... by: DirkSJ
Something that intrigues me more than the above is this question:
Of your zero's, how many are solvable using ALL current techniques with one well chosen filled in cell?
If there are any that remain "unsolvable" with any added known then that is an even harder benchmark. This would lead to a hierarchy of:
- trivial after 1 cell (all your non-zeros)
- solvable after 1 cell (your zeros that can be solved by advanced methods after 1 cell)
- unsolvable after 1 cell (zeros that are still unsolvable after 1 cell)
- trivial after 2 cells (assuming the current theory that all are trivial after 2 cells is true)
It's possible also that the "unsolvable after 1 cell" set has no puzzles in it. Perhaps using all current techniques this is an empty set.
Andrew Stuart writes:
Rephrasing your question, what is the lowest score/grade puzzle we can make with the addition of one extra clue? I agree it is possible some will continue to be unsolvable - just maybe - but we have so few to work with to check. There are 4 in the unsolvable list, 46 in Klaus's set, I think 9 in the 17 clue set and about 80 in the top 50k set. I will test them however, and see what it gives us. Whether it's meaningful with such as small sample I don't know, but fun to try.
Side issue: Bowman's Bingo muddies the waters a lot and I'm wondering what to do with this strategy. It is implemented and available but its trial and error. When I make puzzle for publication I don't include BB when grading so this strategy doesn't affect extremes. But I include it when searching for unsolvables because I don't want that step available for people to solve - or for the solver to finish it with that step.
I'll post again when I have results