One other crucial hint, not really a spoiler in my opinion: A builder apparently cannot make Master if s/he has never done beach cleanup. I gleaned this from careful reading of other posts, having had a LOT of frustration with this issue in previous attempts. So, this time, I made sure to postpone beach cleanup until I really needed it, and then made sure to force every teenager I could find to do it. As a result I now have two master builders, 46 and 52 years old, and maybe thus a shot at the mysterious Puzzle 12, I am told.

Sometimes a random Island Event will force another beach cleanup, but you can't count on this. I'm not absolutely sure the following is completely true, but my understanding is: No beach cleanup experience, no master builder, and you need at least one MB alive when you finally get all your tech levels to solve Puzzle 12.