The New Sudoku Players' Forum

by **coloin** » Mon Apr 24, 2023 4:55 pm

I have completed my 6x6 frame assessment

6x6 A plus 5 - this is the minimum, as 5 clues are always necessary in a crossing band
6x6 B plus 4 - 42 puzzles , 4 patterns
6x6 C plus 4 - > 400K puzzles and no plus 3

Code: Select all: 6x6A +---+---+---+ |125|346|...| |9..|..7|...| |4..|..1|...| +---+---+---+ |5..|..4|..2| |7..|..3|...| |693|752|...| +---+---+---+ |...|...|.7.| |...|...|9.4| |...|.2.|...| +---+---+---+ [6x6A plus 5] 6x6B +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ |...|...|...| |...|...|...| |...|...|...| |...|...|...| |xxx|xxx|...| |xxx|xxx|...| |xxx|xxx|...| |xxx|xxx|..x| |x..|..x|.x.| |x..|..x|.x.| |x..|..x|...| |x..|..x|.x.| +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ |x..|..x|...| |x..|..x|...| |x..|..x|...| |x..|..x|...| |x..|..x|..x| |x..|..x|..x| |x..|..x|x..| |x..|..x|..x| |x..|..x|..x| |x..|..x|x..| |x..|..x|x..| |x..|..x|...| +---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+ |xxx|xxx|...| |xxx|xxx|...| |xxx|xxx|...| |xxx|xxx|...| |...|...|...| |...|...|...| |...|...|..x| |...|...|...| |...|...|.x.| |...|...|.x.| |...|...|.x.| |...|...|.x.| +---+---+---+ 35 puzzles +---+---+---+ 4 puzzles +---+---+---+ 2 puzzles +---+---+---+ 1 puzzle [6x6B plus 4] as JPF found 6x6C +---+---+---+ |...|...|...| |.12|345|6..| |.3.|...|7..| +---+---+---+ |.8.|...|9..| |.9.|.6.|2.4| |.5.|...|3..| +---+---+---+ |.79|218|5..| |...|...|..3| |...|.9.|...| +---+---+---+ [6x6C plus 4] [many thousands of puzzles found] - and/but no plus 3

by **blue** » Mon Apr 24, 2023 9:22 pm

Hi Serg,

Thank you for confirming the 5 patterns from the previous page.
That was quick !

blue wrote:
Serg wrote:Do you have full list of maximal invalid patterns for "5 free boxes" case (B3, B1, S2) and "6 free boxes" case (S1, S3)?

For the "5 free boxes" (4 boxes filled) case ... possibly, but I don't have all of them in one place.
This weekend, I'll look at some old projects, etc., to see what I can put together.

Here's the first batch:

Code: Select all: (O1) (O2) . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | . x . . . . | . . . | . x x . . . | . . . | x x . ------+-------+------ ------+-------+------ . . . | x x x | x x x . . . | x x x | x x x . . . | x x x | x x x . . . | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x ------+-------+------ ------+-------+------ x x x | . . . | x x x x x x | . . . | x x x x x x | x x x | x x x x x x | . . . | x x x x x x | x x x | x x x x x x | x x x | x x x (O3) (O4) (O5) . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . x x | . . . . . . | . . x | . . . . . . | . . . | . . x . . x | . . . | . . . . . x | . . x | . . . . . x | . . x | . . . ------+-------+------ ------+-------+------ ------+-------+------ . . . | x x x | x x x . . . | x x x | x x x . . . | x x x | x x x . . . | x x x | x x x . . . | x x x | x x x . . . | x x x | x x x . . . | x x x | x x x . . . | x x x | x x x . . . | x x x | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | . . . | x x x x x x | . . . | x x x x x x | . . . | x x x x x x | . . . | x x x x x x | . . . | x x x x x x | . . . | x x x x x x | . . . | x x x x x x | . . . | x x x x x x | . . . | x x x

Single line format:

Hidden Text: Show

That covers all of the patterns with boxes 5,6,7,9 full, that aren't isomorphic to a pattern from the original "magic 40" list.

by **blue** » Mon Apr 24, 2023 9:31 pm

The 2nd batch:

Edited: One pattern, the original T43, has been removed from this list, and the numbers for the original T44-T47 have been adjusted downwards.

Code: Select all: (T1) (T2) (T3) . . . | . . . | x x x . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | x x x . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | x x x . . . | . . . | . x x . . . | . . . | . x x ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | x x x | x x x . . . | . . . | x x x . . . | x x x | x x x . . . | x x x | x x x . . x | . . x | x x x x x x | x x x | x x x x x x | . . . | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T4) (T5) (T6) x x x | x x x | x x x . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | . . x . . . | . . . | . x . . . . | . . . | . x . . . . | . . . | . . x . . . | . . . | x x . . . . | . . . | x x . ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | x x x | x x x . . . | . . . | x x x x x x | x x x | x x x x x x | . . . | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T7) (T8) (T9) . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | . . . . . . | . . x | . x x . . . | . . . | . x x . . . | . . x | . . . . . x | . . . | . x x . . x | . . . | . x x x x x | . . . | x x x ------+-------+------ -------+ ------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . x | x x x . . . | . . . | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T10) (T11) (T12) . . . | . . . | x x x . . . | . . . | . . x . . . | . . x | . . x . . . | . . x | . . x . . . | . . . | . . x . . . | . x . | . . x . . x | . . . | . . x . . x | . . . | x x x . . x | . . . | . . x ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . x | x x x . . . | . . . | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T13) (T14) (T15) x x x | x . . | . . . . . . | . . . | . . x . . . | . . . | . . x x . . | . . . | . . . . . . | . x x | . . x . . . | . . x | . . x x . . | . . . | . . . . . x | . . . | . . x . . x | . . x | . . x ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T16) (T17) (T18) . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . x . . . | . . x | . . . . . . | . . x | . . x . . x | . . . | . . x . . x | . . x | x x x . . . | . . x | x x . . x . | . . . | . . x ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . x | x x x . . . | . . x | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T19) (T20) (T21) . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . x . . . | . . x | . . . . . . | . . x | . . . . . x | . . x | . . . x x x | . x . | . . . x x x | . . x | . . . ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . x x | x x x . . . | . . . | x x x . . . | . . . | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T22) (T23) (T24) . . . | . . . | . . . . . . | . . . | . . x . . . | . . . | . . . . . x | . . . | . . . . . . | . . . | . x . . . x | . . . | . . . . . x | . x x | . . x . . . | . x . | x . . . x . | . . . | . . x ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . x | x x x . . . | . x x | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T25) (T26) (T27) . . . | . . . | . . . . . x | . . . | . . . . . . | . . . | . . x . . x | . . . | . . . . . . | . . . | x . . . . . | . . . | . x . . . . | . . . | . x x . . . | . . . | . x x . . x | . . . | x . . ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . x x | x x x . . . | . . x | x x x . . . | . . x | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T28) (T29) (T30) . . . | . . . | . . . . . x | . . . | . . . . . . | . . . | . . . . . x | . . . | . . . . . . | . x . | . . . . . . | . x . | . . . . . . | . . . | x x x . . . | . x . | . . . . . x | . x . | . . . ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . x | x x x . . . | . . x | x x x . . . | . . x | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T31) (T32) (T33) . . x | . . . | . . . . . . | . . . | . . . . . x | . . . | . . . . . . | . . x | . . . . . . | . . x | . . . . . . | . x . | . . . . . . | . . x | . . . . . x | . . x | . . . . . . | . . . | . . x ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . x | x x x . . . | . . x | x x x . . . | . . x | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T34) (T35) (T36) . . x | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . x | . . . | . . . . . x | . . . | . . . . . x | . . . | . . . . . . | . . x | . . . . x . | . . x | . . . . . x | . . x | . . . ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . x | x x x . . . | . . x | x x x . . . | . . x | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T37) (T38) (T39) . . x | . . . | . . . . . . | . . . | . . . . . . | . . x | . . . . . . | . . x | . . . . . . | . . x | . . . . . x | . . . | . . . . . . | . . . | . . x . . x | . . . | . . x . x . | . x . | . . . ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . x | x x x . . . | . . x | x x x . . . | . . . | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T40) (T41) (T42) . . . | . . x | . . . . . . | . . . | . . . x x . | . . . | . . . . . x | . . . | . . . . . x | . . x | . . . . . x | . . . | . . . . . x | . . x | . . . . . x | . . x | . . . . . . | . . x | . . . ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T43) (T44) (T45) . . x | . x . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . x | . . . . . x | . . x | . . . . . x | . . . | . . . . . . | . . . | . . x . x . | . . . | . . x . x . | . . x | . . x ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | . . . | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (T46) . . . | . . . | . . . . x x | . . . | . . . . . . | . . . | . . x ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | . . x | x x x ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x

Single line format:

Hidden Text: Show

Code: Select all: ......xxx......xxx......xxx......xxx......xxx..x..xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T1) .......xx.......xx.......xx......xxx...xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T2) .......xx.......xx.......xx...xxxxxx...xxxxxxxxx...xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T3) xxxxxxxxx........x........x......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T4) .......xx.......x.......xx.......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T5) .......xx.......x.......xx.......xxx...xxxxxxxxx...xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T6) .......xx.....x.xx..x....xx......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T7) .......xx.......xx..x....xx......xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T8) ..............x...xxx...xxx......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T9) ......xxx.....x..x..x.....x......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T10) ........x........x..x...xxx......xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T11) .....x..x....x...x..x.....x......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T12) xxxx.....x........x..............xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T13) ........x....xx..x..x.....x......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T14) ........x.....x..x..x..x..x......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T15) ..............x.....x..xxxx......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T16) ..............x..x.....xxx.......xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T17) ........x..x.....x.x......x......xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T18) .................x..x..x.........xxx......xxx....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T19) ..............x...xxx.x..........xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T20) ..............x...xxx..x.........xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T21) ...........x........x.xx..x......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T22) ........x.......x.....x.x........xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T23) ...........x.......x......x......xxx......xxx....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T24) ...........x.............xx......xxx......xxx....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T25) ..x............x.........xx......xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T26) ........x.......x...x...x........xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T27) ...........x............xxx......xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T28) ..x..........x........x..........xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T29) .............x......x.x..........xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T30) ..x...........x........x.........xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T31) ..............x.....x..x.........xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T32) ..x..........x............x......xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T33) ..x........x...........x.........xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T34) ...........x.......x...x.........xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T35) ...........x........x..x.........xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T36) ..x...........x...........x......xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T37) ..............x.....x.....x......xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T38) .....x.....x.......x..x..........xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T39) .....x.....x........x..x.........xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T40) ...........x..x.....x..x.........xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T41) xx.........x...........x.........xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T42) ..x.x.........x...........x......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T43) ...........x..x....x......x......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T44) ...........x.......x...x..x......xxx......xxx......xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T45) ..........xx..............x......xxx......xxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (T46)

I included (T1), even though it has 5 filled boxes ... since it seems to fit in with the rest of them.
It's a long list, with only a few interesting patterns at the top

That covers all of the patterns with boxes 6,7,8,9 full, that aren't isomorphic to a pattern from the original "magic 40" list.

Don't feel obliged to confirm them ... it would be a big job !

Cheers.

by **blue** » Mon Apr 24, 2023 9:38 pm

Three of the patterns from above, are part of another "family" of similar patterns ... like the earlier one.
The remaining ones ... 5 of 8 ... were unknown to me before Friday.

Code: Select all: (11A) [T5] (11B) [T6] (11C) [O2] . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | . x . . . . | . . . | . x . . . . | . . . | . x . . . . | . . . | x x . . . . | . . . | x x . . . . | . . . | x x . ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | x x x | x x x . . . | x x x | x x x . . . | . . . | x x x . . . | . . . | x x x . . . | x x x | x x x x x x | x x x | x x x x x x | . . . | x x x x x x | x x x | x x x ------+-------+------ ------+-------+------ ------+-------+------ x x x | x x x | x x x x x x | x x x | x x x x x x | . . . | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | . . . | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (12A) (12B) . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | . x . . . . | . . . | . x . . . . | . . . | x x . . . . | . . . | x x . ------+-------+------ ------+-------+------ . . . | x x x | x x x . . . | x x x | x x x . . . | . . . | x x x . . . | x x x | x x x x x x | x x x | x x x x x x | . . . | x x x ------+-------+------ ------+-------+------ x x x | . . . | x x x x x x | . . . | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x (22A) (22B) (22C) . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | . x x . . . | . . . | . x . . . . | . . . | . x . . . . | . . . | . x . . . . | . . . | x x . . . . | . . . | x x . . . . | . . . | x x . ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | . . . | x x x . . . | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | . . . | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x ------+-------+------ ------+-------+------ ------+-------+------ . . . | . . . | x x x . . . | x x x | x x x . . . | x x x | x x x x x x | x x x | x x x x x x | . . . | x x x x x x | . . . | x x x x x x | x x x | x x x x x x | x x x | x x x x x x | x x x | x x x

by **blue** » Mon Apr 24, 2023 10:01 pm

Hi JPF,

I have developed another approach myself, based on ideas developed in problem-solving from the "Patterns Game." I have encountered many of the difficulties mentioned in your text, such as speed of canonicalization, huge sorting, etc., and have developed solutions that are worth what they are worth.
The major disadvantage of my method is that it is not strictly exhaustive.
However, up to now, I have not found any patterns for which my conclusion (valid or invalid) has been proven incorrect.
The general idea is to determine an estimate of the distribution of the number of solutions that puzzles with the given pattern have. From this, the final goal is to find out the minimum value of this distribution. If the minimum value is 1, the pattern is valid, otherwise it is invalid.
The estimation is done recurrently.
It is worth noting that the convergence of the process towards the real distribution is more or less rapid, depending on the pattern in question.

Interesting. When you say "The estimation is done recurrently", do you mean that you make small changes to low solution count puzzles from earlier passes ... hoping for a quick approach to the true minimum ?

I've seen that you, Colin, and Mike (I think) ... seem to favor that approach. I've always been afraid to try it ... worrying that the code will get stuck in a huge backwater of fairly low solution count puzzles, that doesn't have any outlet to puzzles with the lowest count.

Thanks for the insight !

by **Serg** » Tue Apr 25, 2023 8:04 am

Hi, Blue!
Thank you for new maximal invalid patterns!
I've decided to do systematic search for "anticorner" maximal invalid patterns ("corner" pattern has B3,B5,B6,B7,B8,B9 boxes being filled, "anticorner" pattern has B6,B8,B9 boxes being filled). I'll open new thread for that.
The check of 5 patterns you published earlier (B1,B3,S1,S2,S3) was quick because I have my own old program that ideally fits for this task (no adaptation was necessary). The program is fast, but time to check pattern varies from seconds to hours. For example, checking your B1 and B3 patterns together took 3 seconds, but checking B2 pattern alone took 106 seconds.

Serg

by **blue** » Tue Apr 25, 2023 9:09 am

I found a puzzle for the (bogus) T43 pattern listed above.

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

I'll fix the list, after I figure out what went wrong.

I found a comment about it in my old notes : ** TODO: ** CHECK THIS ONE OUT SOME MORE -- UNLIKELY SHAPE
Crap

blue wrote:For patterns in general, there's a possibility of a bugs in the code that "proves" that they really don't have puzzles.
For me, each pattern requires specially tailored code, and alot of it is "copy/paste/edit" code, and sometimes I make mistakes.
There's also a possiblity of logical errors in implemeting the big picture, for a given pattern. Some details below.

Words that have come back to haunt me ...

by **JPF** » Tue Apr 25, 2023 10:08 am

After passing the Coloin test, I decided to take the T43 pattern test.
Fortunately, I only had to make 2 iterations to get a proper puzzle and conclude that this pattern is valid. Here's one:

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

JPF

by **blue** » Tue Apr 25, 2023 10:35 am

Impressive !

While I'm trying to figure out what I did wrong, how about looking into T13, T39 and T52 ?
(And T12)

by **JPF** » Tue Apr 25, 2023 3:22 pm

blue wrote: how about looking into T13, T39 and T52 ?
(And T12)

After spending a reasonable amount of time, I was unable to find any valid puzzles in the patterns T12, T13, T39.
For each of these patterns, the minimum found is 2 solutions, which is not necessarily the case for an invalid pattern.

Additionally, I couldn't find the pattern T52 either.

JPF

by **blue** » Tue Apr 25, 2023 3:39 pm

I thank you greatly.

I've found one bug in by code for T43 ... looking for another.
The first one was the kind of bug that could propagate through "copy/paste/edit", into the other patterns that I mentioned (except for T12).

JPF wrote:Additionally, I couldn't find the pattern T52 either.

My mistake ... T42 !

by **blue** » Tue Apr 25, 2023 8:46 pm

blue wrote:I've found one bug in by code for T43 ... looking for another.
The first one was the kind of bug that could propagate through "copy/paste/edit", into the other patterns that I mentioned (except for T12).

It was just the one bug, and an mistake on my part, that made me think there was another one lurking.
I've removed the original T43, and adjusted the numbering for T44-47.
Each of the (original) T43 subsets, was a isomorphic to a subset of one of the other patters, so nothing else needed changing.

The bug was present in the T13 code too, but after fixing it, it still didn't find a puzzle.

by **blue** » Tue Apr 25, 2023 9:22 pm

coloin wrote:
JPF wrote:Unfortunately, 'my method' is unable to tell whether you have found a puzzle with this pattern or not JPF

Well done ...
Yes that is the same puzzle which I found ... which makes it more likely that it is the only puzzle with this pattern !

Your conjecture was correct ... it is the only puzzle.

I checked it the "old fashioned" way (22h), not with the kind of code that I use in looking for "maximal invalid" patterns.
I think the pattern has too many empty cells for the other method to work well.

If you guys would like another challenge, here are two k-regular, k=2, 18 clue patterns, with only one puzzle each.

Code: Select all: . . . . . . . . . . . 1 1 1 . . . . . 1 . . . 1 1 . . . . 1 . . . . 1 . . 1 . . . . 1 . . . 1 . . . . 1 . . . . 1 1 1 . . 1 . . . . . . 1 1 . . . . . . . . . . .

Code: Select all: . . . 1 . . . . . . . 1 . 1 . . . . . . 1 . 1 . . 1 . . . . 1 . . 1 . 1 . 1 . . . . . 1 . 1 . 1 . . . . . . . 1 . . . 1 . . . . . . . 1 . 1 . . . . . . . 1 . . .

With only 18 clue cells, I'm curious to see how you'ld do.

Cheers.

by **coloin** » Tue Apr 25, 2023 10:13 pm

blue wrote:....Your conjecture was correct ... it is the only puzzle.

Thanks

First one
begin with a random 23C, stepwise to 18C .. with successive {gridchecker +4} generation of a few non minimals ....

Code: Select all: +---+---+---+ +---+---+---+ |...|...|...| |...|...|...| |..1|23.|...| |..1|23.|...| |.4.|..5|2..| |.4.|..5|6..| +---+---+---+ +---+---+---+ |..6|...|.3.| |..2|...|.1.| |.5.|...|7..| --> |.6.|...|4..| |.8.|...|5..| |.5.|...|7..| +---+---+---+ +---+---+---+ |.73|418|.2.| |..3|18.|.2.| |...|..6|498| |...|..6|5..| |...|...|..7| |...|...|...| +---+---+---+ 23C +---+---+---+ 18C

by **JPF** » Tue Apr 25, 2023 11:03 pm

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

5 iterations.

JPF

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