Hi

Serg sorry i missed your reply ..........

to answer

JPF calcultated those figures innthis thread

hereand yes the B9 box will have 0 or 9 clues ....

I see that that 11 clue pattern by-passes your set of impossible patterns ...... hmmmm

No you havnt missed something there ..... i also see that an empty box cant have 9 clues !

I think I was getting ahead of myself there - what I meant probably is that number of ED ways 11 clues over 8 boxes [32465851] is going to be reduced to a great extent with your impossible patterns. But not fully because i managed to construct one which passes.

Anyhow

serg wrote:I don't understand your idea

EDIT

well ... assuming we have proved the 11 clues plus 9 thing - [and we havnt yet i agree][and it might be a very big if]

All 20 clue patterns with 11 plus 9 are impossible

All 19 clue patterns with 11 plus 8

All 17 clue patterns with 11 plus 6

All 14 clue patterns with 11 plus 3

All 13 clue patterns with 11 plus 2 - which is all 13 clue patterns

With respect to the multitude of row and box 9plus13 puzzles i have made - an empty box is a relative rarity.

Less than 1 in 500 in the corner boxes with a full central B5.

The box 9plus11 exercise is actually a simultaneous exercise with 4 crossing patterns.

The number of templates where there are 8 clues [1 per box ] in 8 boxes is small compared to 32465851 ..... ? < 6000

certainly less than ~ 12945 [9^8/ 6^4 *2^3]

- Code: Select all
`+---+---+---+`

|...|...|...|

|.4.|.1.|.9.|

|...|...|...|

+---+---+---+

|...|...|...|

|.1.|.X.|.4.|

|...|...|...|

+---+---+---+

|...|...|...|

|.9.|.4.|.1.|

|...|...|...|

+---+---+---+ 9*9*4*4*4 = 5184

reducing by 2*2*2 for band swaps and reflection leaves at most 648.

EDITWhateverway i tried to estimate the number of ED 9plus8 puzzles without an empty box....

I generated 385 only

- Code: Select all
`001#....................X..X..X....................X..X..X......XXX......XXX..X..XXXX`

002#....................X..X..X....................X..X..X......XXX......XXX..X.X.XXX

003#....................X..X..X....................X..X..X......XXX......XXX.X..X.XXX

......

......

......

382#.................X..X..X..........X.....X.....X..........XXX......XXXX..X..XXX...

383#........X.....X.....X..............X....X.....X.............XXX......XXXX..X..XXX

384#........X.....X.....X..............X....X.....X.............XXX...X..XXXX.....XXX

385#........X.....X.....X.............X.....X.....X.............XXX...X..XXXX.....XXX

adding any 3 would give us all 9plus11 patterns without an empty box, and yes quite a lot of patterns.......

C