i tried to make a new one and it won't let me. in the puzzles, it shows that the golden child one is solved. when the beach fills up with wood again, it shows that puzzle as unsolved until i clear it again. so what's up with this?

The beach is the only puzzle that becomes "unsolved" because of an event, and it can be completed again by clearing the beach of the new debris. Once you have completed the gc puzzle, it remains complete. One per game. If you haven't completed all of the puzzles, that could be a problem. Many people would like to be able to get rid of him (but not until all the other puzzles are complete).