The New Sudoku Players' Forum

by **coloin** » Tue Apr 25, 2023 11:32 pm

Second one
was easier to get several 20C straight off and successive relabling ...

Code: Select all: +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ |6..|8..|...| |x..|8..|...| |...|1..|...| |...|1..|...| |...|1..|...| |..4|.7.|...| |..4|.7.|...| |..8|.2.|...| |..8|.2.|...| |..2|.3.|...| |..1|.2.|.3.| |..1|.2.|.3.| |..1|.4.|.3.| |..1|.4.|.3.| |..4|.5.|.6.| +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ |...|7..|6.8| |...|7..|6.8| |...|7..|8.4| |...|7..|8.4| |...|7..|1.4| |.5.|...|.2.| |.5.|...|.2.| |.5.|...|.7.| |.5.|...|.7.| |.5.|...|.7.| |9.3|...|...| |9.3|...|...| |9.3|...|...| |9.3|...|...| |8.3|...|...| +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ |.4.|..5|...| |.4.|..5|...| |.3.|..9|...| |.3.|..9|...| |.8.|..6|...| |...|.8.|5..| |...|.8.|5..| |...|.8.|2..| |...|.8.|2..| |...|.4.|3..| |...|..3|..9| |...|..3|..x| |...|..3|..1| |...|..3|..x| |...|..5|...| +---+---+---+ 20C +---+---+---+ 4771 sol +---+---+---+19C +---+---+---+ 530 sol +---+---+---+18C

I think the method depends on interconnectivity of the 19C and 20C puzzles here
....I chance on adding 2 clues which resulted in a pattern with has at least an average number [? 20000] of 20C puzzles.
.... maybe picking sub puzzles with low sol count to relabel might be more efficient. I did have to relabel the 19C a couple of times

And Its easier fishing for a puzzle when you know that it is there in the lake

by **JPF** » Wed Apr 26, 2023 12:32 am

For the first pattern, Colin had already posted his solution before I saw the challenge proposed by Blue. So I prioritized solving the second one, which I found not too difficult.
Out of curiosity, I then tackled the first one and to my great surprise, I got the result on the first iteration.

I started with the 18-clue pattern and added a random clue (r9c1). Then, I generated 1000 valid 19-clue puzzles. After removing the excess cell, I obtained a distribution of solutions ranging from 1 to 890.
And it was done!
Moral of the story: You need at least one fish in the lake and some luck on your side!

JPF

by **blue** » Wed Apr 26, 2023 1:14 am

Wow, you guys are amazing :!:

JPF wrote:Moral of the story: You need at least one fish in the lake and some luck on your side!

Knowing a trick or two for low clue counts, seemed to help too

Sometime when I've got nothing exciting to do, I'll have to look into this further.
Thanks for taking up the challenge.

by **coloin** » Thu Apr 27, 2023 2:18 pm

blue wrote:"Should you choose to accept this mission" ... think carefully and good luck.....

Code: Select all: +---+---+---+ |...|...|..,| |...|...|..,| |...|...|..,| +---+---+---+ |...|...|xxx| |...|...|xxx| |...|...|xxx| +---+---+---+ |xxx|xxx|xxx| |xxx|xxx|xxx| |xxx|xxx|xxx| +---+---+---+ needs 4 clues ....? proven

There are 393 ED ways to add 4 clues in the 5 boxes from here
Here are 28 valid puzzles and their min lex pattern
Plus one from JPF's puzzle, which didnt come out in my batch, so almost certainly there are more patterns
Plus a furthur one from blue

Code: Select all: 1....3........5..................198..9...627......543346871952715392864892564371 # .................X.....X..XXXX......XXX......XXX.X....XXXXXXXXXXXXXXXXXXXXXXXXXXX 1...7.....8.................5....894......621......573542317968791864352836592417 # .................X.....X.X.XXX......XXX......XXX.....XXXXXXXXXXXXXXXXXXXXXXXXXXXX 1...8......4.....................3676.....891......542371264958842915673965837124 # .................X.....X.X.XXX......XXX......XXX....X.XXXXXXXXXXXXXXXXXXXXXXXXXXX 1..........67...............4....315......472......968572843691638291547914675823 # .................X.....X.X.XXX......XXX......XXX...X..XXXXXXXXXXXXXXXXXXXXXXXXXXX 1....7......4...............3....968......412......375348961527562374891791825643 # .................X.....X.X.XXX......XXX......XXX.X....XXXXXXXXXXXXXXXXXXXXXXXXXXX 13...........5...................841....9.672......953316948527785263194942571368 # .................X....XX...XXX......XXX......XXX.....XXXXXXXXXXXXXXXXXXXXXXXXXXXX 13...........5...................876...1..392......415395842167742361958816975234 # .................X....XX...XXX......XXX......XXX....X.XXXXXXXXXXXXXXXXXXXXXXXXXXX 1...........27.................1.867......194......523315792648762348951894561372 # .................X....XX...XXX......XXX......XXX..X...XXXXXXXXXXXXXXXXXXXXXXXXXXX 1.8..........9...................153......894.9....627362845971579621348841973562 # .................X....XX...XXX......XXX......XXXX.....XXXXXXXXXXXXXXXXXXXXXXXXXXX 1.............2.8................598......173..8...624345218967716935842982764351 # .................X..X..X......XXX......XXX......XXX.X.XXXXXXXXXXXXXXXXXXXXXXXXXXX 1.....7.....4....................897.9....642......153312645978584927361769813524 # .................X..X..X......XXX......XXX....X.XXX...XXXXXXXXXXXXXXXXXXXXXXXXXXX 1....2......4.6..................493......875......612542371968681925347739864521 # ................XX.....X..XXXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX 1...3.......4.7..................317......824......695546871932712693458938245176 # ................XX.....XX..XXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX 1.7.........96...................693......817......425385642971761598342942731568 # ................XX....XX...XXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX 1..5.......84....................863......495......271532674918641928357897315624 # ..............X..X.....X.X.XXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX 1...2.....5...8..................845......697......312381592476745613928962874531 # ..............X..X....X..X.XXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX 1........8............4.......8..951......423......867314928675598761342762534198 # ........X........X.....X...XXX......XXX......XXX.X....XXXXXXXXXXXXXXXXXXXXXXXXXXX 1........8............96.........654......178......392386921547715864923942735861 # ........X........X....XX...XXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX 1.......9.....3........6.........853......971......462581624397762395148934718625 # ........X........X..X..X......XXX......XXX......XXX...XXXXXXXXXXXXXXXXXXXXXXXXXXX 1.........2............9...4.....317......692......845362914578714528963895673421 # ........X.......X......X...XXX......XXX......XXX.....XXXXXXXXXXXXXXXXXXXXXXXXXXXX 1............3.........2......1..693......427......815314527968592368174678914352 # ........X.......X......X...XXX......XXX......XXX...X..XXXXXXXXXXXXXXXXXXXXXXXXXXX 1..........6...........5.........691.....7352......874391672548574938126682514937 # ........X.......X......X...XXX......XXX......XXX..X...XXXXXXXXXXXXXXXXXXXXXXXXXXX 1..........3.........2...........953....9.168......472362915847714832695985764321 # ........X.......X......X...XXX......XXX......XXX.X....XXXXXXXXXXXXXXXXXXXXXXXXXXX 1...8.......7..........9.........891......672......345315274968872691453946538127 # ........X.......X......XX..XXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX 1.7..........9.........6.........873......654......921742965318865213497931748562 # ........X.......X.....XX...XXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX 1...........4........7.6.........648......325......971314597862572618493968324157 # ........X.......XX.....X...XXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX 1.........7..9........6..........815......962......347549832671732641598861975423 # ........X.....X........X.X.XXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX 1........2.......1...6...........178......694......352592871463734962815861345927 # ........X.....X.....X.....XXXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX ........1.......2......3..4143......256......789......527381469691754283834269157 # ........X.......X......X..XXXX......XXX......XXX......XXXXXXXXXXXXXXXXXXXXXXXXXXX JPF 1.....6.....8..............6.....315......982......476561749238327568149498213567 # .................X..X..X......XXX......XXX.....XXXX...XXXXXXXXXXXXXXXXXXXXXXXXXXX blue

by **JPF** » Thu Apr 27, 2023 5:58 pm

It would be useful to have the list of the 393 ED patterns!

JPF

by **coloin** » Thu Apr 27, 2023 6:38 pm

JPF wrote:It would be useful to have the list of the 393 ED patterns!

here are 393 - updated to be complete - TY

Hidden Text: Show

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by **JPF** » Thu Apr 27, 2023 9:15 pm

Here is the missing pattern:

Code: Select all: ........x........x........x......xxx......xxx.x....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

I will study your question as soon as I have a little more time.

JPF

by **blue** » Fri Apr 28, 2023 4:32 am

Of the 393 4-clue shapes, all but 82 of them are ruled out by the "magic 40" patterms.

Colin provided puzzles for 29 of those, leaving 53.

Hidden Text: Show

Here's one more puzzle with a shape that wasn't in Colin's list

Code: Select all: 1.....6.....8..............6.....315......982......476561749238327568149498213567 x.....x.....x..............x.....xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx -- from the list of 53, above

by **Serg** » Sun Jun 11, 2023 5:53 pm

Hi, Blue!
I am verifying your maximal invalid patterns. Could you post an example of valid puzzle with such shape:

Code: Select all: T24A +-----+-----+-----+ |. . .|. . .|. . .| |. . x|. . .|. . .| |. x .|. . .|. . x| +-----+-----+-----+ |. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|x x x|x x x| +-----+-----+-----+ |x x x|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x| +-----+-----+-----+

This is your T24 pattern with 1 clue added. If T24 is maximal invalid pattern, T24A must has valid puzzles, but I could'n find such examples yet.

Serg

by **JPF** » Mon Jun 12, 2023 9:50 am

I haven't found a valid puzzle with the pattern T24A either. But blue has surprising abilities that we cannot overlook...
If T24A is indeed invalid, it would be a maximal invalid pattern.

JPF

by **blue** » Mon Jun 12, 2023 11:44 am

Serg wrote:I am verifying your maximal invalid patterns.

That's good news !

Could you post an example of valid puzzle with such shape:
Code: Select all
T24A +-----+-----+-----+ |. . .|. . .|. . .| |. . x|. . .|. . .| |. x .|. . .|. . x| +-----+-----+-----+ |. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|x x x|x x x| +-----+-----+-----+ |x x x|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x| +-----+-----+-----+

This is your T24 pattern with 1 clue added. If T24 is maximal invalid pattern, T24A must has valid puzzles, but I could'n find such examples yet.

Here's one ...

Code: Select all: . . . | . . . | . . . . . 7 | . . . | . . . . 2 . | . . . | . . 4 ------+-------+------ . . . | . . . | 7 6 5 . . . | . . . | 4 1 8 . . . | 1 8 7 | 3 9 2 ------+-------+------ 3 4 1 | 2 5 8 | 6 7 9 8 9 6 | 4 7 3 | 5 2 1 5 7 2 | 9 1 6 | 8 4 3

by **JPF** » Mon Jun 12, 2023 10:52 pm

I eventually found a puzzle for this pattern. Moral of the story: Be perseverant and patient even if you're not sure if there's a fish in the lake!

Code: Select all: +-------+-------+-------+ | . . . | . . . | . . . | | . . 1 | . . . | . . . | | . 2 . | . . . | . . 3 | +-------+-------+-------+ | . . . | . . . | 1 4 5 | | . . . | . . . | 3 6 7 | | . . . | 6 1 7 | 2 8 9 | +-------+-------+-------+ | 8 1 2 | 4 5 9 | 7 3 6 | | 6 9 7 | 1 8 3 | 4 5 2 | | 4 3 5 | 7 6 2 | 9 1 8 | +-------+-------+-------+

JPF

by **Serg** » Wed Jun 14, 2023 10:18 am

Hi, Blue!
I'd like to verify full list of maximal invalid patterns published by you in this thread. At the moment I consider "anticorner" patterns only, i.e. patterns which can be morphed to the form with filled B6, B8 and B9 boxes.

"Batch 0" - B1, B3, S1, S2, S3 (5 patterns).
"Batch 1" - O2-O5 (4 patterns, O1 coincides with S2).
"Batch 2" - T1, T4-T46 (44 patterns, T2 coincides with B3, T3 coincides with B1).
"Batch 3" - 12A, 12B (2 patterns, 22A, 22B, 22C - are not anticorner patterns).

Totally: 55 anticorner maximal invalid patterns. Right?

Serg

by **blue** » Wed Jun 14, 2023 9:07 pm

Serg wrote:At the moment I consider "anticorner" patterns only, i.e. patterns which can be morphed to the form with filled B6, B8 and B9 boxes.
(...)
Totally: 55 anticorner maximal invalid patterns. Right?

55, right.
That's 4 more than I hoped you were checking ... so "good news", still.

Cheers.

by **Serg** » Fri Jun 16, 2023 4:21 pm

Hi, Blue!
I finished checks and can confirm that 55 published by you in this thread anticorner maximal invalid patterns are really maximal invalid. I checked patterns' invalidity and maximality. This is the list of checked patterns.

Serg wrote:"Batch 0" - B1, B3, S1, S2, S3 (5 patterns).
"Batch 1" - O2-O5 (4 patterns, O1 coincides with S2).
"Batch 2" - T1, T4-T46 (44 patterns, T2 coincides with B3, T3 coincides with B1).
"Batch 3" - 12A, 12B (2 patterns, 22A, 22B, 22C - are not anticorner patterns).

Totally: 55 anticorner maximal invalid patterns.

Really I checked not exact published patterns, but their families, having the same clue configuration in all boxes except for B5 box. So, I searched for all proper configuration of the B5 box. This is example of such patterns family.

Code: Select all: B1/B3 +-----+-----+-----+ |. . .|. . .|. x x| |. . .|. . .|. x x| |. . .|. . .|. x x| +-----+-----+-----+ |. . .| |x x x| |. . .| ? |x x x| |x x x| |x x x| +-----+-----+-----+ |x x x|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x| +-----+-----+-----+

It's interesting that in all cases, except one, all published patterns were reproduced. (In this example B1 and B3 patterns were rediscovered.) But T23 patterns family

Code: Select all: T23+ +-----+-----+-----+ |. . .|. . .|. . x| |. . .|. . .|. x .| |. . .|. x .|x . .| +-----+-----+-----+ |. . .| |x x x| |. . .| ? |x x x| |. . .| |x x x| +-----+-----+-----+ |x x x|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x| +-----+-----+-----+

produced 1 additional (to T23) invalid pattern:

Code: Select all: T23A +-----+-----+-----+ |. . .|. . .|. . x| |. . .|. . .|. x .| |. . .|. x .|x . .| +-----+-----+-----+ |. . .|. . .|x x x| |. . .|. . .|x x x| |. . .|. x .|x x x| +-----+-----+-----+ |x x x|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x| +-----+-----+-----+

This pattern is invalid, but not maximal. It cannot be extended by adding clues to B1, B2, B4, B5 boxes (all those extentions led us to valid patterns), but can be extended by adding clues to B3 box, up to filling all the box. It's not curious, because resulting pattern

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 x|x x x| |x x x|x x x|x x x| +-----+-----+-----+

is isomorph of T1 maximal invalid pattern. So, no new patterns from my side.

Serg

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