After playing 10 hours of Blue Prince, and reaching the tipping point where the game goes from: "Waiting for the RNG to let me progress" to: "Having enough goals presented that there is always something to do", I've come to the conclusion that it really is a nicer experience if you can share puzzles and hints with other players.
If you're playing Blue Prince, and you want to discuss puzzles you're on - here's a spoiler thread!
I will start with a hint I gave out to someone who hadn't reached that tipping point I mentioned, and needed more of a hook to keep playing.
After you draft the commisary, you will find a hint about a puzzle regarding the illustrations on the walls of most rooms. What to do with this isn't clear untill it is explicitly given to you in another room later, but if you want to work on it before you are handed the answer, here's my hint.
Using the commisary room hint, observe the picture pairs, and note your answers down on a 5x9 grid of the house. I think this format is present for other puzzles too.