Of the 200 B159plus3 puzzles I have ....99% were of the 1st pattern
and to serg .... Im afraid that its a crude method - if a puzzle is not found in reasonable time the chances are that the pattern doesnt have valid puzzles ...
but a pattern either has puzzles or it doesnt ... even some 18C patterns just dont have puzzles ... even though similar patterns differing by 1 clue do !!
Ask for patterns that they dont have puzzles 2
Re: Ask for patterns that they dont have puzzles 2
by coloin » Sat Jul 04, 2020 8:40 pm
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Sat Jul 04, 2020 8:43 pm
JPF wrote:Here is an other one with symmetry:
- Code: Select all
2 . . | . . . | . . 8
7 . . | 3 . 9 | . . 6
5 . . | . . . | . . 1
-------+-------+-------
6 . . | . 8 . | . . 7
3 . . | . . . | . . 2
4 . 9 | . . . | 3 . 5
-------+-------+-------
8 . . | . . . | . . 4
9 . . | . . . | . . 3
1 2 3 | 4 5 6 | 7 8 9
JPF
very good ....
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Re: Ask for patterns that they dont have puzzles 2
by JPF » Tue Jul 07, 2020 2:36 pm
5 clues is never enough?
It can work with 6 clues but B3 has to be 0 and at least one B5,B7 = 0
Here are examples:
Conjecture: with 5 clues, Min sol. = 5
JPF
- Code: Select all
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|...|...|xxx|
|...|...|xxx|
|...|...|xxx|
+---+---+---+
|...|xxx|xxx|
|...|xxx|xxx|
|...|xxx|xxx|
+---+---+---+
It can work with 6 clues but B3 has to be 0 and at least one B5,B7 = 0
Here are examples:
- Code: Select all
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|72.|...|...| |...|.8.|...| |...|...|...| |...|..3|...|
|...|5..|...| |..5|...|...| |1..|7..|...| |.65|...|...|
|..6|...|...| |2.7|...|...| |.26|...|...| |..7|...|...|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|...|...|217| |...|5..|197| |..8|...|197| |8..|...|214|
|..4|3..|685| |...|...|635| |...|.2.|685| |...|...|678|
|...|...|394| |6..|...|284| |...|...|324| |...|...|395|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|...|485|963| |...|821|963| |...|487|961| |...|754|963|
|...|971|852| |...|764|852| |...|163|852| |3..|169|852|
|...|632|741| |...|935|471| |...|952|743| |...|832|741|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
- Code: Select all
+---+---+---+ +---+---+---+
|...|6..|...| |...|69.|...|
|9.2|...|...| |3..|...|...|
|3..|...|...| |74.|...|...|
+---+---+---+ +---+---+---+
|.6.|...|189| |...|...|317|
|.8.|...|675| |..6|...|295|
|...|...|324| |...|...|684|
+---+---+---+ +---+---+---+
|...|514|963| |...|821|963|
|...|793|852| |...|764|852|
|...|862|741| |...|953|741|
+---+---+---+ +---+---+---+
Conjecture: with 5 clues, Min sol. = 5
JPF
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Re: Ask for patterns that they dont have puzzles 2
by m_b_metcalf » Tue Jul 07, 2020 4:52 pm
JPF wrote:Conjecture: with 5 clues, Min sol. = 5
First stab:
- Code: Select all
. . . 3 . . . . .
4 . . . . . . . .
9 . . . . . . . .
. 5 . . . . 1 2 3
. 3 . . . . 4 5 6
. . . . . . 7 8 9
. . . 2 7 9 8 6 4
. . . 5 3 8 2 7 1
. . . 1 6 4 9 3 5 14 solution(s)
Mike
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Re: Ask for patterns that they dont have puzzles 2
by JPF » Tue Jul 07, 2020 5:09 pm
I should have given an example:
JPF
- Code: Select all
+---+---+---+
|.82|...|...|
|...|...|...|
|...|.45|...|
+---+---+---+
|...|...|275|
|...|...|698|
|5..|...|314|
+---+---+---+
|...|281|936|
|...|674|852|
|...|953|741|
+---+---+---+ 5 sol.
JPF
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Re: Ask for patterns that they dont have puzzles 2
by JPF » Tue Jul 07, 2020 5:32 pm
BTW 5 clues are enough for this pattern:
EDIT : 4 clues are enough...
JPF
- Code: Select all
+---+---+---+
|xxx|...|...|
|xxx|...|...|
|xxx|...|...|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|...|xxx|xxx|
|...|xxx|xxx|
|...|xxx|xxx|
+---+---+---+
- Code: Select all
+---+---+---+
|123|...|.6.|
|456|.3.|...|
|789|...|...|
+---+---+---+
|...|..1|...|
|...|...|..7|
|.3.|...|...|
+---+---+---+
|...|367|219|
|...|189|654|
|...|542|378|
+---+---+---+
EDIT : 4 clues are enough...
- Code: Select all
+---+---+---+
|123|...|...|
|456|...|...|
|789|...|...|
+---+---+---+
|...|.5.|...|
|..2|...|..1|
|...|.4.|...|
+---+---+---+
|...|784|539|
|...|293|617|
|...|165|428|
+---+---+---+
JPF
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Fri Jul 10, 2020 4:12 pm
Thanks for those 2 patterns ... I will update the list,
5 clues are probably never enough
as 5 clues are only just needed for
maybe Serg can show that adding 5 clues is impossible with his list of invalid crossing patterns ...
and
I suspect we have proof that 2 clues are never enough for this pattern
5 clues are probably never enough
- Code: Select all
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|...|...|xxx|
|...|...|xxx|
|...|...|xxx|
+---+---+---+
|...|xxx|xxx|
|...|xxx|xxx|
|...|xxx|xxx|
+---+---+---+
as 5 clues are only just needed for
- Code: Select all
+---+---+---+
|1..|..2|...|
|...|...|..3|
|.4.|...|...|
+---+---+---+
|...|293|651|
|...|654|987|
|.5.|781|432|
+---+---+---+
|...|176|329|
|...|529|148|
|...|438|576|
+---+---+---+ valid 36plus5
maybe Serg can show that adding 5 clues is impossible with his list of invalid crossing patterns ...
and
I suspect we have proof that 2 clues are never enough for this pattern
- Code: Select all
+---+---+---+ +---+---+---+
|xxx|xxx|...| |123|869|...|
|xxx|xxx|...| |456|732|...|
|xxx|xxx|...| |789|415|...|
+---+---+---+ +---+---+---+
|...|...|...| |2..|.4.|...|
|...|...|...| |...|...|.5.|
|...|...|...| |...|...|...|
+---+---+---+ +---+---+---+
|...|xxx|xxx| |...|597|812|
|...|xxx|xxx| |...|186|534|
|...|xxx|xxx| |...|324|796|
+---+---+---+ +---+---+---+ valid 36plus3 puzzle
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Re: Ask for patterns that they dont have puzzles 2
by JPF » Fri Jul 10, 2020 9:30 pm
For this pattern B1359, one is enough but in the right box:
JPF
- Code: Select all
+---+---+---+
|xxx|...|xxx|
|xxx|...|xxx|
|xxx|...|xxx|
+---+---+---+
|...|xxx|...|
|...|xxx|...|
|...|xxx|...|
+---+---+---+
|...|...|xxx|
|...|...|xxx|
|...|...|xxx|
+---+---+---+
+---+---+---+
|123|...|495|
|456|...|783|
|789|...|612|
+---+---+---+
|...|143|...|
|...|657|...|
|...|829|...|
+---+---+---+
|...|...|879|
|.9.|...|354|
|...|...|126|
+---+---+---+
JPF
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Re: Ask for patterns that they dont have puzzles 2
by jovi_al01 » Sun Jun 26, 2022 8:51 pm
coloin wrote:I generated all the ED 237083 ways to fill B1B5B9. There was no puzzle adding 2 clues.
On adding 3 clues to approx 1/3 of all the 237083 B1B5B9there were 200 27plus3 puzzles,
so probably there are around 600 of such 27plus3 puzzles. [presently have 500]
i've found that there are 684 of them:
Hidden Text: Show
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Re: Ask for patterns that they dont have puzzles 2
by JPF » Tue Jun 28, 2022 2:16 pm
Hi jovi_al01
Interesting results!
As mentioned here, there are 5 B1B5B9 (or B3B5B7) + 3 ed-patterns.
Your 684 list can be split in 4 ed patterns.
if you have done an exhaustive search (I didn't check) it shows that the 5th pattern :
JPF
Interesting results!
As mentioned here, there are 5 B1B5B9 (or B3B5B7) + 3 ed-patterns.
Your 684 list can be split in 4 ed patterns.
- Code: Select all
M1 M2 M3 M4
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|...|...|123| |...|...|123| |...|...|123| |...|...|123|
|...|...|456| |...|...|456| |...|...|456| |...|...|456|
|...|...|789| |...|...|789| |...|...|789| |...|..1|789|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|...|124|...| |...|124|...| |...|123|...| |...|142|...|
|...|763|...| |...|389|...| |...|469|...| |...|687|...|
|..7|895|...| |..8|675|...| |..4|578|...| |..6|539|...|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
|136|...|...| |147|...|...| |158|..7|...| |195|...|...|
|285|..1|.4.| |632|...|..1| |296|.8.|...| |463|...|..5|
|479|...|...| |985|..7|...| |437|...|...| |782|...|...|
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
7 669 2 6
if you have done an exhaustive search (I didn't check) it shows that the 5th pattern :
- Code: Select all
+---+---+---+
|...|...|xxx|
|...|...|xxx|
|...|...|xxx|
+---+---+---+
|...|xxx|...|
|...|xxx|...|
|..x|xxx|...|
+---+---+---+
|xxx|...|...|
|xxx|...|...|
|xxx|.xx|...|
+---+---+---+
JPF
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Tue Jun 28, 2022 9:09 pm
Hi jovi_al01
Great work
All your puzzles are unique and we have another pattern without puzzles !
Its prompted me to revisit this topic from another angle ....
from your list of puzzles, removing clues there were only 17 21C puzzles [ and no 20C puzzles]
Great work
All your puzzles are unique and we have another pattern without puzzles !
Its prompted me to revisit this topic from another angle ....
from your list of puzzles, removing clues there were only 17 21C puzzles [ and no 20C puzzles]
- Code: Select all
......1........456......78....12.......457..2..36.....2.9..8...4.6......75.......
......1........456......78....12.......457..2..36.....2....8...4.6......751......
........3......4.6......789...1.3........72....3869...25..4.....79......8.6......
........3......4.6......789...1.3........72....3869...25..4.....71......8.9......
......1........4.6......789...123......45......7.8..3.1.3......285......4..6.....
......1........4.6......789...12.......457.....7.8..3.1.3......285......4..6.....
.......23......456.....1..9....4.......789.....265....174.......9....8..6.5......
.......23......456.....1..9....4.......789.....256....174.......9....8..5.6......
.......23......456.....1.8.....4.......879.....256....184.......9......75.6......
.......23......456.....1.8.....4.......879.....265....184.......9......76.5......
......123......45.......7.....124......76......38......6...9...482......7.1.....8
......12.......456......7......2.......397..8..468....35.......7....1...986......
.......23.......5.......789...124......6.3.....89.....17.......2...5....349.....1
.......23.......5.......789...124......6.3.....8.7....17.......2...5....349.....1
......1.3......456.......89...124.......78.....6.3....173...2...4...5....2.......
......1.3.......56......789...124.......78.....6.3....173...2...4...5....2.......
........3......456......789...124.......78.....6.3....173...2...4...5....2.......
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Re: Ask for patterns that they dont have puzzles 2
by jovi_al01 » Sat Aug 06, 2022 2:55 am
Hi JPF! Yes, I believe my search was exhaustive.
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Re: Ask for patterns that they dont have puzzles 2
by Robin122 » Tue Jan 24, 2023 1:29 pm
You think there are some very intriguing kinds of patterns, but I don't believe that proving these hypotheses would be very useful in real life. For instance, I believe it will be much more effective to know all maximal patterns with 2 free bands (the third band must consist of boxes containing 9 clues each; I believe there should be several hundreds of such patterns) than to follow the rule "Each 2 bands of any valid puzzle must contain more 7 clues." (Perhaps you recall my experiment where I tried to eliminate vertically symmetric patterns with 18 clues; if your rule were valid, it would be able to eliminate roughly 7300 designs from a total of 200000.)
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Re: Ask for patterns that they dont have puzzles 2
by jovi_al01 » Fri Jan 27, 2023 11:29 pm
I hate to break it to you, Robin122, but I believe this is "real life." 
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Re: Ask for patterns that they dont have puzzles 2
by jovi_al01 » Fri Mar 17, 2023 9:37 pm
apologies if this result has been shared before, but i've found that there are exactly 50 ED puzzles with the perimeter entirely given + 2 more clues.
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