The New Sudoku Players' Forum

by **coloin** » Fri Mar 17, 2023 11:25 pm

Well done,
I had originally postulated that 3 clues was required

Code: Select all: +---+---+---+ |982|356|174| |7..|...|..8| |3..|...|..6| +---+---+---+ |1..|...|..2| |2.9|...|..3| |4..|.1.|..5| +---+---+---+ |5..|...|..7| |8..|...|..9| |673|289|541| +---+---+---+ valid puzzle with 2 clues

Have you added +2 to all the perimeter combinations ?

by **JPF** » Sat Mar 18, 2023 8:08 pm

jovi_al01 wrote: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.

Good job! but I'm not sure your list is complete.
For example, here are 9 more:

Code: Select all: 1234567894.......59.......12.......787..6...45.......36.......23.......8781293546 1234567894.......59.......15.......387..6...42.......83.......76.......2789213456 1234567894.......68.......12.......55...9...76.......39.......27..6....4364712598 1234567899.......14.......62.......55...8...76.......38.......27..6....4364792518 1234567898.......65..2....32.......44...8...17.......56.......29.......7375192468 1234567898.......17.......569......25...1...73.......42.......34.......6961327458 1234567896.......59.......12.......64...8...75.......37..3....48.......2346712598 1234567896.......58.......12.......64...9...75.......37..3....49.......2346712598 1234567899.......17.......565......28...9...73.......44.......62.......3569327418

JPF

by **jovi_al01** » Sun Mar 19, 2023 1:00 am

interesting! i had assumed my list was complete, but there was a power outage in the middle of it which forced me to restart it. i thought i'd picked up where i left off, but perhaps i didn't!

by **coloin** » Sun Mar 19, 2023 12:21 pm

It seems that adding 2 clues to a perimeter set of clues isnt a very efficient way to generate these

From 0.15M perimiter sets only 4 puzzles were found, only one was new.

Code: Select all: 1234567894.......69.......33..9...525.......87.......48.......76.......5295387641

From 0.4M perimiter sets only 4 puzzles were found, and two were new

Code: Select all: 1234567898.......35.......64....7..13.......86......952.......79.......4714869532 1234567896.......57.......23...2...64.......35.......82.......48...7...1964183527

a very approx figure would be maybe there is around 75-120 valid puzzles in total with around 5-10M perimeter sets.

by **JPF** » Sun Mar 19, 2023 10:58 pm

Here is a new list (70 puzzles) including all the puzzles posted above:

Hidden Text: Show

There are only 3 ed-patterns in the list:

Code: Select all: +---+---+---+ +---+---+---+ +---+---+---+ |123|456|789| |123|456|789| |123|456|789| |4..|...|..5| |4..|...|..6| |8..|...|..3| |9..|...|..1| |7..|...|..1| |5..|...|..1| +---+---+---+ +---+---+---+ +---+---+---+ |2..|...|..7| |3..|...|..5| |4..|...|..8| |87.|.6.|..4| |5..|.9.|..8| |7..|.1.|..4| |5..|...|..3| |6..|...|..2| |6..|..7|..2| +---+---+---+ +---+---+---+ +---+---+---+ |6..|...|..2| |9..|...|..3| |9..|...|..6| |3..|...|..8| |8..|6..|..4| |3..|...|..7| |789|213|546| |246|813|957| |216|873|495| +---+---+---+ +---+---+---+ +---+---+---+

The question then is: are these patterns valid or not?

Code: Select all: +---+---+---+ +---+---+---+ |xxx|xxx|xxx| |xxx|xxx|xxx| |x..|...|..x| |x..|...|..x| |x..|...|..x| |x..|...|..x| +---+---+---+ +---+---+---+ |x..|...|..x| |x..|...|..x| |x..|.xx|..x| |x..|.x.|..x| |x..|...|..x| |x..|...|..x| +---+---+---+ +---+---+---+ |x..|...|..x| |x..|...|..x| |x..|...|..x| |x.x|...|..x| |xxx|xxx|xxx| |xxx|xxx|xxx| +---+---+---+ +---+---+---+

JPF

by **Serg** » Sun Mar 19, 2023 11:41 pm

Hi, JPF!

JPF wrote:The question then is: are these patterns valid or not?
Code: Select all
+---+---+---+ +---+---+---+ |xxx|xxx|xxx| |xxx|xxx|xxx| |x..|...|..x| |x..|...|..x| |x..|...|..x| |x..|...|..x| +---+---+---+ +---+---+---+ |x..|...|..x| |x..|...|..x| |x..|.xx|..x| |x..|.x.|..x| |x..|...|..x| |x..|...|..x| +---+---+---+ +---+---+---+ |x..|...|..x| |x..|...|..x| |x..|...|..x| |x.x|...|..x| |xxx|xxx|xxx| |xxx|xxx|xxx| +---+---+---+ +---+---+---+

The second pattern is invalid, because it is subset of invalid Magic Pattern

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

Serg

by **JPF** » Mon Mar 20, 2023 12:04 am

Hi Serg!
Yes, of course! Thanks.

JPF

by **coloin** » Mon Mar 20, 2023 1:11 am

JPF wrote:The question then is: are these patterns valid or not?

considering there are only 5 ED half perimeter pattern sets, it still seems a big ask to check completely even a single one of the patterns

Code: Select all: +---+---+---+ |123|456|789| |4..|...|...| |5..|...|...| +---+---+---+ |2..|...|...| |3..|...|...| |7..|...|...| +---+---+---+ |8..|...|...| |9..|...|...| |6..|...|...| +---+---+---+

Finding the first perimeter pattern plus 2 was the feat

Here are 5 more

Code: Select all: 1234567896.......57.......33...6...24.......65.......82.......48...7...1964381527 6845972311.......65.......78.......47.......339..6...54.......89.......2271834569 6845972311.......65.......78.......47.......339..6...52.......94.......8971834562 4571892361.......96.......45...7.6.88.......29.......12.......53.......7748562193 9814753266.......97.......44....95.11.......72.......33.......28.......5549321768

by **JPF** » Mon Mar 20, 2023 7:21 pm

fishing party:

Code: Select all: 1234567896.......49.......28.......75...9...37.4.....62.......54.......8398725641

JPF

by **JPF** » Tue Mar 21, 2023 11:46 pm

Here's a last list of 93 ed-puzzles incorporating the previous posts. It's probably incomplete, but I'm stopping fishing for this type of puzzles for the sake of saving electricity

Hidden Text: Show

JPF

by **coloin** » Wed Mar 22, 2023 9:24 am

I found 16 more overnight ... 12 that you found and 4 that were new,

Code: Select all: 8914753264.......86.......95..8....11.......72.......39...8...27.......5385921764 6834752199.......37..1....58....3..12.......74.......83.......21.......4529841736 1684753299.......57...8...64....9..35.......72.......83.......28.......4694723851 8196753246.......72.......95.....7.11....9..87.......33.......69.......5476351892

by **JPF** » Thu Mar 23, 2023 8:58 pm

Edited:
.....
incorrect results.

Based on a random sample of 50000 perimeters, the average number of solutions/perimeter is 118000.

JPF

by **coloin** » Fri Mar 24, 2023 12:00 pm

Great work ...and my previous assumptions were eroneous on multiple levels ... :oops:

Each solution grid has [not 9x9} 9x36x9 / 2 = 1458 perimeter sets

by **JPF** » Sat Mar 25, 2023 5:46 pm

To complete the results on perimeters:
Edited:
....
incorrect results

In some perimeters, a few digits can be placed. ~~It seems that the maximum number of placeable digits is 4.~~
Here is an example:

Code: Select all: +---+---+---+ +---+---+---+ |123|456|789| |123|456|789| |4..|...|..5| |4..|...|..5| |9..|...|..1| |9.5|...|.41| +---+---+---+ +---+---+---+ |2..|...|..4| |2..|...|..4| |7..|...|..8| |7..|...|..8| |5..|...|..3| |5..|...|..3| +---+---+---+ +---+---+---+ |8..|...|..2| |8..|...|..2| |6..|...|..7| |6.2|...|8.7| |357|281|496| |357|281|496| +---+---+---+ +---+---+---+

The placement can be easy as in the above case or more difficult as in the following examples:

Code: Select all: +---+---+---+ +---+---+---+ |123|456|789| |123|456|789| |5..|...|..6| |5..|...|..6| |7..|...|..2| |7.6|...|..2| +---+---+---+ +---+---+---+ |4..|...|..1| |4..|...|..1| |6..|...|..3| |6..|...|..3| |2..|...|..8| |2..|...|..8| +---+---+---+ +---+---+---+ |3..|...|..5| |3..|...|..5| |9..|...|..7| |9..|...|.67| |865|179|234| |865|179|234| +---+---+---+ +---+---+---+ SER=8.3

or

Code: Select all: +---+---+---+ +---+---+---+ |123|456|789| |123|456|789| |5..|...|..6| |5..|...|3.6| |7..|...|..1| |7..|...|..1| +---+---+---+ +---+---+---+ |4..|...|..8| |4..|...|..8| |6..|...|..5| |6..|...|..5| |2..|...|..3| |2..|...|..3| +---+---+---+ +---+---+---+ |3..|...|..4| |3..|...|..4| |9..|...|..7| |9..|...|..7| |845|917|632| |845|917|632| +---+---+---+ +---+---+---+ SER=7.9

JPF

by **blue** » Sat Mar 25, 2023 8:48 pm

coloin wrote:Great work ...and my previous assumptions were eroneous on multiple levels ...
Each solution grid has [not 9x9} 9x36x9 / 2 = 1458 perimeter sets

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.

JPF wrote:The one with the greatest number of solutions has 6,676,496 solutions

Here are a few with larger counts:

Hidden Text: Show

Here's one with 5 solvable cells:

Hidden Text: Show

"More homework": find 3 more "frame + 2" puzzles.

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