In the puzzle solitaire game of Cubic, there are variously colored unit blocks in some configuration. The player is allowed to drag blocks to horizontally adjacent and unoccupied positions.
Gravity pulls unsupported blocks down into available spaces.
When more than one block of the same color come into contact, they disappear. The goal is to remove all the colored blocks. An example of a puzzle is shown in Figure 1. We use differently numbered blocks instead of colored blocks. We will show that the question of whether or not a given Cubic position is solvable is NP-complete.