champagne wrote:If we switch from a strict -3+3 to a strict -4+4, I have more difficulties with your "originally empty" adjustment.

This would match better in my feeling with a {-1+1 to -3+3} versus a {-1+1 to -4+4} comparison, but I learned for long to be wrong against your view

Think about this: "same shape, different clues", "almost the same shape, not almost the same clues" ...

For a strict {-n,+n}, really the only (*) thing you can ignore is placing the original clue value in a "+" cell that's also a "-" cell.

Taking that into account, would change the "5 candidates" number that I used, but only only a small amount.

The "5" in the (5^n) factor is isn't exact, anyway.

It's just a number has worked well in other calculations, when actual numbers have been compared.

With so few filled cells remaining, after "{-3}" or "{-4}", it might be too small.

Technically, it seems like it should increase slightly, as 'n' increases.

Cheers.

Added: (*) - "Only" isn't quite correct. If after the "-n" operation is performed, there are two empty rows, for example, then the "+n" cells could give a shape that would share cells with the original puzzle (in those rows) if the rows were swapped.