Large rodent native to Central and South America (6)
Wading bird sacred to the Ancient Egyptians (4)
Shrek, Shaun or Dolly? (5)
Feathers McGraw, Chilly Willy or Pingu? (7)
Captain Nemo's submarine in Jules Verne's Twenty Thousand Leagues Under the Seas (8)
Shakespeare play, The Taming of the _____ (5)
Favourite food of Obelix in the Asterix ...
At least not if the solution space is a countable infinite set, or smaller.
In that case, we can compute the finite time person 2) will need to find the solution found by person 1) by enumeration, making the strategy of 2) a computable function and therefore violating the constraints of the question.
Response to edit:
The "does not have to be perfect-...
Building from PartyHatPanda's answer,
they form the answer:
(New account, but I've been a lurker for months in the PSE. Solved the grid independently but from this computer it's hard to share a photo with the final solution).
From the facts about the first grid
My first guess of the genre was
Naturally, the next step would be
It is not very hard, if we focus on the number 5:
Now to the second grid. With transcribed numbers, the grid to solve is this:
Starting with R4 and focusing on fives,
Then it gets a little harder...
Reading the sums of each ...
I knew that there was already an answer; I'm posting this to show a cleaner path to the solution.
First of all,
Then we apply the boundary logic:
Then there's a highway of basic deductions.
We can extend the white boundary a bit
Finally, spotting a small contradiction finishes the game:
Partial answer - solved Shingoki, have guesses for 3 categories but not certain
The Shingoki's solution is:
The 16 symbols are:
Here are the categories:
And there is a character fitting all four of these categories:
Solving the Shingoki
Initial deductions get us here:
More progress can be made in one of the corners:
Next, look at the 4 ...
Some initial deductions:
In the bottom right,
And now, there's not much progress that can be made without thinking more globally.
Continuing with this newfound knowledge,
Finishing it off:
The final answer:
If there is exactly one way to fill out the grid in a valid way, then that can be found without using any logic based on uniqueness. (It may be very painful, and require brute-forcing a lot, but it won't be impossible to find.)
If there are exactly two valid ways to fill out the grid, then uniqueness logic cannot help you. You can never make a deduction ...
Okay, so I solved the whole puzzle :) I will use this specific puzzle to showcase several interesting deductions. Each picture will show one deduction I consider non-trivial, and in between pictures I will make trivial deductions. In this post, "trivial" deductions are:
if a cell has all its borders spoken for (e.g. a 3 that has one border shaded),...
This answer is meant to supplement PartyHatPanda's and Arturo's answers as it only focuses on the logical deduction of the grid (as requested by the OP in the question's comments). For the actual answer, refer to those contributions instead.
The solution is:
Remarks on setting the initial values:
Here I explain the thought processes that actually led me to settle on this combination of starting numbers. However, please also read @Retudin's answer as I think they've done a nice job of explaining this part diagrammatically...
First, we can make some obvious deductions on the bottom and bottom left. On the bottom left, we need the anvil to be in the bottom left corner and the balloon to be blocked by the wall, since if it was switched the balloon would have no anchor. (Similar logic applies for future deductions.)
Next, a few more deductions. The 2x1 at R8C7-8 region can only go ...
The “key deduction” involves
This allows us to make our first breakthrough:
The remainder of the puzzle is fairly straightforward:
And we can finally finish it off:
(Let me know if any steps need to be elaborated on further - after the key deduction the rest of the deductions seemed simple, but there may be something non-obvious I missed.)