I checked that your puzzles are not in my list, which is therefore incomplete.
So my count is also incorrect.
I will try to see where my mistake is.
Thank you for checking.
JPF
Ask for patterns that they dont have puzzles 2
Re: Ask for patterns that they dont have puzzles 2
by JPF » Sat Mar 25, 2023 11:04 pm
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Sun Mar 26, 2023 5:10 pm
blue wrote:The correct number is 27*27 = 729.
-- 27 ways to choose two rows in different bands.
-- 27 ways to choose two columns in different stacks.
Indeed that is a better and correct way to look at it !
blue wrote:"More homework": find 3 more "frame + 2" puzzles.
I suspect enough energy has been burned with my randon generation approach !!
Hopefully thats the lot !
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Sun Mar 26, 2023 5:16 pm
As a subset of the outside perimeter puzzles
we can easily find the middle frame plus 2 puzzles
here are the 5 possible patterns, with over 300 puzzles
Serg's patterns have already shown tht one clue added to the outside frame and this middle frame is never enough.
we can easily find the middle frame plus 2 puzzles
- Code: Select all
+---+---+---+
|...|...|...|
|.64|798|31.|
|.7.|...|.5.|
+---+---+---+
|.5.|...|.6.|
|.3.|...|.4.|
|.8.|...|.7.|
+---+---+---+
|.2.|...|.9.|
|.91|547|82.|
|...|...|...|
+---+---+---+
here are the 5 possible patterns, with over 300 puzzles
- Code: Select all
..........6479831..7.....5..5.2...6..3..5..4..8.....7..2.....9..9154782..........
..........1254679..9.....3..5.....8..3..9..25.7.....4..8.....7..2983761..........
..........1345679..9.....2..8.....7..5..3.21..2.....3..6.....4..3172895..........
..........1246579..5.....6..6.....59.4..7..1..3.....8..9.....4..7189652..........
..........1245679..6.....4..5....97..4..2..3..9.....1..2.....5..3178946..........
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...|
|.64|798|31.| |.12|546|79.| |.13|456|79.| |.12|465|79.| |.12|456|79.|
|.7.|...|.5.| |.9.|...|.3.| |.9.|...|.2.| |.5.|...|.6.| |.6.|...|.4.|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|.5.|2..|.6.| |.5.|...|.8.| |.8.|...|.7.| |.6.|...|.59| |.5.|...|97.|
|.3.|.5.|.4.| |.3.|.9.|.25| |.5.|.3.|21.| |.4.|.7.|.1.| |.4.|.2.|.3.|
|.8.|...|.7.| |.7.|...|.4.| |.2.|...|.3.| |.3.|...|.8.| |.9.|...|.1.|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|.2.|...|.9.| |.8.|...|.7.| |.6.|...|.4.| |.9.|...|.4.| |.2.|...|.5.|
|.91|547|82.| |.29|837|61.| |.31|728|95.| |.71|896|52.| |.31|789|46.|
|...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ 28plus2
Serg's patterns have already shown tht one clue added to the outside frame and this middle frame is never enough.
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Sun Mar 26, 2023 5:47 pm
And as a natural follow-up
these frames have an as yet unelucidated minima
these frames have an as yet unelucidated minima
- Code: Select all
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...|
|.12|345|6..| |.12|354|6..| |...|...|...| |...|...|...| |...|...|...| |...|...|...|
|.4.|...|7..| |.4.|...|5..| |.61|234|5..| |..1|234|5..| |..1|234|...| |...|123|...|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|.7.|...|8..| |.6.|...|3..| |.1.|...|6..| |..6|...|4..| |..2|..5|...| |...|8.4|...|
|.5.|...|9..| |.7.|...|2..| |.2.|...|8..| |..5|...|3..| |..3|..6|...| |...|2.5|...|
|.2.|...|1..| |.5.|...|4..| |.3.|...|4..| |..2|...|1..| |..8|..7|...| |...|3.6|...|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|.9.|...|2..| |.89|576|1..| |.45|678|9..| |..4|751|6..| |..6|498|...| |...|987|...|
|.87|436|5..| |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...|
|...|...|...| 7x6 |...|...|...| 6x6 |...|...|...| 6x5 |...|...|...| 5x5 |...|...|...| 5x4 |...|...|...| 5x3
+---+---+---+ 22 +---+---+---+ 20 +---+---+---+ 18 +---+---+---+ 16 +---+---+---+ 14 +---+---+---+ 12
Last edited by coloin on Tue Mar 28, 2023 4:39 pm, edited 1 time in total.
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Sun Mar 26, 2023 5:47 pm
- Code: Select all
+---+---+---+ +---+---+---+
|...|...|...| |...|...|...|
|.12|345|6..| |.12|456|9..|
|.6.|...|7..| |.9.|...|4..|
+---+---+---+ +---+---+---+
|.2.|...|8..| |.8.|...|6..|
|.5.|.78|9..| |.5.|.3.|2.1|
|.4.|..9|1.2| |.4.|...|3.5|
+---+---+---+ +---+---+---+
|.3.|...|28.| |.6.|...|1.4|
|.98|764|3..| |.31|728|5..|
|...|...|...| |...|...|...|
+---+---+---+ 22plus5 +---+---+---+ 22plus4
- coloin
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Re: Ask for patterns that they dont have puzzles 2
by JPF » Sun Mar 26, 2023 8:10 pm
the "frame" could be:
JPF
- Code: Select all
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|xxx|xxx|xxx| |xxx|xxx|xx.| |.xx|xxx|xx.| |.xx|xxx|xxx| |.xx|xxx|xx.| |...|...|...|
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.| |.xx|xxx|xx.|
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.| |.x.|...|.x.|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.| |.x.|...|.x.|
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.| |.x.|...|.x.|
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.| |.x.|...|.x.|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.| |.x.|...|.x.|
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.xx|xxx|xxx| |.xx|xxx|xx.| |.xx|xxx|xx.|
|xxx|xxx|xxx| |xxx|xxx|xx.| |.xx|xxx|xx.| |...|...|...| |...|...|...| |...|...|...|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
9x9 9x8 9x7 8x8 8x7 7x7
JPF
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Sun Mar 26, 2023 8:16 pm
indeed but they can all be a subset of the 9x9 .... remove one clue per row/column
in the 7x7 example above , it allows 2 clues per r/c to be removed and still be valid
So these examples are possible
in the 7x7 example above , it allows 2 clues per r/c to be removed and still be valid
- Code: Select all
+---+---+---+ +---+---+---+ +---+---+---+
|654|798|321| |6.4|798|3.1| |...|...|...|
|1..|...|..8| |...|...|...| |.64|798|31.|
|7..|...|..5| |7..|...|..5| |.7.|...|.5.|
+---+---+---+ +---+---+---+ +---+---+---+
|5..|2..|..6| |5..|2..|..6| |.5.|2..|.6.|
|3..|.5.|..4| |3..|.5.|..4| -> |.3.|.5.|.4.|
|8..|...|..7| |8..|...|..7| |.8.|...|.7.|
+---+---+---+ +---+---+---+ +---+---+---+
|2..|...|..9| |2..|...|..9| |.2.|...|.9.|
|4..|...|..3| |...|...|...| |.91|547|82.|
|931|547|862| |9.1|547|8.2| |...|...|...|
+---+---+---+ +---+---+---+ +---+---+---+
So these examples are possible
- Code: Select all
|xxx|xxx|xxx| |xxx|xxx|xx.| |.xx|xxx|xx.| |.xx|xxx|xxx| |.xx|xxx|xx.|
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.|
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.|
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.|
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.x.|...|..x| |.x.|...|.x.|
|x..|...|..x| |x..|...|.x.| |.x.|...|.x.| |.xx|xxx|xxx| |.xx|xxx|xx.|
|xxx|xxx|xxx| |xxx|xxx|xx.| |.xx|xxx|xx.| |...|...|...| |...|...|...|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
9x9 9x8 9x7 8x8 8x7
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|654|798|321| |654|798|31.| |.64|798|31.| |.64|798|321| |.64|798|31.|
|1..|...|..8| |1..|...|.8.| |.1.|...|.8.| |.1.|...|..8| |.1.|...|.8.|
|7..|...|..5| |7..|...|.5.| |.7.|...|.5.| |.7.|...|..5| |.7.|...|.5.|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|5..|2..|..6| |5..|2..|.6.| |.5.|2..|.6.| |.5.|2..|..6| |.5.|2..|.6.|
|3..|.5.|..4| |3..|.5.|.4.| |.3.|.5.|.4.| |.3.|.5.|..4| |.3.|.5.|.4.|
|8..|...|..7| |8..|...|.7.| |.8.|...|.7.| |.8.|...|..7| |.8.|...|.7.|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|2..|...|..9| |2..|...|.9.| |.2.|...|.9.| |.2.|...|..9| |.2.|...|.9.|
|4..|...|..3| |4..|...|.3.| |.4.|...|.3.| |.91|547|862| |.91|547|82.|
|931|547|862| |931|547|82.| |.91|547|82.| |...|...|...| |...|...|...|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
Last edited by coloin on Tue Mar 28, 2023 4:16 pm, edited 1 time in total.
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Re: Ask for patterns that they dont have puzzles 2
by JPF » Sun Mar 26, 2023 11:20 pm
just in case, one more:
JPF
- Code: Select all
1234567896.......18.......35.......82...3...64.......23....2..47.......5956184237
JPF
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Re: Ask for patterns that they dont have puzzles 2
by blue » Mon Mar 27, 2023 4:15 am
coloin wrote:rect way to look at it !blue wrote:"More homework": find 3 more "frame + 2" puzzles.
I suspect enough energy has been burned with my randon generation approach !!
Hopefully thats the lot !
That was my way of saying that I thought that at 97, you guys had found all but 3 of them.
Good work all around !
JPF has found #98. Nice !
Spoiler (homework hint):
Hidden Text: Show
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Re: Ask for patterns that they dont have puzzles 2
by JPF » Mon Mar 27, 2023 10:29 am
Here they are:
JPF
- Code: Select all
+---+---+---+ +---+---+---+
|123|456|789| |123|456|789|
|8..|...|..1| |6..|...|..3|
|7..|...|..6| |9..|...|..2|
+---+---+---+ +---+---+---+
|6..|3..|..8| |4..|2..|..6|
|5..|.7.|..2| |7..|.3.|..5|
|9..|...|..5| |5..|...|..1|
+---+---+---+ +---+---+---+
|2..|...|..4| |3..|...|..8|
|3..|...|..7| |2..|...|..7|
|478|621|953| |851|679|324|
+---+---+---+ +---+---+---+
- Code: Select all
1234567898.......17.......66..3....85...7...29.......52.......43.......7478621953
1234567896.......39.......24..2....67...3...55.......13.......82.......7851679324
JPF
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Tue Mar 28, 2023 4:34 pm
Great work , well found. It would have been a long time fishing for those last 2 !
We now have 100 9x9 frame plus 2 clues puzzles [ presumable the total by exhaustive search]
I wonder was it easier to scan the 3 patterns - or add 2 clues to all the 9x9 frames !!!!
It seems that 22 plus 2 clues [7x6] is impossibe
There is no 9x9 plus 2 which allows 4 clues to be removed from r1c89 and r9c89. [I found only one which allows 3 of the 4 clues to be removed]
Likewise the 7x7 case
Only the 7x7C is solvable with plus2 clues
We now have 100 9x9 frame plus 2 clues puzzles [ presumable the total by exhaustive search]
I wonder was it easier to scan the 3 patterns - or add 2 clues to all the 9x9 frames !!!!
- Code: Select all
+---+---+---+ +---+---+---+ +---+---+---+
|...|...|...| |...|...|...| |...|...|...|
|.12|345|6..| |.12|456|9..| |.12|435|6..|
|.6.|...|7..| |.9.|...|4..| |.4.|6..|3..|
+---+---+---+ +---+---+---+ +---+---+---+
|.2.|...|8..| |.8.|...|6..| |.7.|...|58.|
|.5.|.78|9..| |.5.|.3.|2.1| |.3.|.4.|2..|
|.4.|..9|1.2| |.4.|...|3.5| |.2.|...|7..|
+---+---+---+ +---+---+---+ +---+---+---+
|.3.|...|28.| |.6.|...|1.4| |.5.|...|9..|
|.98|764|3..| |.31|728|5..| |.63|187|4..|
|...|...|...| |...|...|...| |...|...|...|
+---+---+---+ 22plus5 +---+---+---+ 22plus4 +---+---+---+ 22plus3 7x6 plus 3 [minimum]
It seems that 22 plus 2 clues [7x6] is impossibe
There is no 9x9 plus 2 which allows 4 clues to be removed from r1c89 and r9c89. [I found only one which allows 3 of the 4 clues to be removed]
Likewise the 7x7 case
- Code: Select all
+---+---+---+ +---+---+---+
|xx.|xxx|x..| |123|456|7..|
|x..|...|x..| |9.8|...|2..|
|x..|...|x..| |4..|...|5..|
+--.+---+---+ +---+---+---+
|x..|...|x..| |8..|...|6.1|
|x..|...|x..| |5..|7..|3..|
|x..|...|x..| |3..|...|8..|
+---!---+---+ +---+---+---+
|xx.|xxx|x..| |795|128|4..|
|...|...|...| |...|.6.|...|
|...|...|...| |...|...|.7.|
+---+---+---+ +---+---+---+ 7x7A plus5 ....prob not minimum
7x7A
+---+---+---+ +---+---+---+
|...|...|...| |...|...|...|
|xxx|xxx|x..| |182|435|6..|
|x..|...|x..| |4..|6..|3..|
+---+---+---+ +---+---+---+
|x..|...|x..| |7..|...|58.|
|x..|...|x..| |3..|.4.|2..|
|x..|...|x..| |2..|...|7..|
+---+---+---+ +---+---+---+
|x..|...|x..| |5..|...|9..|
|xx|xxx|x..| |693|187|4..|
|...|...|...| |...|...|...|
+---+---+--- +---+---+---+ 7x7B plus3 [minimum]
7x7B
+---+---+---+ +---+---+---+
|...|...|...| |...|...|...|
|.xx|xxx|xx.| |.12|435|6..|
|.x.|...|.x.| |.4.|6..|3..|
+---+---+---+ +---+---+---+
|.x.|...|.x.| |.7.|...|58.|
|.x.|...|.x.| |.3.|.4.|2..|
|.x.|...|.x.| |.2.|...|7..|
+---+---+---+ +---+---+---+
|.x.|...|.x.| |.5.|...|9..|
|.xx|xxx|xx.| |.63|187|4..|
|...|...|...| |...|...|...|
+---+---+---+ +---+---+---+ 7x7C plus2 [minimum]
Only the 7x7C is solvable with plus2 clues
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Re: Ask for patterns that they dont have puzzles 2
by JPF » Tue Mar 28, 2023 6:17 pm
As a by-product of the previous study and if blue confirms it, the following pattern is invalid:
It is even a maximum invalid pattern i.e. the addition of any clue makes it valid:
JPF
- Code: Select all
+---+---+---+
|xxx|xxx|xxx|
|x..|...|..x|
|x..|...|..x|
+---+---+---+
|x..|...|..x|
|x..|xx.|..x|
|x..|...|..x|
+---+---+---+
|x..|...|..x|
|x..|...|..x|
|xxx|xxx|xxx|
+---+---+---+
It is even a maximum invalid pattern i.e. the addition of any clue makes it valid:
- Code: Select all
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|123|456|789| |123|456|789| |123|456|789| |123|456|789|
|5..|...|..2| |9..|...|..6| |4..|...|..6| |8..|...|..2|
|8..|7..|..6| |5..|..3|..2| |8..|...|1.3| |6..|...|..4|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|7..|...|..5| |7..|...|..3| |6..|...|..7| |4..|...|3.1|
|9..|52.|..4| |6..|98.|..4| |9..|38.|..4| |9..|28.|..5|
|6..|...|..1| |4..|...|..1| |3..|...|..2| |7..|...|..6|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|4..|...|..8| |2..|...|..7| |7..|...|..1| |2..|...|..8|
|2..|...|..3| |3..|...|..8| |2..|...|..5| |5..|...|..3|
|359|861|247| |861|327|495| |594|167|238| |386|529|147|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
- Code: Select all
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|123|456|789| |123|456|789| |123|456|789| |123|456|789|
|4..|...|..6| |7..|...|..2| |6..|...|..3| |4..|...|..6|
|9..|...|..2| |6..|...|..4| |7..|...|..4| |9..|...|..5|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|5..|...|..4| |4..|.7.|..6| |4..|..7|..6| |7..|...|..3|
|6..|21.|5.7| |9..|24.|..7| |9..|32.|..5| |5..|174|..2|
|8..|...|..3| |5..|...|..3| |5..|...|..8| |6..|...|..8|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|7..|...|..1| |2..|...|..1| |8..|...|..7| |3..|...|..7|
|2..|...|..5| |3..|...|..8| |2..|...|..1| |8..|...|..4|
|316|597|428| |876|321|495| |316|978|542| |246|738|591|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
JPF
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Re: Ask for patterns that they dont have puzzles 2
by blue » Wed Mar 29, 2023 8:56 am
JPF wrote:As a by-product of the previous study and if blue confirms it, the following pattern is invalid:
Confirmed. (I had done an exhaustive search -- two, actually, using different methods)
It is even a maximum invalid pattern i.e. the addition of any clue makes it valid:
Amazing ! Nice work.
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Re: Ask for patterns that they dont have puzzles 2
by blue » Wed Mar 29, 2023 9:07 am
For Colin:
One with an empty frame ...
- Code: Select all
+---+---+---+
|714|356|2..|
|8..|...|7..|
|3..|...|5..|
+---+---+---+
|2..|4..|1.9|
|6..|...|3..|
|5..|...|4..|
+---+---+---+
|167|943|8..|
|...|...|...|
|...|2..|..7|
+---+---+---+ 7x7A plus 4
One with an empty frame ...
- Code: Select all
+---+---+---+
|391|682|5..|
|7..|...|9..|
|5..|...|8..|
+---+---+---+
|2..|...|45.|
|1..|...|7.9|
|8..|...|1..|
+---+---+---+
|672|415|3..|
|...|2..|...|
|...|.9.|...|
+---+---+---+ 7x7A plus 4
- blue
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- Joined: 11 March 2013
Re: Ask for patterns that they dont have puzzles 2
by Serg » Wed Mar 29, 2023 10:50 pm
Congratulatons to JPF for finding new maximum invalid pattern! It was great to see so fast confirmation of this by blue! Could you biefly describe your method, blue?
Serg
Serg
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- Location: Russia
