## 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

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

Posts: 2376
Joined: 10 February 2008

### Re: minimum number of clues per band/stack

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
coloin

Posts: 1877
Joined: 05 May 2005

### Re: minimum number of clues per band/stack

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
Serg
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Posts: 701
Joined: 01 June 2010
Location: Russia

### Re: minimum number of clues per band/stack

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.
champagne
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Joined: 02 August 2007
Location: France Brittany

### Re: minimum number of clues per band/stack

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`
dobrichev
2016 Supporter

Posts: 1779
Joined: 24 May 2010

### Re: minimum number of clues per band/stack

dobrichev wrote:Which pattern?

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.........

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.
champagne
2017 Supporter

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Joined: 02 August 2007
Location: France Brittany

### Re: minimum number of clues per band/stack

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.........   191.34....9.57..9.36..8..25..96..........8...7.................4.....65............   191.34....9.57..9.36..8..25..96..........8...7.................4.....95............   191.34....9.571...36..8..25..96..........3...7.................4.....95............   191.34....9.571...36..8..25..96..........8...7.................4.....95............   191.34....9.571..2.6..8..25..96..........3...7.................4.....95............   191.34....9.571..2.6..8..25..96..........8...7.................4.....95............   191.34....94.71..2.6..8..25..96..........3...7.................4.....95............   191.34....94.71..2.6..8..25..96..........8...7.................4.....95............   1912.45..8...7.8.6..6.92..1..24............73................1..........52.........   1912.45..8...7.8.6..6.92..1..24............79................1..........52.........   19`
dobrichev
2016 Supporter

Posts: 1779
Joined: 24 May 2010

### Re: minimum number of clues per band/stack

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
JPF
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Location: Paris, France

### Re: minimum number of clues per band/stack

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.
dobrichev
2016 Supporter

Posts: 1779
Joined: 24 May 2010

### Re: minimum number of clues per band/stack

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............
champagne
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Location: France Brittany

### Re: minimum number of clues per band/stack

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
Using coloin's post below, here are the 144 puzzles:

Hidden Text: Show
Code: Select all
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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
2017 Supporter

Posts: 4022
Joined: 06 December 2005
Location: Paris, France

### Re: minimum number of clues per band/stack

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
dobrichev
2016 Supporter

Posts: 1779
Joined: 24 May 2010

### Re: minimum number of clues per band/stack

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
`000000000000000001000023000000000000000400005026000000432178569561934728879562314000000000000000001000023000000000000000400005026000000478132569561879324932564718000000000000000001000023000000000000000400005026000000478562139512739684963184257000000000000000001000023000000000000000400005026000000431782569567139824982564317000000000000000001000023000000000000000400005026000000473182569562739814918564327000000000000000001000023000000000000000400005026000000432576189581942637769138254000000000000000001000023000000000000000400005026000000462738159573196284918542637000000000000000001000023000000000000000400005026000000471586239539142678862937154000000000000000001000023000000000000000400005026000000462578139593164278817932654000000000000000001000023000000000000000400005026000000437182569562739814981564327000000000000000001000023000000000000000400005026000000471568239562934178839172654`

4 different 54 clue double bands with a total of 864 grid solutions.....
/6 for the row swaps = 144 puzzles
C
coloin

Posts: 1877
Joined: 05 May 2005

### Re: minimum number of clues per band/stack

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.
champagne
2017 Supporter

Posts: 7138
Joined: 02 August 2007
Location: France Brittany

### Re: minimum number of clues per band/stack

Code: Select all
`3+4+103+5+93+6+83+7+74+4+94+5+84+6+75+5+75+6+6`

I see much work there.
dobrichev
2016 Supporter

Posts: 1779
Joined: 24 May 2010

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