Interesting logic puzzle

[Vort]

@zil2 introduced us to logic puzzles in, what was it, 2019 or so. Since then, I have solved thousands of puzzles off of the Puzzle Baron site. I came upon a puzzle from that site recently that, while it is indeed solvable, is solvable only by accepting that there exists exactly one unique solution. Well, duh. How is this a big deal?

Only because in every other case I can think of, the puzzle becomes obviously determinate simply by working through the clues. This is the first puzzle example I remember that requires you to simply guess at the right answer and see if the puzzle solves all the way through. If it does not, that's not the right answer, so try another guess.

Obviously, the puzzle is partially solvable purely by using the logic clues, but only to a point. And that point leaves quite a few answers open. At the end, you find exactly one path (from many) that leads you to a unique solution. All other paths lead to indeterminate answers. You know you've got the right solution when you find something that solves, while every other possibility leaves you hanging.

Maybe I'm wrong. I welcome correction if this puzzle really is solvable by means other than blind brute force. But I think it is not.

240730x7-T906ML.pdf

[zil2]

20 minutes ago, Vort said:

This is the first puzzle example I remember that requires you to simply guess at the right answer and see if the puzzle solves all the way through. If it does not, that's not the right answer, so try another guess.

You haven't been working through them long enough - it happens occasionally. I hate it when this happens. Sometimes you can use scratch paper to work out an "either" or "of these" clue and don't have to go far to see which will work - I like the extra challenge of those. But I hate the ones that make you work in pencil filling out most of the grid before you can see the conflict (or solution).

Sometimes I'm tempted to try all the possibilities to see if there really is only one solution, but usually laziness and frustration make me leave it at solved.

Those other two sites are worse - they make you guess at things outside the clues - very annoying. In a way, I'm glad I've done all their puzzles and there won't be more. 

Edited August 11 by zil2

[zil2]

Forgot to mention, sometimes I can find the solution by elimination - e.g. if Tabitha's work is one of two prices, then any wood or item that's neither of those prices can't be hers. Sometimes that gets you through, sometimes not. (My 1/4" wide ruler gets a lot of use on those 4x7 puzzles.  )

Edited August 11 by zil2

[Vort]

8 minutes ago, zil2 said:

Forgot to mention, sometimes I can find the solution by elimination - e.g. if Tabitha's work is one of two prices, then any wood or item that's neither of those prices can't be hers. Sometimes that gets you through, sometimes not. (My 1/4" wide ruler gets a lot of use on those 4x7 puzzles.  )

Yes, I do a lot of that sort of "backward elimination".

As I was showering, I realized that my OP is really just a fancy way of saying that the answer is indeterminate. If you can come up with any solution that fits the clues, then that solution by definition is valid and cannot be meaningfully distinguished from the "correct" solution. I'm clearly playing fast and loose with what the "solution" means, to some extent at least. I need to think about this some more.