hendrik_monard wrote:I cannot recall any specific case of puzzles with the same solution but different B7B+ ratings. To draw a definitive conclusion on this, larger numbers of new grids would have to be investigated.
I can't see any a priori reason why this would be impossible. What happens very often is the BRT-expand of a B7B+ minimal puzzle having B6B- minimals.
But who knows if you consider only B7B+ puzzles; then, very strange things happen, such as the resolution paths having a gap of eliminations between B7B and their BxB.
Just seeing your second post.
hendrik_monard wrote:Some second thoughts about different BxB ratings for a given solution. There are now a large number of minimals of non minimal B7B+ puzzles available. Has someone tested if among those minimals there are some with different BxB ratings? I imagine that this could be the case for 'higher' expansions.
If you don't restrict the minimals to those in B7B+, you'll easily find counter-examples, even puzzles in T&E(1).
I've done a quick statistical study of the minimals of BRT and BRT+1 expands of B7B+ minimals. See details in [HCCS2], sections 6.2.3 and 6.2.4. For the 3 known B14B, we can already say that all the minimals of their BRTR+1 expands are in B14B or in B6B- or T&E(1). I'll see if I can extract relevant information for other individual puzzles.
hendrik_monard wrote:Or is this theoretically impossible?
Probably like many questions in Sudoku, if true of all the known examples: impossible to prove.
hendrik_monard wrote:I can imagine that some 'higher' expansion has a lower BxB rating. In that case you would have different BxB rating for the same solution. Or must the search be limited to minimal puzzles or min_expands?
Between the characteristics of minimals of BRT and BRT+1 expansions, I didn't see much difference.
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