In Hopping Mappy, the object of the game is to collect the eight treasures on each stage to complete it and move on to the next level. To get around, Mappy rides on a pogo stick instead of just walking or whatever like a normal police mouse. Mappy can only move up, down, left, and right because the Mouse Police didn't bother training him to move diagonally. However there are cats to avoid, and they are also on pogo sticks, so Mappy needs to watch out, otherwise he may end up pogoing his way to certain doom! He and the cats can only touch the center of each square on a stage, leaving them to move in a grid pattern.
An unoffical, unlicensed conversion of Hopping Mappy was released on the X68000 under the name Tiny Hopping Mappy.