On shelves at a Humanetics facility in Huron, Ohio, skulls stare from their eyeless sockets, shiny and silver. Around a corner, a rack is filled with squishy, peach-toned arms, legs, torsos and butts.

As avid puzzlers know full well, the humble jigsaw puzzle is a thing of beauty in multiple ways. Not only are jigsaws an absorbing time sink, but multiple studies have demonstrated they are good for ...