Welcome! This is my thread I had an idea about after seeing the lack of single puzzle solutions on YouTube. To help the community, and myself in the future, below will be every single puzzle solution and event Pokémon location and how to get them. Be aware that there ARE spoilers below! If you do not want to have anything spoiled, do not watch / read ahead!
I decided to color code these based on difficulty, they are:
If you want an easy way to do the puzzles (such as the Turtwig one), click here: http://www.instructables.com/id/How-To-Solve-The-15-Puzzle/
Green: Easy
Yellow