A varient here is OWB [One Wonky Box] sudoku

Heres an example of an easy puzzle [ not sure how to remove more clues manually]

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

|385|...|71.|

|..7|...|689|

|691|...|.34|

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

|...|62.|897|

|...|179|.56|

|...|.5.|1.3|

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

|15.|9.8|.4.|

|.68|731|2..|

|739|5.2|..1|

+---+---+---+ 44 clues

The WB [Wonky Box] is Box 9, and it only has numbers 1-6

There are 3 positions in Box 9 without a clue [ but here not defined]

looking at it structurally

Ive only found 4 possible solution grid forms with OWB [One Wonky Box]in Box 9

- Code: Select all

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

|175|839|462|

|364|215|789|

|982|764|153|

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

|546|927|318|

|813|456|297|

|729|183|645|

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

|697|341|52x|

|458|672|931|

|231|598|x74|

+---+---+===+ 2 loci with no possible clue in B9, Type 1

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

|175|839|246|

|364|215|978|

|982|764|315|

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

|546|927|831|

|813|456|729|

|729|183|564|

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

|697|342|15x|

|231|598|4x7|

|458|671|x92|

+---+---+---+ 3 loci with no possible clue in B9, Type 2

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

|127|598|463|

|439|762|851|

|568|314|972|

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

|614|823|597|

|783|159|246|

|952|647|138|

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

|895|231|6x4|

|346|975|x1x|

|271|486|3x5|

+---+---+---+ 4 loci with no possible clue in B9 Type 3

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

|698|237|145|

|743|815|629|

|215|946|873|

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

|976|458|231|

|132|769|458|

|854|321|796|

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

|569|183|xx2|

|327|594|x1x|

|481|672|3xx|

+---+---+---+ 6 loci with no possible clue in in B9 Type 4

Removing clues wont necessarily give challenging puzzles, or maybe they will ....

Ive shown B9 as the box with the wonky clues [IMO B9 is easier to visualize] but B5 might be more aesthetic.

The clues in B9 could easily be limited to 1-7,1-6,1-5 or 1-3. and the no-clue positions could be defined, this would give us puzzles with less clues than above.

With computer solvers the difficulty would step up if the wonky box was not defined, and if the clue numbers in the WB was also not defined

although it would have to be that only one of the 9 potential wonky boxes has a unique valid OWB puzzle !

Looking at it structurally...The filling of the B9 box is primarily / solely dependant on the filling of B3B6B7B8

There must therefore be more ways to these OWB solution grids than vanilla 9*9 sudoku solution grids

in 100000 random B3B6B7B8 fillings only 12.9% had a valid B9 [ as in non-wonky], the remaining 87% had Wonky Boxes

in a smaller sample, of the 4 invalid types 1:2:3:4 found their incidence ratio was 24:10:1:0

In the most common type with 2 impossible cells, for example , there are 2 other cells with 2 more options, and these would have to be givens

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

|...|...|123|

|...|...|569|

|...|...|784|

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

|...|...|618|

|...|...|352|

|...|...|497|

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

|893|765|...|

|465|312|..X|

|127|489|X..|

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

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

| 5679 4578 4689 | 5689 4579 4678 | 1 2 3 |

| 237 13478 1248 | 128 2347 13478 | 5 6 9 |

| 23569 135 1269 | 12569 2359 136 | 7 8 4 |

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

| 23579 3457 249 | 259 234579 347 | 6 1 8 |

| 679 1478 14689 | 1689 479 14678 | 3 5 2 |

| 2356 1358 1268 | 12568 235 1368 | 4 9 7 |

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

| 8 9 3 | 7 6 5 | 2 4 1 |

| 4 6 5 | 3 1 2 | 89 7 X |

| 1 2 7 | 4 8 9 | X 3 56 |

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

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

|...|...|123|

|...|...|569|

|...|...|784|

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

|...|...|618|

|...|...|352|

|...|...|497|

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

|893|765|241|

|465|312|.7X|

|127|489|X3.|

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

......123......569......784......618......352......49789376524146531287.127489.35

......123......569......784......618......352......49789376524146531287.127489.36

......123......569......784......618......352......49789376524146531297.127489.35

......123......569......784......618......352......49789376524146531297.127489.36

Anyhow

The whole point of this is whether anyone can easily program a simple solver ...

...and remove more clues and see how hard the puzzles might be ,

or maybe more usefully a program to count the number of OWB solutions [9] for multi solution puzzles ....