The hint in the bathroom claims they all have a plane of symmetry.
This is incorrect. None of them do. They're all 2-dimensional.
So I assume the hint was supposed to be they all have line symmetry (mirrored).
Unfortunately, that's also incorrect. Using sadgamer7x's mapping, only 3,4;1,3;3,3;4,3;1,2;2,2;3,2;1,1;3,1 have line symmetry.
So I assumed the hint was supposed to be they all have rotational symmetry.
Unfortunately, that's incorrect. 1,3 that looks like a downward arrow is not rotationally symmetric.
So I thought, maybe the pairs upon pairs was trying to say only look at symbols that have line symmetry on two axes. That gives 3,4;3,3;4,3;1,2;1,1;3,1.
And so on... I could do this all day. Hence, why I can't see the path to the correct answer here.
This is why these puzzles are poor. Follow me here...
A riddle with a mapping of 1-to-1 of riddle to answer isn't a riddle, it's a question with a correct answer. That's a quiz. Can be fun, but not what your audience is expecting when you call your game "Lisa's Cryptic Quest".
A riddle with a mapping of 1-to-several answers with one answer being most probable is a riddle most people will get and is fun.
A riddle with a mapping of 1-to-many answers and only a few being probable is a good riddle. A lot of people will get it and have fun by solving something with some risk of being wrong. As not everyone will get it, those that do will feel like they're "smart" or in an exclusive group.
A riddle with a mapping of 1-to-2 magnitude answers is an exhaustible (brute force) guessing game. Only enjoyable by people with time on their hands. Those people will enjoy it due to the cascade of dopamine when they finally solve it and feel even more "exclusive". However, most people will start to feel frustrated and left out.
A riddle with a mapping of 1-to-3+ magnitude answers is a lottery. This is not what you want if you want the majority of people to enjoy the riddle. Almost everybody will leave feeling frustrated.
These mappings get compounded when to solve a particular riddle multiple algorithms are needed and there's no guidance/constraints/context to know when an algorithm change is necessary. And what may be "obvious" never is without sufficient context. For example, this entire post is gibberish to someone unfamiliar with English even though what I'm saying here is obvious to the English-reading world.
As a result, unfortunately, what you have in this game is a bunch of lotteries. But now armed with this knowledge, hopefully the next riddle game you make will be more enjoyable for more people and you can find the sweet spot you're aiming for with your game.
Sorry this was so long, but it should be obvious I really like Cabin by the Lake or I wouldn't care this much about your game design. :)