coloin wrote: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
C
Hi coloin,
I started with a different view on the patterns.
This is the split of existing patterns I gave earlier
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The split on row 1 (for the entire file) is the following
1111..1.. 1
1111..... 387
111...... 1847
11.11.1.. 26
11.11.... 1235
11.1..1.. 6537
11.1..... 39031
11....... 86
1..1..... 2
In that split, I consider the max lexical canonical form of the pattern.
In that view, your example is part of the start 11....... 86
We have shown that the last start is fully covered.
In between, we could have puzzles with the start 1.. 1.. 1.. but none has been found so far.
I had 2 weeks off, and I was thinking before departure of ways to explore that part of the 17 (may be 18) clues field.
Likely to find nothing, but I think it makes sense to do it.
I drafted some code to go in that direction, but I am locked on other priorities for 2 or 3 days
