Abstract: A spherical logical puzzle is disclosed comprising four interconnected branches, each of which defines a branch axis and comprises a fixed puzzle segment of arcuate triangular shape connected thereto, the segment being rotatable about its respective branch axis; a plurality of free puzzle segments are also provided comprising six arcuate square puzzle segments and four arcuate triangular puzzle segments, the free and fixed puzzle segments being coupled together to form a sphere; the segments are capable of adopting a plurality of positions relative to one another, and are movable between these positions by relative rotation of the segments in planes perpendicular to the branch axes.