Wow

So 1 LS grid and 1 LS puzzle

I think I was nearly getting there !

And the reason I nearly twigged this ....is because I was thinking about the bands

In sudoku we have

3 bands of 3 rows, and 3 bands of 3 columns [6 3-bands] 416 ED with 44 gangsters.

in each 3-band there are 3 2-row bands.

each 3-band can be solved with minimum 2,3,4,5,6 clues depending which one of the 416 it is

each 2-row [15 ED] can be solved with minumum 1,2 or 3 clues depending which one of the 15 it is

- Code: Select all
`000000000000000000000000000000000000000000000000000000000000000123456789456789123`

000000000000000000000000000000000000000000000000000000000000000123456789456789132

000000000000000000000000000000000000000000000000000000000000000123456789456789231

000000000000000000000000000000000000000000000000000000000000000123456789457189236

000000000000000000000000000000000000000000000000000000000000000123456789457189263

000000000000000000000000000000000000000000000000000000000000000123456789457189326

000000000000000000000000000000000000000000000000000000000000000123456789457189623

000000000000000000000000000000000000000000000000000000000000000123456789457189632

000000000000000000000000000000000000000000000000000000000000000123456789457289163

000000000000000000000000000000000000000000000000000000000000000123456789457289613

000000000000000000000000000000000000000000000000000000000000000123456789457289631

000000000000000000000000000000000000000000000000000000000000000123456789457389612

000000000000000000000000000000000000000000000000000000000000000123456789457389621

000000000000000000000000000000000000000000000000000000000000000123456789457893612

000000000000000000000000000000000000000000000000000000000000000123456789457893621

However in LS world

In each solition grid there are 36 2-rows [and 36 2-columns] [9*8 / 2!]

{12,13,14,15,16,17,18,19,23,24,25,26,27,28,29,34,35,36,37,38,39,45,46,47,48,49,56,57,58,59,67,68,69,78,79,89}

there are therefore 9*8*7 / 3! = 84 3-rows [and 84 3-columns]

So potentially there may well be 84 different 3-rows ... hmmm

least said for now i think

apart from mmentioning the BC grid

- Code: Select all
`123456789`

231564897

312645978

456789231

564897312

645978123

789231564

897312645

978123456 most lex-minimal LS BC

123456789

234567891

345678912

456789123

567891234

678912345

789123456

891234567

912345678 most lex-minimal BC valid sudoku

So in LS World

In this grid there are only 2 types of 2-rows

Im not clear exactly how many types of 3-rows .....[?]

At least 1 of the 84 are solvable in 2 clues [3-row/band 29]

Some of the other 3-rows maybe need 6 clues .....[?]

And going back to the puzzle

- Code: Select all
`1234.....`

234......

34.......

4........

.........

........5

.......56

......567

.....5678

there are 9!*9! ways to row swap the puzzle , and blue has found that 21 of those ways result in a valid [ED sudoku] puzzle