minimum number of clues per band/stack

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

Re: minimum number of clues per band/stack

Postby eleven » Thu Nov 06, 2014 10:33 pm

i love it to see, that not only my sudoku conjectures are (almost always) wrong.
good work.
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Re: minimum number of clues per band/stack

Postby coloin » Thu Nov 06, 2014 11:11 pm

No you werent wrong ! [yet]
eleven wrote: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
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Re: minimum number of clues per band/stack

Postby Serg » Fri Nov 07, 2014 12:26 pm

Hi, champagne!
champagne wrote: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
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Re: minimum number of clues per band/stack

Postby champagne » Fri Nov 07, 2014 5:27 pm

Serg wrote:Hi, champagne!
champagne wrote: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.
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Re: minimum number of clues per band/stack

Postby dobrichev » Fri Nov 07, 2014 6:16 pm

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
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Re: minimum number of clues per band/stack

Postby champagne » Fri Nov 07, 2014 9:59 pm

dobrichev wrote: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.
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Re: minimum number of clues per band/stack

Postby dobrichev » Fri Nov 07, 2014 10:56 pm

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
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Re: minimum number of clues per band/stack

Postby JPF » Sat Nov 08, 2014 12:50 am

There is probably a bunch of ed puzzles with that pattern.
Here are some of them including those already given by champagne:
Code: Select all
.................1....23...............4....5.26......412578369563942817798136524
.................1....23...............4....5.26......413572689598146237762938154
.................1....23...............4....5.26......413576289568942137792138654
.................1....23...............4....5.26......413576289592148637768932154
.................1....23...............4....5.26......413576289598142637762938154
.................1....23...............4....5.26......417568239592134678863972154
.................1....23...............4....5.26......431567289562984137789132654
.................1....23...............4....5.26......431572689562948137789136254
.................1....23...............4....5.26......431572689582946137769138254
.................1....23...............4....5.26......431572689589146237762938154
.................1....23...............4....5.26......432576189569148237781932654
.................1....23...............4....5.26......437182569561739824982564317
.................1....23...............4....5.26......437182569582769314961534827
.................1....23...............4....5.26......461537289582964137739182654
.................1....23...............4....5.26......461578239532946187789132654
.................1....23...............4....5.26......461578239532964178879132654
.................1....23...............4....5.26......461578239539142687782936154
.................1....23...............4....5.26......462578139513942687798136254
.................1....23...............4....5.26......462578139513946287798132654
.................1....23...............4....5.26......462578139531946287789132654
.................1....23...............4....5.26......462578139593142687718936254
.................1....23...............4....5.26......462738159537192684981546237
.................1....23...............4....5.26......462738159578192634913546287
.................1....23...............4....5.26......462738159587196234931542687
.................1....23...............4....5.26......463572189592148637718936254
.................1....23...............4....5.26......463572189598146237712938654
.................1....23...............4....5.26......467138259512974638893562174
.................1....23...............4....5.26......467138259532796184981542637
.................1....23...............4....5.26......467138259581792634932546187
.................1....23...............4....5.26......467138259582796134931542687
.................1....23...............4....5.26......467532189581769234932184657
.................1....23...............4....5.26......467582139531769284982134657
.................1....23...............4....5.26......467832159582179634913564278
.................1....23...............4....5.26......471582369539146728862937514
.................1....23...............4....5.26......471832569568197324932546718
.................1....23...............4....5.26......472138569531964728869572314
.................1....23...............4....5.26......472586139531942678869137254
.................1....23...............4....5.26......472836159538192674961547238
.................1....23...............4....5.26......472836159568197234931542678
.................1....23...............4....5.26......478132569531896724962547318
.................1....23...............4....5.26......478132569532869714961574328
.................1....23...............4....5.26......478132569532896714961547328
.................1....23...............4....5.26......478132569561897324932546718
.................1....23...............4....5.26......478132569562789314913564827
.................1....23...............4....5.26......478132569562879314931564728
.................1....23...............4....5.26......478136259512798634963542187
.................1....23...............4....5.26......478136259513792684962548137
.................1....23...............4....5.26......478136259562798134913542687
.................1....23...............4....5.26......478136259563792184912548637

dobrichev,what is the right command line to find any 17 or 18 clue puzzles?

JPF
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Re: minimum number of clues per band/stack

Postby dobrichev » Sat Nov 08, 2014 1:59 am

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

This removes redundant clues from the given puzzles. You may run it even on full grids, but then have to wait some ages.
Then you should somehow filter the output, the size is in the second column.
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Re: minimum number of clues per band/stack

Postby champagne » Sat Nov 08, 2014 6:38 am

some more out of my check, as far as I can see, 3 of them are not in the list posted by jpf

12345678945718962389632714528..........7..3.................4......98............
12345678945718962389632714528..........7..3.................4......92............
12345678945718962389632714528..........6..3.................4......98............
12345678945718962389632714528..........6..3.................4......92............
12345678945718962389632741528..........7..3.................1......98............
12345678945718962389632741528..........7..3.................1......92............
12345678945718962389632741528..........6..3.................1......98............
12345678945718962389632741528..........6..3.................1......92............
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Re: minimum number of clues per band/stack

Postby JPF » Sat Nov 08, 2014 10:03 am

dobrichev wrote:gridchecker --similar --removeredundant < in.txt > out.txt
....
Then you should somehow filter the output, the size is in the second column.
Thanks. I didn't see any second column, but I managed without it.
champagne wrote:some more out of my check, as far as I can see, 3 of them are not in the list posted by jpf
With your addition, I get a total of 133.
Using coloin's post below, here are the 144 puzzles:

Hidden Text: Show
Code: Select all
.................1....23...............4....5.26......412537689598164237763982154
.................1....23...............4....5.26......412578369563942817798136524
.................1....23...............4....5.26......412578369593146827768932514
.................1....23...............4....5.26......412578369593164728867932514
.................1....23...............4....5.26......412738569573196824968542317
.................1....23...............4....5.26......412738569578196324963542817
.................1....23...............4....5.26......413567289562984137798132654
.................1....23...............4....5.26......413567289592184637768932154
.................1....23...............4....5.26......413572689562948137798136254
.................1....23...............4....5.26......413572689598146237762938154
.................1....23...............4....5.26......413576289562948137798132654
.................1....23...............4....5.26......413576289568942137792138654
.................1....23...............4....5.26......413576289592148637768932154
.................1....23...............4....5.26......413576289598142637762938154
.................1....23...............4....5.26......413782569578169324962534817
.................1....23...............4....5.26......417568239562934178893172654
.................1....23...............4....5.26......417568239592134678863972154
.................1....23...............4....5.26......417582369593146728862937514
.................1....23...............4....5.26......417586239563942178892137654
.................1....23...............4....5.26......417586239593142678862937154
.................1....23...............4....5.26......417832569583169724962574318
.................1....23...............4....5.26......417832569583196724962547318
.................1....23...............4....5.26......417836259582197634963542178
.................1....23...............4....5.26......417836259583192674962547138
.................1....23...............4....5.26......431567289562984137789132654
.................1....23...............4....5.26......431572689562948137789136254
.................1....23...............4....5.26......431572689569148237782936154
.................1....23...............4....5.26......431572689582946137769138254
.................1....23...............4....5.26......431572689589146237762938154
.................1....23...............4....5.26......431576289562948137789132654
.................1....23...............4....5.26......431576289589142637762938154
.................1....23...............4....5.26......431782569567139824982564317
.................1....23...............4....5.26......431782569587169324962534817
.................1....23...............4....5.26......432178569561934728879562314
.................1....23...............4....5.26......432178569571964328869532714
.................1....23...............4....5.26......432178569581946327769532814
.................1....23...............4....5.26......432567189561984237789132654
.................1....23...............4....5.26......432567189569184237781932654
.................1....23...............4....5.26......432576189561948237789132654
.................1....23...............4....5.26......432576189569148237781932654
.................1....23...............4....5.26......432576189581942637769138254
.................1....23...............4....5.26......432576189589142637761938254
.................1....23...............4....5.26......437182569561739824982564317
.................1....23...............4....5.26......437182569562739814981564327
.................1....23...............4....5.26......437182569581769324962534817
.................1....23...............4....5.26......437182569582769314961534827
.................1....23...............4....5.26......437562189561789234982134657
.................1....23...............4....5.26......461537289582964137739182654
.................1....23...............4....5.26......461578239532946187789132654
.................1....23...............4....5.26......461578239532964178879132654
.................1....23...............4....5.26......461578239539142687782936154
.................1....23...............4....5.26......461738259537192684982546137
.................1....23...............4....5.26......461738259587192634932546187
.................1....23...............4....5.26......462537189518964237793182654
.................1....23...............4....5.26......462537189581964237739182654
.................1....23...............4....5.26......462537189589164237731982654
.................1....23...............4....5.26......462537189598164237713982654
.................1....23...............4....5.26......462578139513942687798136254
.................1....23...............4....5.26......462578139513946287798132654
.................1....23...............4....5.26......462578139513964278897132654
.................1....23...............4....5.26......462578139531942687789136254
.................1....23...............4....5.26......462578139531946287789132654
.................1....23...............4....5.26......462578139531964278879132654
.................1....23...............4....5.26......462578139539142687781936254
.................1....23...............4....5.26......462578139539146287781932654
.................1....23...............4....5.26......462578139539164278871932654
.................1....23...............4....5.26......462578139593142687718936254
.................1....23...............4....5.26......462578139593146287718932654
.................1....23...............4....5.26......462578139593164278817932654
.................1....23...............4....5.26......462738159537192684981546237
.................1....23...............4....5.26......462738159537196284981542637
.................1....23...............4....5.26......462738159573192684918546237
.................1....23...............4....5.26......462738159573196284918542637
.................1....23...............4....5.26......462738159578192634913546287
.................1....23...............4....5.26......462738159578196234913542687
.................1....23...............4....5.26......462738159587192634931546287
.................1....23...............4....5.26......462738159587196234931542687
.................1....23...............4....5.26......463178259512934678897562134
.................1....23...............4....5.26......463178259518942637792536184
.................1....23...............4....5.26......463572189512948637798136254
.................1....23...............4....5.26......463572189518946237792138654
.................1....23...............4....5.26......463572189592148637718936254
.................1....23...............4....5.26......463572189598146237712938654
.................1....23...............4....5.26......463782159572139684918564237
.................1....23...............4....5.26......463782159578169234912534687
.................1....23...............4....5.26......467138259512974638893562174
.................1....23...............4....5.26......467138259531792684982546137
.................1....23...............4....5.26......467138259532796184981542637
.................1....23...............4....5.26......467138259581792634932546187
.................1....23...............4....5.26......467138259582796134931542687
.................1....23...............4....5.26......467532189581769234932184657
.................1....23...............4....5.26......467532189581796234932148657
.................1....23...............4....5.26......467582139513946278892137654
.................1....23...............4....5.26......467582139531769284982134657
.................1....23...............4....5.26......467582139593146278812937654
.................1....23...............4....5.26......467832159582179634913564278
.................1....23...............4....5.26......467832159582197634913546278
.................1....23...............4....5.26......467832159583169274912574638
.................1....23...............4....5.26......467832159583196274912547638
.................1....23...............4....5.26......471568239562934178839172654
.................1....23...............4....5.26......471582369532946718869137524
.................1....23...............4....5.26......471582369539146728862937514
.................1....23...............4....5.26......471586239539142678862937154
.................1....23...............4....5.26......471832569538169724962574318
.................1....23...............4....5.26......471832569538196724962547318
.................1....23...............4....5.26......471832569568179324932564718
.................1....23...............4....5.26......471832569568197324932546718
.................1....23...............4....5.26......471836259538192674962547138
.................1....23...............4....5.26......472138569513796824968542317
.................1....23...............4....5.26......472138569518796324963542817
.................1....23...............4....5.26......472138569531964728869572314
.................1....23...............4....5.26......472138569561974328839562714
.................1....23...............4....5.26......472138569563792814918546327
.................1....23...............4....5.26......472138569568792314913546827
.................1....23...............4....5.26......472536189518792634963148257
.................1....23...............4....5.26......472568139561934278839172654
.................1....23...............4....5.26......472568139569134278831972654
.................1....23...............4....5.26......472586139531942678869137254
.................1....23...............4....5.26......472586139539142678861937254
.................1....23...............4....5.26......472836159538192674961547238
.................1....23...............4....5.26......472836159568197234931542678
.................1....23...............4....5.26......473182569518769324962534817
.................1....23...............4....5.26......473182569562739814918564327
.................1....23...............4....5.26......473562189512789634968134257
.................1....23...............4....5.26......478132569513769824962584317
.................1....23...............4....5.26......478132569513796824962548317
.................1....23...............4....5.26......478132569531869724962574318
.................1....23...............4....5.26......478132569531896724962547318
.................1....23...............4....5.26......478132569532869714961574328
.................1....23...............4....5.26......478132569532896714961547328
.................1....23...............4....5.26......478132569561879324932564718
.................1....23...............4....5.26......478132569561897324932546718
.................1....23...............4....5.26......478132569562789314913564827
.................1....23...............4....5.26......478132569562798314913546827
.................1....23...............4....5.26......478132569562879314931564728
.................1....23...............4....5.26......478132569562897314931546728
.................1....23...............4....5.26......478136259512798634963542187
.................1....23...............4....5.26......478136259513792684962548137
.................1....23...............4....5.26......478136259531892674962547138
.................1....23...............4....5.26......478136259562798134913542687
.................1....23...............4....5.26......478136259562897134931542678
.................1....23...............4....5.26......478136259563792184912548637
.................1....23...............4....5.26......478562139512739684963184257
.................1....23...............4....5.26......478562139561839274932174658

With a more exhaustive approach, we can certainly get much more.

Among those 144=133+11 puzzles, here are 17 18s and ... no 17:
Code: Select all
.................1....23...............4....5.26......4....2.3.5.3..6.788..1..6..
.................1....23...............4....5.26......4....2.7.5....763.81.9..2..
.................1....23...............4....5.26......4....2.7.5.7..6.388..1..6..
.................1....23...............4....5.26......4....6.3.53...2.788..1..2..
.................1....23...............4....5.26......4....6.3.53.7...899..1..2..
.................1....23...............4....5.26......4....6.7.5....723.8.19..6..
.................1....23...............4....5.26......4....6.8.58...2.377..1..2..
.................1....23...............4....5.26......4....6.8.58.9...377..1..2..
.................1....23...............4....5.26......4....736.5..8..7..98.1...2.
.................1....23...............4....5.26......4...6..3.5...3.27.8.19..6..
.................1....23...............4....5.26......4...6..3.5..7..28.9.71..6..
.................1....23...............4....5.26......4...6..7.5...7.23.8.19..6..
.................1....23...............4....5.26......4..1...2.53.7..8.49....63..
.................1....23...............4....5.26......4..1...2.57.8..3.49....67..
.................1....23...............4....5.26......4..5...7.5....763.81.9..2..
.................1....23...............4....5.26......4.71...6.5..7..82.9...6.3..
.................1....23...............4....5.26......47.1...2.5..7..8..9....836.

JPF
Last edited by JPF on Sun Nov 09, 2014 10:38 pm, edited 2 times in total.
JPF
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Re: minimum number of clues per band/stack

Postby dobrichev » Sun Nov 09, 2014 7:23 am

JPF wrote:I didn't see any second column, but I managed without it.

The latest Win32 version of gridchecker, v1.23, is here - https://sites.google.com/site/dobrichev/gridchecker
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Re: minimum number of clues per band/stack

Postby coloin » Sun Nov 09, 2014 6:55 pm

JPF wrote:With a more exhaustive approach, we can certainly get much more.....

Well no need, assuming there isnt a different double band solvable with 7 clues
Here are the remaining 11 puzzles making up to 144
Code: Select all
000000000000000001000023000000000000000400005026000000432178569561934728879562314
000000000000000001000023000000000000000400005026000000478132569561879324932564718
000000000000000001000023000000000000000400005026000000478562139512739684963184257
000000000000000001000023000000000000000400005026000000431782569567139824982564317
000000000000000001000023000000000000000400005026000000473182569562739814918564327
000000000000000001000023000000000000000400005026000000432576189581942637769138254
000000000000000001000023000000000000000400005026000000462738159573196284918542637
000000000000000001000023000000000000000400005026000000471586239539142678862937154
000000000000000001000023000000000000000400005026000000462578139593164278817932654
000000000000000001000023000000000000000400005026000000437182569562739814981564327
000000000000000001000023000000000000000400005026000000471568239562934178839172654

4 different 54 clue double bands with a total of 864 grid solutions.....
/6 for the row swaps = 144 puzzles
C
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Re: minimum number of clues per band/stack

Postby champagne » Sun Nov 09, 2014 7:53 pm

coloin wrote:Well no need, assuming there isnt a different double band solvable with 7 clues

C


This is still hard for me, but I accept that we have small chances to find another lot of 3_4_27

If I look at the existing 17 clues, I see 2 things

a) no 3+5+9
b) a very small number of 4+4+9

If in the same way it could be possible through the analysis of 4+4+27 and 3+5+27 to show that we have covered the 17 clues field, It would be a significant step to see whether other 17 clues can been found.
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Re: minimum number of clues per band/stack

Postby dobrichev » Sun Nov 09, 2014 8:21 pm

Code: Select all
3+4+10
3+5+9
3+6+8
3+7+7
4+4+9
4+5+8
4+6+7
5+5+7
5+6+6

I see much work there.
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