I'd never done sudoku before and was a little disappointed to find it was so mechanistic. I'd sort of expected there to be some degree of exploration and backtracking, or perhaps having to solve multiple digits simultaneously while attempting to keep it all in your head. Is this puzzle representative of normal sudoku puzzles or do the additional constraints change it?
On the other hand, backtracking feels much more mechanistic to me. A dumb computer can guess and backtrack and check constraints with a simple algorithm. Humans ought to do better than that—with more logic and more deduction.
Check out a Hitori. It's kind of an "inverse Sudoku". More difficult puzzles always get to a point where you have to guess the state of a certain field and then backtrack if you were wrong.
Basically the challenge is in finding the thought process that leads you to an answer.
The kinds of puzzles done on this channel tend to be pretty tough. the designers of the puzzle usually make it so that there's really one good path for solving (and brute forcing _really doesn't work_ relative to thinking hard about the problem).
There's a lot of stuff going on in this puzzle that's not at all present in normal sudoku, and things like "OK let's try and look for where _all the 3s could be at once_" is easier said than done.
I guess to me if still _feels_ a bit like brute force. You just go over all the squares and all the rules in a loop, adding and eliminating possible digits. There don't seem to be any sticking points where it's not clear how to make progress.
The "exploration and backtracking" you mention originally is the brute force method of solving sudoku by computer: recursive backtracking. If you want an example of sticking points, I'd recommend the Robin Hood sudoku:
It can be brute forced with enough patience, but the fun for me comes in developing intuition on where to look next. The hints of a sudoku have meaning: they lead to the completed grid. Finding the next step in the puzzle amounts to understanding some of its construction.
I guess the bit I'm missing is why the miracle sudoku (the two I can find) are special. As far as I can tell, they don't require any intuition at all, you just sit down and work through the rules that are right in front of you. Surely they're much easier than normal sudoku because of the extra rules? Are they noteworthy because of the construction of the puzzle, rather than the solving of it?
It's mostly about the construction. The "miracle" part refers to just two clues (filled-in numbers) leading to a unique solution, which is a ridiculously low number.
