I FINALLY figured it out - because I am so smart - it is the LIGHTS! This puzzle makes the sounds when the piece is returned to the puzzle - the chip underneath recognizes that it goes dark when the piece is placed in the right spot and makes the noise. So, it turns out we do not have a puzzle-playing ghost, or basement monsters who like kittens. Thank goodness.
P.S. I am only telling you this because you may have this puzzle too and you are currently being terrorized by it as we were. It's a public service announcement, if you will.


















