Most of my bulletin board space is inside of my science lab, but I have a bulletin board that is in the hallway just outside of the science lab. Last year I taught all of middle school science as well as grade 8 math, and I used this bulletin board for math puzzles. I put the puzzle in the centre of the board and underneath I added a folder where students could put their solutions. When it was time for a new puzzle in the centre, I removed the old puzzle and put it either on the right or left side of the new one. I included the answer to the old puzzle and highlighted any correct solutions that students had given. Eventually the board around the centre puzzle got filled with old puzzles and solutions, and it was then that I emptied the board and started fresh.
When I originally designed the bulletin board, I had thought that only middle school students would take interest. However, there was a grade 4 classroom right beside mine, and I was pleasantly surprised to see those students hovering around my puzzle board on a regular basis. They liked the challenge of the harder problems, and I think they ended up attempting solutions more often than my own students. See my puzzle website list for inspiration of what to put on your own bulletin board.