The construction and balancing puzzle of the present invention utilizes multiple differently shaped parts which are assembled vertically on a stand to form particular designs. During the assembling or construction, the assembled parts must be balanced at all times. The basic puzzle piece is an injection molded cube and the remaining puzzle pieces are fabricated by joining several cubes together in a single plane. The stand or base includes a flat bottom to be supported on a table and the upper portion is made from two upwardly facing walls that are at an angle of 90 degrees with respect to each other to form a V. Each of the two walls of the base has a length that is preferably one and one-half times the length of the cube that makes the basic puzzle piece.