Only a handful of occasions where I looked at FAQs, mostly when it gets to the point of me being stuck where I actually get pissed off. Only happened on a couple puzzles on Hard+ modes. And the music puzzle in SH1 when I was younger and had no idea how any of that stuff even made sense lol.
I hate the moment that I have do decide if I'll keep trying or look for help. To solve a good puzzle is a unique moment and I can't forgive myself when I look at the right answer - why in the Gods name I wasn't able to discover???
I've never had a problem with a Silent Hill puzzle on any mode that I had to look up the answer. But, on subsequent playthroughs I'll look them up if I don't remember what they are just because I don't feel like dealing with finding the code or reading a long poem and interpreting it again.
"Chaos is merely the realm of the infinite possibilities. Imagination is merely a spinning wheel pulling threads of reality from that realm. Thought is merely a loom weaving those threads into the fabric of existence." -Someone
Theoretically, all puzzles can be solved by a human, but can take days, and the game will remain stopped until the player found the answer. In my case, translating a large poem is an extra plus hard job. After a day, I declare myself beated by the puzzle and get the answer.
Analyzing myself, I can discover, with some work, the puzzles that involves logic and math, but in rare situations I can solve with long poetic texts - it's to hard to translate. There is one in SH3 with some "nursery song" (I think is a lullaby) that I didn't understand even with a long explanation in the FAQ. Maybe even the writer couldn't understand too, since you can go through without all codes...