Ah, that's interesting; perhaps there's more to difficulty grading than I've so far done. Perhaps I ought to be paying attention, at each stage of deduction, to how many possible deductions there are to be made; if you ever get down to a point where there's only one thing you can deduce, that's harder than if there are always eight or nine things you could usefully be doing.
On the other hand, it seems to me that a puzzle entirely composed of a single linear chain of reasoning, where there was only one deduction to be made at any stage, might actually be quite easy because every time you filled in a number you'd be easily able to find the next step just by asking yourself "now what additional information have I gained right here?", and wouldn't have to go looking over the whole grid each time. It's all terribly difficult and subjective.
I think it's different - some of the deductions themselves may be harder or easier to spot. I think it's easier to do positional elimination within a 3x3 cell than on a row/column (only need to scan 6 intersecting elements, vs. 12 on a row, and those elements don't cover the whole board), and I think there's some other factors, too. I suspect also that it's easier with lots of filled-in positions, where you don't need so many clues from outside the cell.
For a really advanced analysis, you could generate a "tech tree" for being able to discover the contents of cells. As you get more information on each cell, they move from being indeterminate through being hard-to-deduce (many scattered clues, no redundancy) to being easy (much redundancy, few clues needed, those that are are close at hand). The easiest puzzles would have a solution path with no hard deductions on, and the hardest would have critical points where you have to make one tough deduction before you proceed. In between would be puzzles where you have a choice of hard deductions - making one makes the others easy.
I'm already distinguishing blockwise positional elimination from row- or column-wise positional elimination; that's what separates my Trivial and Basic difficulty levels.
However, I agree this could be done better by paying attention to the number of empty cells. Basic difficulty level also introduces numeric elimination (observing that all but one of the possible numbers in a given square are ruled out, which will probably be due to a combination of row, column and block clues); but this is the obvious method of deduction used to fill in the last number in a block, a row, or a column, and that's definitely something that ought to be allowed in Trivial level. (Currently, in any puzzle labelled Trivial, there's always a blockwise-positional-elimination way to fill in any such single empty cell :-)
So perhaps I should rejig Trivial versus Basic so that all those modes of deduction are permitted in both levels, but it checks how quantitatively complex the deductions are in each case. Hmmm.
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On the other hand, it seems to me that a puzzle entirely composed of a single linear chain of reasoning, where there was only one deduction to be made at any stage, might actually be quite easy because every time you filled in a number you'd be easily able to find the next step just by asking yourself "now what additional information have I gained right here?", and wouldn't have to go looking over the whole grid each time. It's all terribly difficult and subjective.
For a really advanced analysis, you could generate a "tech tree" for being able to discover the contents of cells. As you get more information on each cell, they move from being indeterminate through being hard-to-deduce (many scattered clues, no redundancy) to being easy (much redundancy, few clues needed, those that are are close at hand). The easiest puzzles would have a solution path with no hard deductions on, and the hardest would have critical points where you have to make one tough deduction before you proceed. In between would be puzzles where you have a choice of hard deductions - making one makes the others easy.
However, I agree this could be done better by paying attention to the number of empty cells. Basic difficulty level also introduces numeric elimination (observing that all but one of the possible numbers in a given square are ruled out, which will probably be due to a combination of row, column and block clues); but this is the obvious method of deduction used to fill in the last number in a block, a row, or a column, and that's definitely something that ought to be allowed in Trivial level. (Currently, in any puzzle labelled Trivial, there's always a blockwise-positional-elimination way to fill in any such single empty cell :-)
So perhaps I should rejig Trivial versus Basic so that all those modes of deduction are permitted in both levels, but it checks how quantitatively complex the deductions are in each case. Hmmm.