The jigsaw puzzle includes a baseplate used with attachable puzzle pieces. The baseplate has multiple upward-facing engagement mechanisms that are engaged with corresponding and complementary puzzle piece rear-facing engagement mechanisms. The rear-facing engagement mechanisms and the complementary puzzle piece rear-facing engagement mechanisms are designed so as to leave an access space between the bottom of the puzzle piece and the top surface of the baseplate to facilitate removal of the puzzle pieces. A prying object (pry tool, user's fingertip, toy, or the like) can be inserted in to the access space to easily remove the puzzle pieces after play, storage, or display.