A valid move is one of the following: (1) a chain of jumps over other pieces vertically, horizontally, or diagonally to other unoccupied spaces on the board, or (2) a single-space step in any direction to any unoccupied space. Although it is to your advantage to set up long chains of jumps (since the entire chain only counts as a single move), single-space steps are equally important in minimizing your score. There is no Halma board which can be solved entirely with chains of jumps; all minimal solutions require at least one single-space step.