1. A three-dimensional puzzle game apparatus executing a game for solving a three-dimensional puzzle in a virtual three-dimensional space, comprising: a processing system including one or more processors, the processing system configured to at least: display a three-dimensional puzzle including a plurality of blocks arranged in each of three-dimensional directions of said virtual three-dimensional space and information as a hint for searching a block to be left from an arbitrary block row; determine whether or not a deleting instruction is performed on any one of the blocks on the basis of input information from a pointing device, the pointing device being configured to designate a position based on a two-dimensional coordinate placed on a screen in which the three-dimensional puzzle is displayed; calculate a gaze from the position designated by said pointing device; specify a designated block to which said deleting instruction is performed by calculating an intersection point between said gaze and a surface of each block; determine whether or not the designated block to which said deleting instruction is performed is a block to be left when said deleting instruction is performed on said block; erase the designated block on which said deleting instruction is performed when the designated block to which said deleting instruction is performed is not a block to be left; and determine whether or not said three-dimensional puzzle is solved by determining whether or not all the remaining blocks are said block to be left by forming a three-dimensional model indicative of a solution.