Well done in completing that search. You have shown that there are no new 17s which have a maximum of 2 clues [ not 3] in all rows or columns or boxes in the puzzle.
Edit
unfortunatly it is not that easy - as usual
One would need to search all the max lex 18 clue patterns which begin with
11. ... ... and also max 2 clues in a box
one example ....
- Code: Select all
+---+---+---+
|12.|...|...|
|...|34.|...|
|...|...|56.|
+---+---+---+
|7..|..1|...|
|..8|...|..2|
|...|.9.|..3|
+---+---+---+
|.4.|...|.9.|
|..5|...|8..|
|...|6.7|...|
+---+---+---+
which probably is a bigger task
If we were to find all known 17s [surely the objective of the thread ] .....
we would "simply" have to generate "all" the 9plus12s, 9plus13s and 9plus14s.
removing clues from the 9 to give 5plus12s, 4plus13s and 3plus14s.
posssibly all the 9plus14s are within a {-1+1] [?]
The 9 clues are either 9 clues in the first row or 9 clues in the central box
9plus12s are relatively remote - but this is not the case with 9plus13s ......
At the present time even adding 9plus11 clues is too big a task [ ? none exist] - even with reductions.
A clever way to do it might be out there
Avoiding dealing with 9plus15s would be a prerequisite / start ......
C