my goal when making this one-page design was for anyone reading it to know everything they would need to implement the puzzle in-game.
The constraint here was that the document had to be one page maximum. Because of this, I had to pick out what information was essential-- basically, I had to find the load-bearing parts of the puzzle and ignore everything else.
The approach I took was the same one I use when designing puzzles: I started from the solution and worked my way back. Any mechanics that were necessary to reach the solution, I included a concise description of. I did the same with any clues the player needed in order to come to the right conclusion. And, of course, I included the solution itself (It would be very difficult to implement the puzzle without knowing what its completion conditions are).
Doing this was a great exercise in thinking from a production perspective. As a game designer, I'm usually trying to put myself in the player's shoes. But members of the art and programming team need to know different things than a potential player or fellow game designer would. Overall, this challenge made me much more confident in my ability to communicate my designs to non-designers.