The New Sudoku Players' Forum

by **StrmCkr** » Tue Jan 09, 2018 2:40 am

Code: Select all: 123|456|789 45*|***|*** ***|AAA|BBB ----------- 2..|...|... ...|...|... ...|...|... ----------- ...|...|... ...|...|... ...|...|...

starting with A then B cell there is precisely 360 valid permutations to cycle through for digits

Code: Select all: 123|456|789 45F|DDD|EEE CCC|AAA|BBB ----------- 2..|...|... ...|...|... ...|...|... ----------- ...|...|... ...|...|... ...|...|...

this reduces C,D,E sectors to 1 set of 3 numbers each with 6 possible arrangement {permutations}
and cell F as a single digit choice.

the first band has exactly 360 * 6*6*6 *1 different unique arrangements
specifically : = 77,760 different unique arrangements

add to the mixed digit cycling (1..9) and you have 77,760 * 9! ==> 77,760 * 362,880 =>> 28,217,548,800 arrangements for band 1.

2nd stage

Code: Select all: 123|456|789 45F|DDD|EEE CCC|AAA|BBB ----------- 2HH|FFF|GGG ...|...|... ...|...|... ----------- ...|...|... ...|...|... ...|...|...

cycle the combinations of 3 digits from 13456789 for section F cycling each of the 6 potential permutation of that combination removing line of sight permutations that are invalid.
cycle the combinations of 3 digits from (13456789 - selection F) for position G then cycle each of the 6 potential permutations
that leaves H locations as pair of digits {fixed or not}

this is where we note a problem carrying forward

best illustrated with examples.

Stage three problem and solution:

Code: Select all: 123|456|789 45F|DDD|EEE CCC|AAA|BBB ----------- 2HH|FFF|GGG ***|***|*** ***|iii|*** ----------- ...|...|... ...|...|... ...|...|...

the problem arise from selection of combination of valid numbers In i

Code: Select all: .---------------------------.---------------------.------------------------. | 1 2 3 | 4 5 6 | 7 8 9 | | 4 5 6789 | 19 17 179 | 23 236 236 | | 679 679 679 | 3 2 8 | 4 1 5 | :---------------------------+---------------------+------------------------: | 2 13 1 | 7 9 4 | 6 5 8 | | 568 68 568 | 12 13 123 | 9 479 47 | | 79 479 479 | 6 8 5 | 123 23 123 | :---------------------------+---------------------+------------------------: | 356789 1346789 12456789 | 12589 13467 12379 | 123589 234679 123467 | | 356789 1346789 12456789 | 12589 13467 12379 | 123589 234679 123467 | | 356789 1346789 12456789 | 12589 13467 12379 | 123589 234679 123467 | '---------------------------'---------------------'------------------------'

take the above grid, selection i matches selection h's combination set. {658} that leaves a combination set of 123 in the middle row.

when we choose "I" as 123 the middle row is always left as 658! meaning row 4 and 5 can be swapped and will off set the solution count. by a factor of 2.

Code: Select all: .---------------------------.---------------------.------------------------. | 1 2 3 | 4 5 6 | 7 8 9 | | 4 5 6789 | 9 17 179 | 23 236 236 | | 679 679 679 | 3 2 8 | 4 1 5 | :---------------------------+---------------------+------------------------: | 2 13 1 | 7 9 4 | 6 5 8 | | 79 479 479 | 568 68 5 | 123 23 123 | | 56 68 568 | 1 3 2 | 9 479 47 | :---------------------------+---------------------+------------------------: | 356789 1346789 12456789 | 25689 14678 13579 | 123589 234679 123467 | | 356789 1346789 12456789 | 25689 14678 13579 | 123589 234679 123467 | | 356789 1346789 12456789 | 25689 14678 13579 | 123589 234679 123467 | '---------------------------'---------------------'------------------------'

a solution is the use a Combination set and Fix the last 5 positions for col 1. {instead of permutations.}

that way each potential permutation can only be applied to each row once in rows 5,6 and again for rows 678 if we don't fix all 5 spots we also have a 3! row swap problem in the last band.

Stage three:

Code: Select all: 123|456|789 45F|DDD|EEE CCC|AAA|BBB ----------- 2HH|FFF|GGG J**|***|*** J**|iii|*** ----------- K..|...|... K..|...|... K..|...|...

J is a fixed Combination of 2 digits selected from ([1,2,3,4,5,6,7,8,9] - ([1,4,2] + [active digit in R3C1 of C if single, else j cannot reduce R3C1 to [] ]))
where R56C1 <> digits from [h] {as H is always a pair of locked digits}
solving R56C1 in sequential order

K is a fixed Combination of 3 digits selected from ([1,2,3,4,5,6,7,8,9] - ([1,4,2] + [active digit in R3C1 of C if single else j+F cannot reduce R3C1 to []] + step above))
solving R789C1 in sequential order

then proceed to select a 3 digit combinations for "i" as ( [1,2,3,4,5,6,7,8,9] - (f + R6C1)) and cycle the 6 permutations.
which leaves all the *'s cells as 1 set of 3 digit each with 1-6 potential permutations.

Stage 4, to be continued.

by **coloin** » Wed Sep 26, 2018 8:32 pm

coloin wrote:A long time ago I was surprised that there were only 5 essentially different row and column combinations [not 150 !] - it looks like you found all 5
I found that 9 more clues are needed to complete to a puzzle [i could not find 8 clues]
Of course there are 81 of these combinations in each solution grid - so most solution grids should have at least one of these 5 .....

coloin wrote:interestingly, here are the 5 different rowcols

the approx incidence in 2430 rowcols was
Code: Select all
000000001000000002000000003000000004000000005000000006000000007000000008123478569 - 80 [#1] 000000001000000002000000003000000004000000005000000006000000007000000008124378569 -162 [#2] 000000001000000002000000003000000004000000005000000006000000007000000008124578369 -980 [#3] 000000001000000002000000003000000004000000005000000006000000007000000008127458369 -557 [#4] 000000001000000002000000003000000004000000005000000006000000007000000008147258369 -651 [#5] 2430

So there are 81 of these row/column crossings in each solution grid ....

The MC grid is composed of all 81 x [#5]

Code: Select all: *-----------* +---+---+---+ +---+---+---+ |...|...|..1| |5..|...|4.1| |.7.|...|4.1| |...|...|..2| |.9.|4..|..2| |...|.6.|..2| |...|...|..3| |..1|.8.|..3| |...|...|..3| |---+---+---| +---+---+---+ +---+---+---+ |...|...|..4| |.2.|9..|..4| |...|..7|..4| |...|...|..5| |..6|.1.|8.5| |..6|...|..5| |...|...|..6| |...|...|..6| |3..|..1|..6| |---+---+---| +---+---+---+ +---+---+---+ |...|...|..7| |...|.6.|1.7| |.2.|...|..7| |...|...|..8| |...|...|..8| |...|...|.58| |147|258|369| |147|258|369| |147|258|369| *-----------*[#5] +---+---+---+ MCgrid with 13 clues solving it +---+---+---+ [#5] solved with 9 clues

maybe [#3] is just common and [#1] is just rare

Explain ?

by **Serg** » Thu Sep 27, 2018 8:38 pm

Hi, coloin!

coloin wrote:interestingly, here are the 5 different rowcols

the approx incidence in 2430 rowcols was
Code: Select all
000000001000000002000000003000000004000000005000000006000000007000000008123478569 - 80 [#1] 000000001000000002000000003000000004000000005000000006000000007000000008124378569 -162 [#2] 000000001000000002000000003000000004000000005000000006000000007000000008124578369 -980 [#3] 000000001000000002000000003000000004000000005000000006000000007000000008127458369 -557 [#4] 000000001000000002000000003000000004000000005000000006000000007000000008147258369 -651 [#5] 2430

Interesting! But "rowcol" configuration (17 cells) resembles two-box (2 boxes sharing the same band) configuration (18 clues). There are 10 e-d two-box configurations. (Right?)

I have no explanations of rowcols' properties.

Serg

by **coloin** » Fri Sep 28, 2018 9:08 pm

Code: Select all: +---+---+---+ |...|.95|..1| |...|...|..2| |.64|...|..3| +---+---+---+ |...|...|..4| |7..|.1.|..5| |...|...|.36| +---+---+---+ |...|...|2.7| |..6|...|..8| |123|478|569| +---+---+---+ [#1] with puzzle solved by adding 9 clues

Well ... I think its all down to the morphing and relabeling.

If you fix column 9 - there are 6*5 * 6! ways to put a clue in row 9 = 21600

however you can swap and relabel both cols and stacks and col 7 and 8
6*6*2*2 = 144
21600/144 = 150 [the figure in Mathimagic's first post in this thread ! ]

but it boils down to 5 in the end somehow !

by **StrmCkr** » Mon Oct 01, 2018 6:55 am

000000001000000002000000003000000004000000005000000006000000007000000008123478569 - 80 [#1]
000000001000000002000000003000000004000000005000000006000000007000000008124378569 -162 [#2]
000000001000000002000000003000000004000000005000000006000000007000000008124578369 -980 [#3]
000000001000000002000000003000000004000000005000000006000000007000000008127458369 -557 [#4]
000000001000000002000000003000000004000000005000000006000000007000000008147258369 -651 [#5]

in reverse generation these 5 should be the only configurations seen by my code that generates all grids. to show what i mean i first had to transpose the grids then do a digit swap to equate my starting position:

Code: Select all: .---------------------------.------------------------------.------------------------------. | 1 2 3 | 4 5 6 | 7 8 9 | | 4 5 6789 | 123789 123789 123789 | 1236 1236 1236 | | 6789 6789 6789 | 123789 123789 123789 | 123456 123456 123456 | :---------------------------+------------------------------+------------------------------: | 2 1346789 1456789 | 1356789 1346789 1345789 | 1345689 1345679 1345678 | | 356789 1346789 1456789 | 12356789 12346789 12345789 | 12345689 12345679 12345678 | | 356789 1346789 1456789 | 12356789 12346789 12345789 | 12345689 12345679 12345678 | :---------------------------+------------------------------+------------------------------: | 356789 1346789 12456789 | 12356789 12346789 12345789 | 12345689 12345679 12345678 | | 356789 1346789 12456789 | 12356789 12346789 12345789 | 12345689 12345679 12345678 | | 356789 1346789 12456789 | 12356789 12346789 12345789 | 12345689 12345679 12345678 | '---------------------------'------------------------------'------------------------------'

your posted 5 grids changed to match. {to show how i did it exta same steps on each of the 5 grids }

000000001000000002000000003000000004000000005000000006000000007000000008123478569

transpose (anti diagonal)
digit swaps
1 -> 9
8 -> 2
7 -> 3
4 -> 6
{this is the only one of the 5 grids that needs these extra 2 steps}
5 -> 6
Col swap: 5 -> 6

Code: Select all: 1234567894........6........2........3........5........7........8........9........

now for the other's the same process as above generates them to these 5 grids.

Code: Select all: 1234567894........6........2........3........5........7........8........9........ 1234567894........6........2........3........7........5........8........9........ 1234567894........7........2........3........5........6........8........9........ 1234567894........7........2........5........6........3........8........9........ 1234567894........7........2........5........8........3........6........9........

alright I can explain this pretty easy now that i have it converted to match my grid generator and can also figure out how it is 5 and not 10.

Code: Select all: 123|456|789 45F|DDD|EEE CCC|AAA|BBB ----------- 2..|...|... ...|...|... ...|...|... ----------- ...|...|... ...|...|... ...|...|...

the first band has exactly 360 * 6*6*6 *1 different unique arrangements
specifically : = 77,760 different unique arrangements

on inspection this number appears correct... it actually isn't.
{my initial calculations failed to realize that if CCC = 789, then there is actually only 1 unique arrangement and 3 permutations.

that means CCC+F is a quad set of 6789 digits where F can be any of the 4,

however CCC can assign 6 to any of the spots, where the position of the "2/3 of 789" can be directly swapped with each-other.

which means R3C1 HAS 2 CHOICES.
6 OR 7

{where my initial calculations has 4 permutations for what could be in R3C1. }
indicating that for each of the 77,760 arrangements on Col 1 has 10 configurations.

now the fun part.
R4C2 is fixed as a 2.

if we choose 6 at r3C3
I know that these 3 digit sets are swap-able with them selves.
[789 ]
[123]
[456]

and that 5 can only exists in box 4 or box 6
with exactly enough cells that 789 exists together or can rotate through
and that 2-3 can freely swap to change box 4-7 to be identical in all arrangements
= 2 ways to place digit 5.

if we choose 6 @ R3C3 then Digit 5 is locked to box 4 or 7. {2 choices} -> 2 potential arrangements

if we choose 7 @ R3C3 then Digit 6 is locked to box 4 or 7 { 2 choices} & Digit 5 is locked to box 4 or 7. {2 choices} => 3 potential arrangement of both digits

{either 5 is paired with 6, alone, or with 8. doesn't matter which configuration as they can swap to form one another => 3 different arrangements}

so yah.... if u can understand this and write it out better..
this is your proof of why there is only 5 different arrangements for cols+ row.

{this potential will drastically reduce my initial calculation run time down by a huge factor}

by **coloin** » Sat Oct 06, 2018 12:27 am

Yes there are only 5 ED rowcols

Code: Select all: ........1........2........3........4........5........6........7........8123478569 [#1] ........1........2........3........4........5........6........7........8124378569 [#2] ........1........2........3........4........5........6........7........8124578369 [#3] ........1........2........3........4........5........6........7........8127458369 [#4] ........1........2........3........4........5........6........7........8147258369 [#5]

in #1

Code: Select all: +---+---+---+ |...|...|..1| |...|...|..2| |...|...|..3| +---+---+---+ |...|...|..4| |...|...|..5| |...|...|..6| +---+---+---+ |...|...|..7| |...|...|..8| |123|ccc|xx9| +---+---+---+

it easy to see that 78 has to be in ccc, leaving the 456 to be filled one way

But its not clear why there should be a paucity of #1 in the counting

Except there are only 20 ED ways to fill in this pattern

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

For #1, a can only be 1234 - and there is only one ED way to complete Box 9

Code: Select all: +---+---+---+ |...|...|..1| |...|...|..2| |...|...|..3| +---+---+---+ |...|...|..4| |...|...|..5| |...|...|..6| +---+---+---+ |...|...|aa7| |...|...|aa8| |123|478|569| +---+---+---+

here are the other ED ways

Code: Select all: ........1........2........3........4........5........6........7........8123478569 [#1] ........1........2........3........4........5........6......417......328123478569 1 ........1........2........3........4........5........6........7........8124378569 [#2] ........1........2........3........4........5........6......427......318124378569 2 ........1........2........3........4........5........6......147......328124378569 ........1........2........3........4........5........6........7........8124578369 [#3] ........1........2........3........4........5........6......127......458124578369 ........1........2........3........4........5........6......157......248124578369 ........1........2........3........4........5........6......217......548124578369 6 ........1........2........3........4........5........6......417......258124578369 ........1........2........3........4........5........6......427......518124578369 ........1........2........3........4........5........6......527......148124578369 ........1........2........3........4........5........6........7........8127458369 [#4] ........1........2........3........4........5........6......247......518127458369 ........1........2........3........4........5........6......257......148127458369 3 ........1........2........3........4........5........6......517......428127458369 ........1........2........3........4........5........6........7........8147258369 [#5] ........1........2........3........4........5........6......127......458147258369 ........1........2........3........4........5........6......147......258147258369 ........1........2........3........4........5........6......217......458147258369 ........1........2........3........4........5........6......217......548147258369 ........1........2........3........4........5........6......247......158147258369 8 ........1........2........3........4........5........6......257......148147258369 ........1........2........3........4........5........6......527......148147258369 ........1........2........3........4........5........6......527......418147258369

I generated 100000 random grids and counted the rowcol.

Code: Select all: ........1........2........3........4........5........6........7........8123478569 [#1] 4363 ........1........2........3........4........5........6........7........8124378569 [#2] 13315 ........1........2........3........4........5........6........7........8124578369 [#3] 48617 ........1........2........3........4........5........6........7........8127458369 [#4] 11140 ........1........2........3........4........5........6........7........8147258369 [#5] 22565 100000

We have explained why #1 has a 4.3% / 1 in 20 incidence
But #3 occurs 48% of the time despite only a 6 in 20 incidence [30%]
And #5 occurs 22% of the time despite a 8 in 20 incidence [40%]
So more explaining to do I guess !

by **coloin** » Sat Oct 06, 2018 6:04 pm

Strangely enough this

Code: Select all: +---+---+---+ |...|...|..1| |...|...|..2| |...|...|..3| +---+---+---+ |...|...|..4| |...|...|..5| |...|...|..6| +---+---+---+ |...|...|417| |...|...|328| |123|478|569| +---+---+---+

[#1] pattern with a representative box9 completed.
Despite its apparent rarity [there are 81 of these patterns in each solution grid] it was present in 967/1000 random solution grids ...

And the 6th of the [#3] patterns was present in 997/1000 random solution grids

by **blue** » Thu Feb 08, 2024 11:13 am

coloin wrote:A long time ago I was surprised that there were only 5 essentially different row and column combinations [not 150 !] - it looks like you found all 5
I found that 9 more clues are needed to complete to a puzzle [i could not find 8 clues]
Of course there are 81 of these combinations in each solution grid - so most solution grids should have at least one of these 5 .....

coloin wrote:interestingly, here are the 5 different rowcols

the approx incidence in 2430 rowcols was
Code: Select all
000000001000000002000000003000000004000000005000000006000000007000000008123478569 - 80 [#1] 000000001000000002000000003000000004000000005000000006000000007000000008124378569 -162 [#2] 000000001000000002000000003000000004000000005000000006000000007000000008124578369 -980 [#3] 000000001000000002000000003000000004000000005000000006000000007000000008127458369 -557 [#4] 000000001000000002000000003000000004000000005000000006000000007000000008147258369 -651 [#5] 2430

I found 3 "rowcol+8" puzzles, all for rowcol [#5].
After a good amount of effort, I couldn't find any more.
These may be the only three (?).
They're {-2,+2} related ... with only 2 solution grids.

I was totally suprized to see that they could all be given 180 degree rotational symmetry, down to the clue level ...

puzzle(r, c) = 10 - puzzle(10 - r, 10 - c)

Code: Select all: +-------+-------+-------+ +-------+-------+-------+ +-------+-------+-------+ | . . . | . 4 . | . . . | | . . . | . 4 . | . . . | | . . . | . 4 . | . . . | | . . . | . 2 . | 1 . . | | . . . | . 2 . | 1 . . | | . . . | . 2 . | 1 . . | | . . 6 | . 9 . | . 3 . | | . . 6 | . 9 . | . 3 . | | . . 6 | . 9 . | . 7 . | +-------+-------+-------+ +-------+-------+-------+ +-------+-------+-------+ | . . . | . 7 . | . . 4 | | . . . | . 7 . | . 6 . | | . . . | . 7 . | . 6 . | | 1 2 3 | 4 5 6 | 7 8 9 | | 1 2 3 | 4 5 6 | 7 8 9 | | 1 2 3 | 4 5 6 | 7 8 9 | | 6 . . | . 3 . | . . . | | . 4 . | . 3 . | . . . | | . 4 . | . 3 . | . . . | +-------+-------+-------+ +-------+-------+-------+ +-------+-------+-------+ | . 7 . | . 1 . | 4 . . | | . 7 . | . 1 . | 4 . . | | . 3 . | . 1 . | 4 . . | | . . 9 | . 8 . | . . . | | . . 9 | . 8 . | . . . | | . . 9 | . 8 . | . . . | | . . . | . 6 . | . . . | | . . . | . 6 . | . . . | | . . . | . 6 . | . . . | +-------+-------+-------+ +-------+-------+-------+ +-------+-------+-------+ ....4........2.1....6.9..3.....7...41234567896...3.....7..1.4....9.8........6.... ....4........2.1....6.9..3.....7..6.123456789.4..3.....7..1.4....9.8........6.... ....4........2.1....6.9..7.....7..6.123456789.4..3.....3..1.4....9.8........6....

They're all "singles solvable"

by **Serg** » Sun Feb 11, 2024 8:28 am

Hi, blue!

blue wrote:I found 3 "rowcol+8" puzzles, all for rowcol [#5].
After a good amount of effort, I couldn't find any more.
These may be the only three (?).
They're {-2,+2} related ... with only 2 solution grids.

I was totally suprized to see that they could all be given 180 degree rotational symmetry, down to the clue level ...
for clue cells: puzzle(r, c) = 10 - puzzle(10 - r, 10 - c)
Code: Select all
+-------+-------+-------+ +-------+-------+-------+ +-------+-------+-------+ | . . . | . 4 . | . . . | | . . . | . 4 . | . . . | | . . . | . 4 . | . . . | | . . . | . 2 . | 1 . . | | . . . | . 2 . | 1 . . | | . . . | . 2 . | 1 . . | | . . 6 | . 9 . | . 3 . | | . . 6 | . 9 . | . 3 . | | . . 6 | . 9 . | . 7 . | +-------+-------+-------+ +-------+-------+-------+ +-------+-------+-------+ | . . . | . 7 . | . . 4 | | . . . | . 7 . | . 6 . | | . . . | . 7 . | . 6 . | | 1 2 3 | 4 5 6 | 7 8 9 | | 1 2 3 | 4 5 6 | 7 8 9 | | 1 2 3 | 4 5 6 | 7 8 9 | | 6 . . | . 3 . | . . . | | . 4 . | . 3 . | . . . | | . 4 . | . 3 . | . . . | +-------+-------+-------+ +-------+-------+-------+ +-------+-------+-------+ | . 7 . | . 1 . | 4 . . | | . 7 . | . 1 . | 4 . . | | . 3 . | . 1 . | 4 . . | | . . 9 | . 8 . | . . . | | . . 9 | . 8 . | . . . | | . . 9 | . 8 . | . . . | | . . . | . 6 . | . . . | | . . . | . 6 . | . . . | | . . . | . 6 . | . . . | +-------+-------+-------+ +-------+-------+-------+ +-------+-------+-------+ ....4........2.1....6.9..3.....7...41234567896...3.....7..1.4....9.8........6.... ....4........2.1....6.9..3.....7..6.123456789.4..3.....7..1.4....9.8........6.... ....4........2.1....6.9..7.....7..6.123456789.4..3.....3..1.4....9.8........6....

They're all "singles solvable"

Curious discovery! All (very rare) members of "rowcol+8" family have rotation symmetry... It contradicts with common sense!
I tried to generate new "rowcol+8" puzzles, but couldn't get even "rowcol+9". Such puzzles are really very rare.

Serg

by **coloin** » Sun Feb 11, 2024 10:39 pm

Indeed well done on finding those RowCol plus 8 puzzles.
Looking back at this thread -it seems Mathemagics {RIP} was counting minlex solutions .
The actual solution count for a RowCol [17 clues] should be much higher.
I will update the relevant thread for those 17plus8s !

Maybe I will attempt to find other box/row/col plus7

Code: Select all: Adding 6 clues is never enough ? 10+---+---+---+ +---+---+---+ |...|...|..x| |...|..7|..1| |...|...|..x| |5..|.4.|..2| |...|...|..x| |...|...|..3| +---+---+---+ +---+---+---+ |...|...|..x| |.1.|3..|..4| |...|...|..x| |...|1..|..5| |...|...|..x| |2..|...|..6| +---+---+---+ +---+---+---+ |...|...|xxx| |...|...|367| |...|...|xxx| |...|...|258| |xxx|xxx|xxx| |763|852|149| +---+---+---+ +---+---+---+ valid 21plus7 [1021 found]

by **blue** » Mon Feb 12, 2024 2:21 am

coloin wrote:I will update the relevant thread for those 17plus8s !

Yeah, I figured this wasn't the right place to post these, but I couldn't find the proper thread.
Please post a link.
Maybe Pat can/will move these latest posts to there.

coloin wrote:Maybe I will attempt to find other box/row/col plus7
Code: Select all
Adding 6 clues is never enough ? 10+---+---+---+ +---+---+---+ |...|...|..x| |...|..7|..1| |...|...|..x| |5..|.4.|..2| |...|...|..x| |...|...|..3| +---+---+---+ +---+---+---+ |...|...|..x| |.1.|3..|..4| |...|...|..x| |...|1..|..5| |...|...|..x| |2..|...|..6| +---+---+---+ +---+---+---+ |...|...|xxx| |...|...|367| |...|...|xxx| |...|...|258| |xxx|xxx|xxx| |763|852|149| +---+---+---+ +---+---+---+ valid 21plus7 [1021 found]

I couldn't find a "+6" after a short while.
I'm at 1233 "+7's" and counting ...

Serg wrote:I tried to generate new "rowcol+8" puzzles, but couldn't get even "rowcol+9". Such puzzles are really very rare.

I have 2,480,064 of the "rowcol+9's", and it's easy enough to find more. Maybe not so rare ?

by **coloin** » Mon Feb 12, 2024 2:28 am

I’ve updated this thread
ask-for-patterns-that-they-dont-have-puzzles-2

by **coloin** » Mon Feb 19, 2024 8:27 pm

blue wrote:...I'm at 1233 "+7's" and counting ...

As an exercise I started from scratch and after a lot of effort I finally found a few more "+7s" ... up to 1205 now.and counting ! ..... and very unlikely to be a +6
You seemed to find them pretty quickly though.
Removing a clue from generated "+8s" finds them ... or perhaps you did something more clever.

Maybe check this one is in your list ? It doesnt have repeating minirows in horizontal band 1 or or vertical band 1 :roll:

Code: Select all: +---+---+---+ |123|456|789| |457|...|...| |689|...|...| +---+---+---+ |2..|.9.|...| |3..|...|65.| |8..|...|3..| +---+---+---+ |5..|...|...| |7..|..3|2..| |9..|8..|...| +---+---+---+

THe majority of the puzzles have both bands a repeating minirow.

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

by **blue** » Wed Feb 21, 2024 5:18 pm

coloin wrote:
blue wrote:...I'm at 1233 "+7's" and counting ...

As an exercise I started from scratch and after a lot of effort I finally found a few more "+7s" ... up to 1205 now.and counting ! ..... and very unlikely to be a +6

Hi Colin,

The thing I was running at the time, stopped at 1280 "+7's" ... and I stopped too.
Running it some more (~3 core hours), I got another 120, to make 1400.
They have slowed to a trickle.
A +6 seems extremely unlikely.

You seemed to find them pretty quickly though.
Removing a clue from generated "+8s" finds them ... or perhaps you did something more clever.

That's more or less what I do.
I do {-2,+1} on the "+8's" too, but anything produced, could be gotten with {-2,+2} producing a puzzle with a redundant clue.

Maybe check this one is in your list ? It doesnt have repeating minirows in horizontal band 1 or or vertical band 1
Code: Select all
+---+---+---+ |123|456|789| |457|...|...| |689|...|...| +---+---+---+ |2..|.9.|...| |3..|...|65.| |8..|...|3..| +---+---+---+ |5..|...|...| |7..|..3|2..| |9..|8..|...| +---+---+---+

This one wan't in my list, but it came in the last batch that I mentioned.
All in all, I have 12 puzzles without repeating mini-rows/mini-cols (in band 1 / stack 1).

Code: Select all: 123456789457......689......2...7...58........96.......3......6.5..91....7.....8.. 123456789457......689......2..7....48........96.......3......6.5..19....7.....8.. 123456789457......689......2.1..7..38.....5..9........3....2...5.......47...8.... 123456789457......689......2.47....38.....5..9........3..2.....5.......67...8.... 123456789457......689......2.47....18.....5..9........3..2.....5.......67...8.... 123456789457......689......2.......63......5.7..8.....5....7...8........9...62..4 (*) 123456789457...3..689......2....9..63........7........5...1....8..37....9.......2 123456789457...3..689......2....9..63........7........5...1....8..73....9.......2 123456789457......689.....12....8..63........54.......7.....42.8........9....1... 123456789457......689.....12....8..63........54.......7.....52.8........9....1... 123456789457......689......2....1.3.5........9..8.....3.....4..7.......58.1..3... 123456789457......896...3..2........6...8..5.7...3....3.....2..5..2.....9..7.....

================================

I have one more thing for your post in the ("proper") thread:

Code: Select all
Adding 4 clues is never enough ? (...) 9+---+---+---+ +---+---+---+ |...|...|...| |...|...|...| |...|...|...| |...|...|..1| |...|...|...| |...|.23|...| +---+---+---+ +---+---+---+ |...|...|...| |...|...|...| |...|...|...| |...|4..|..5| |xxx|xxx|xxx| |926|358|417| +---+---+---+ +---+---+---+ |xxx|xxx|xxx| |467|582|139| |xxx|xxx|xxx| |513|946|278| |xxx|xxx|xxx| |892|137|654| +---+---+---+ needs 5 clues +---+---+---+ valid 36plus5

Here's a +4.

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

There are lots of them ... (> 34000).
This one came from a "27+8" with a 4-clue row.

================================

P.S. : One correction too, for that post.

Code: Select all
14+---+---++--- |...|...|...| |...|...|...| |...|...|...| +---+---+---+ |...|...|...| |...|...|...| |...|...|...| +---+---+---+ |...|...|xxx| |...|...|xxx| |xxx|xxx|xxx| +---+---+---+ only 4 15plus9s of this pattern have been found. 123456789456......789..................6.1....9......5.4..8..........6........3.1 123456789456......789.......4.......6............9..1.........4.3..8..........6.1 123456789456......789.......4.......6............9..1.......4...3..8..........6.1 123456789456......789......6.........4...........9..1.........4.3..8..........6.1

The 4th puzzle is a morph of the 2nd.
The missing one is:

Code: Select all: 123456789457......896.....................16.....89......6........1.36...8.......

by **coloin** » Thu Feb 22, 2024 8:02 pm

Stirling work...
I have ammended and cleaned up the thread. !

Clearly there is morph in my list of the "4" 15plus9s. Though I very much doubt whether I found that 4th one. It would be very unlikely ! as It doesnt have the repeating minirow

And of course well found on those 36plus4 puzzles...an excellent method but I think its a case of not knowing to look because I presumed it wasnt possible... :oops:

Looking ino why I couldnt easily find a 36plus4 .....
Fixing the clues in the first 5 rows.... In your puzzle there are 280 similar ways to rotate othe 4 rows / 36 clues. [gangster plus 1 row]

So It is difficult to choose the 36clues - so your way is the best way to find them - although out of a big collection of 8plus27band - there was not one with 4 clues in a row like yours....

4 clues plus 36 is the minimum - If 3 clues are in band 1, 1 clue is needed in rows 4&5 as we have here, If 2 clues are in band 1, 4 clues are needed in rows 4&5.

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