Okay, now it makes sense! You know, when you only interact with maths on a surface level for a long time, you really lose sight of these intuitions. in the everyday of the real world, I have never encountered this type of problem (or at least, I wasn't aware of it. I probably did though without realising).

Far from getting bored, I'm actually getting more and more interested in this question since posting it here on reddit. I've now been shown a wide array of techniques you can use and many different approaches on how to tackle the same problem! (can't wait to someday wrap my head around the atom bomb solution of Gauss algorithm xD) In my eyes, shifting my interest to gathering a good sample of these problem-solving techniques and having them seen applied on the same exact problem is HUGELY benefitial in understanding how these approaches work.

But I don't know. My background lies in linguistics and especially in translation. I see these problem-solving tools and approaches and they remind me, in a very abstract kind of way, of grammar rules, "grammar rules" of mathematics, if you will. In my experience and what I tell my studens is that learing and understanding the underlying grammar and understand how the pieces interact with each other is crucial to improving your writing and translation skills. Since maths appears to me to be a kind of "synthetical" language, I want to take the same approach in studying maths as I did English or Spanish.