Puzzles are distributed
Blue Prince does not hand you a puzzle screen. Clues sit in room descriptions, notes, and item effects, often in rooms that look like filler. The Antechamber and Room 46 themselves are gated by layered puzzles you assemble over many days.
Collecting without grinding
Read every room description as you enter. The line you skim on day two is often the key to a lock on day nine. The room database keeps those descriptions in one place so you can revisit them.
Sigils, codes and notes
Several puzzles use in-world codes and marked rooms. When you find a clue, note which room type it appeared in; many solutions want you to return to that exact type with new information.
Patience over force
Most progression locks are solved by routing the right room, not by brute force. If a door will not open, the answer is usually a clue you have not connected yet.