up to now your patterns are isomorphic:

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


JPF

[champagne]

Hi champagne,

interesting!

Up to now your patterns are isomorphic:

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


JPF

That's a reason why I think that it would be anyway a good idea to make a full search using blue's "optimal" basis.

It could be also that some of these puzzles are morphs of the same one. My ~66000 pattern basis is not as well done as blue's basis.

Last but not least in the wider scope of that thread, it will be interesting to see whether the found puzzles can give new 17 clues.

So far we have no 17 clues puzzle with 3+4+10 and (if my memory is still good) only 9 patterns giving some 4+4+9 puzzles

PS: I split the 66000 patterns base in lots of 100 puzzles. The processing is a kind of sequential one.

[coloin]

It would be astounding if a 3+4+27 did have a valid puzzle - but since no one has looked at the 12e11 possibilities.....C

I am astounded !
To be fair its a lot harder to find something if you think its not actually there .... and now in retrospect looking for {3+5+27} puzzles might have been a more productive way to find a {3+4+27}.
However, well done for persevering - in some respects it would have been a bit flat if blue/dobrichev had done that big search - only to conclude that they didn't exist - and now that you have found several, the puzzles do look very empty !!!.
C

[coloin]

And there are at least a good few more of that pattern ........101 off my first run using those as seeds .....C
Edit - which is to be expected as there will be one puzzle for each of the different 416 bands of the particular gangster. ....
C

[eleven]

i love it to see, that not only my sudoku conjectures are (almost always) wrong.
good work.

[coloin]

No you werent wrong ! [yet]

So, if i made no mistake, this pattern is invalid:

Code: Select all

    1 1 1
    1 1 2
    9 9 9

However....looking into champagnes puzzles
These are the 3 minlex representations of the double band containing the 7 clues - in the 16 puzzles posted

Code: Select all

000000000000000000000000000123456789457189263698732145285691374764325918931847526 # 264 sols     
000000000000000000000000000123456789457189263698732145285691374764523918931847526 # 264 sols     
000000000000000000000000000123456789457289163896317245364921578572638914918745632 # 192 sols

a new one

Code: Select all

12345678954782961368971354221............73................5..........24.........

minlex representation of the double band with 7 clues

Code: Select all

000000000000000000000000000123456789457289163896317245364921578572638914981745632 # 144 sols

864 sols total / 6 = 144 puzzles therefore so far [4 different gangsters I think]


Looking at the pattern
The double clues in a box do appear to need to be horizontal perhaps..... so maybe hope for 3 other 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  valid pattern
 
 . . . | . . . | . . .
 . . . | . . . | . . x
 . . . | . x x | . . .
-------+-------+-------
 . . . | . . . | . . x
 . . . | x . . | . . .
 . x x | . . . | . . .
-------+-------+-------
 x x x | x x x | x x x
 x x x | x x x | x x x
 x x x | x x x | x x x
 
 . . . | . . . | . . .
 . . . | . . . | . . x
 . . . | . x x | . . .
-------+-------+-------
 . . . | . . . | . . .
 . . . | x . . | . x .
 . x x | . . . | . . .
-------+-------+-------
 x x x | x x x | x x x
 x x x | x x x | x x x
 x x x | x x x | x x x
 
 . . . | . . . | . . .
 . . . | . . . | . . x
 . . . | . x x | . . .
-------+-------+-------
 . . . | . . . | . x .
 . . . | x . . | . . .
 . x x | . . . | . . .
-------+-------+-------
 x x x | x x x | x x x
 x x x | x x x | x x x
 x x x | x x x | x x x

C

[Serg]

Hi, champagne!

It seems that the conjecture is dead.

Very surprising result! I was sure {3,4,27} valid puzzes don't exist. Well done!
But coloin's conjecture number 2 - "There don't exist valid 9plus11 puzzles" is still standing not proven/disproven.

Serg

[champagne]

Hi, champagne!

It seems that the conjecture is dead.

Very surprising result! I was sure {3,4,27} valid puzzes don't exist. Well done!
But coloin's conjecture number 2 - "There don't exist valid 9plus11 puzzles" is still standing not proven/disproven.

Serg

That result is a surprise, I agree. A key point for some studies in the field of low clues count is to see whether that pattern has valid puzzles ( and how many) in the 17 18 clues areas.

From past work I made with mladen, I think this is a question to be solved by grid checker, My simple soft does not work. I don't have the expertise to do it, so if mladen can answer, he is welcome.

[dobrichev]

Which pattern?

Taking this puzzle

Code: Select all

12345678954782961368971354221............73................5..........24.........

gridchecker --similar --removeredundant < in.txt > out.txt

gives 3582 puzzles, including these two 19s

Code: Select all

..34...8.54..29.1..89.1.5..21............73................5..........24.........   19
..34...8..47.29.1..89.1.5..21............73................5..........24.........   19


[champagne]

Which pattern?

Hi mladen

you in some way confirm that you have the key.

If i am right, the current file of known 3+4+27 is he following (to coloin, sorry if I miss understood some of your posts)


12345678945718962368927314524............79................1..........54......... ED=1.5/1.2/1.2
12345678945718962368927314524............79................1..........52......... ED=1.5/1.2/1.2
12345678945718962368927314524............73................1..........54......... ED=1.5/1.2/1.2
12345678945718962368927314524............73................1..........52......... ED=1.5/1.2/1.2
12345678945718962368927315424............79................1..........48......... ED=1.5/1.2/1.2
12345678945718962368927315424............79................1..........45......... ED=1.5/1.2/1.2
12345678945718962368927315424............73................1..........48......... ED=1.5/1.2/1.2
12345678945718962368927315424............73................1..........45......... ED=1.5/1.2/1.2
12345678945718923669873251496...........7.8...............2...........91.........
12345678945718923669873251496...........7.8...............2...........61.........
12345678945718923669873251496...........7.3...............2...........91.........
12345678945718923669873251496...........7.3...............2...........61.........
12345678945718923669873251496..........8...7.................4.....95............
12345678945718923669873251496..........8...7.................4.....65............
12345678945718923669873251496..........3...7.................4.....95............
12345678945718923669873251496..........3...7.................4.....65............
12345678954782961368971354221............73................5..........24.........

Question to mladen
Is there any 17 clues puzzle fitting with that 34 clues target??

Side question , but not so important to-day

Is there any 18 clues puzzle fitting with that 34 clues target??

If I am right, this is the best area where grid checker can help us.

[dobrichev]

I am surprised by existance of such unbalanced 18s. Here they are.

Code: Select all

..345..8...7.8.6..6.92..1..24............73................1..........52.........   18
..345..8...7.8.6..6.92..1..24............79................1..........52.........   18


Below are the 19s

Hidden Text: Show

Code: Select all

..34...8..47.29.1..89.1.5..21............73................5..........24.........   19
..34...8.54..29.1..89.1.5..21............73................5..........24.........   19
..345..8...7.8..236.92..1..24............79................1..........45.........   19
..345..8...7.8..236.92..1..24............79................1..........48.........   19
..345..8...7.8..236.92..1..24............79................1..........52.........   19
..345..8...7.8..236.92..1..24............79................1..........54.........   19
..345..8...7.8.6...892...4524............73................1..........52.........   19
..345..8...7.8.6...892.31..24............73................1..........52.........   19
..345..8...7.8.6...892.31..24............79................1..........52.........   19
..345..8...7.8.6..6.9.731..24............73................1..........52.........   19
..345..8...7.8.6..6.9.731..24............79................1..........52.........   19
..345..8...7.8.6..6.92...4524............73................1..........52.........   19
..345..8...7.8.6..6.92...4524............79................1..........52.........   19
..345..8...7.8.6.3.892..1..24............73................1..........45.........   19
..345..8...7.8.6.3.892..1..24............73................1..........48.........   19
..345..8...7.8.6.3.892..1..24............73................1..........52.........   19
..345..8...7.8.6.3.892..1..24............73................1..........54.........   19
..345..8...7.8.6.3.892..1..24............79................1..........45.........   19
..345..8...7.8.6.3.892..1..24............79................1..........48.........   19
..345..8...7.8.6.3.892..1..24............79................1..........52.........   19
..345..8...7.8.6.3.892..1..24............79................1..........54.........   19
..345..8...7.8.6.36.92..1..24............73................1..........45.........   19
..345..8...7.8.6.36.92..1..24............73................1..........48.........   19
..345..8...7.8.6.36.92..1..24............73................1..........54.........   19
..345..8...7.8.6.36.92..1..24............79................1..........45.........   19
..345..8...7.8.6.36.92..1..24............79................1..........48.........   19
..345..8...7.8.6.36.92..1..24............79................1..........54.........   19
..345..8...7.8.62..892..1..24............73................1..........45.........   19
..345..8...7.8.62..892..1..24............73................1..........48.........   19
..345..8...7.8.62..892..1..24............73................1..........52.........   19
..345..8...7.8.62..892..1..24............73................1..........54.........   19
..345..8...7.8.62..892..1..24............79................1..........45.........   19
..345..8...7.8.62..892..1..24............79................1..........48.........   19
..345..8...7.8.62..892..1..24............79................1..........52.........   19
..345..8...7.8.62..892..1..24............79................1..........54.........   19
..345..8...7.8.62.6.92..1..24............73................1..........45.........   19
..345..8...7.8.62.6.92..1..24............73................1..........48.........   19
..345..8...7.8.62.6.92..1..24............73................1..........54.........   19
..345..8...7.8.62.6.92..1..24............79................1..........45.........   19
..345..8...7.8.62.6.92..1..24............79................1..........48.........   19
..345..8...7.8.62.6.92..1..24............79................1..........54.........   19
..345..8...7.89.2.6.92..1..24............73................1..........45.........   19
..345..8...7.89.2.6.92..1..24............73................1..........48.........   19
..345..8...7.89.2.6.92..1..24............73................1..........52.........   19
..345..8...7.89.2.6.92..1..24............73................1..........54.........   19
..345..8...7.89.2.68.2..1..24............73................1..........45.........   19
..345..8...7.89.2.68.2..1..24............73................1..........48.........   19
..345..8...7.89.2.68.2..1..24............73................1..........52.........   19
..345..8...7.89.2.68.2..1..24............73................1..........54.........   19
..345..8...7.896...892..1..24............73................1..........52.........   19
..345..8...7.896...892..1..24............79................1..........52.........   19
..345..8...71.9.2.68.2..1..24............73................1..........45.........   19
..345..8...71.9.2.68.2..1..24............73................1..........48.........   19
..345..8...71.9.2.68.2..1..24............73................1..........52.........   19
..345..8...71.9.2.68.2..1..24............73................1..........54.........   19
..345..8...71.96...892..1..24............73................1..........52.........   19
..345..8...71.96...892..1..24............79................1..........52.........   19
..345..8..57.8.6...892..1..24............73................1..........52.........   19
..345..8..57.8.6...892..1..24............79................1..........52.........   19
..345..89..7.8..2.6.92..1..24............73................1..........45.........   19
..345..89..7.8..2.6.92..1..24............73................1..........48.........   19
..345..89..7.8..2.6.92..1..24............73................1..........52.........   19
..345..89..7.8..2.6.92..1..24............73................1..........54.........   19
..345..89..7.8.6...892..1..24............73................1..........52.........   19
..345..89..7.8.6...892..1..24............79................1..........52.........   19
..345.7....7.8..236.92..1..24............79................1..........48.........   19
..345.7....7.8.6.3.892..1..24............73................1..........48.........   19
..345.7....7.8.6.3.892..1..24............79................1..........48.........   19
..345.7....7.8.62..892..1..24............73................1..........48.........   19
..345.7....7.8.62..892..1..24............79................1..........48.........   19
..345.7....7.8.62.6.92..1..24............73................1..........48.........   19
..345.7....7.8.62.6.92..1..24............79................1..........48.........   19
..345.7....7.89.2.6.92..1..24............73................1..........48.........   19
..345.7....7.89.2.68.2..1..24............73................1..........48.........   19
..345.7.9..7.8..2.6.92..1..24............73................1..........45.........   19
..345.7.9..7.8..2.6.92..1..24............73................1..........48.........   19
..345.7.9..7.8..2.6.92..1..24............73................1..........52.........   19
..345.7.9..7.8..2.6.92..1..24............73................1..........54.........   19
..345.7.9..7.8.6...892..1..24............73................1..........52.........   19
..345.7.9..7.8.6...892..1..24............79................1..........52.........   19
..345.78...7.8.6...892..1..24............73................1..........52.........   19
..345.78...7.8.6...892..1..24............79................1..........52.........   19
..3456.8...7.8..2.6.92..1..24............73................1..........45.........   19
..3456.8...7.8..2.6.92..1..24............73................1..........48.........   19
..3456.8...7.8..2.6.92..1..24............73................1..........52.........   19
..3456.8...7.8..2.6.92..1..24............73................1..........54.........   19
..3456.8...7.8.6...892..1..24............73................1..........52.........   19
..3456.8...7.8.6...892..1..24............79................1..........52.........   19
..34567....7.8..2.6.92..1..24............73................1..........48.........   19
.234....9.57..9.36..8..25..96..........8...7.................4.....65............   19
.234....9.57..9.36..8..25..96..........8...7.................4.....95............   19
.234....9.571...36..8..25..96..........3...7.................4.....95............   19
.234....9.571...36..8..25..96..........8...7.................4.....95............   19
.234....94.71...36..8..25..96..........3...7.................4.....95............   19
.234....94.71...36..8..25..96..........8...7.................4.....95............   19
.2345..8...7.8.6...892..1..24............73................1..........52.........   19
.2345..8...7.8.6...892..1..24............79................1..........52.........   19
1.34....9.57..9.36..8..25..96..........8...7.................4.....65............   19
1.34....9.57..9.36..8..25..96..........8...7.................4.....95............   19
1.34....9.571...36..8..25..96..........3...7.................4.....95............   19
1.34....9.571...36..8..25..96..........8...7.................4.....95............   19
1.34....9.571..2.6..8..25..96..........3...7.................4.....95............   19
1.34....9.571..2.6..8..25..96..........8...7.................4.....95............   19
1.34....94.71..2.6..8..25..96..........3...7.................4.....95............   19
1.34....94.71..2.6..8..25..96..........8...7.................4.....95............   19
12.45..8...7.8.6..6.92..1..24............73................1..........52.........   19
12.45..8...7.8.6..6.92..1..24............79................1..........52.........   19