Abstract: A two-dimensional cyclic game for creating and implementing puzzles and the like includes a two-dimensional playing field of either planar or curved configurations, a plurality of fixed sites defined on the playing field, and a plurality of game objects occupying the fixed sites. The game objects are movable only in groups. The groups are repositionable through performance of a series of consecutive moves to restore the game objects on the sites to a desired pattern. Also, in each of the moves, the game objects in a selected one of the groups are cyclically moved simultaneously in a given direction through translation or rotation along an endless cyclic path. In each cyclic translational move, the game objects of the selected one group are moved such that one of the game objects of the selected group located adjacent to a first portion of the playing field border is moved off the field at the first portion thereof and back onto the playing field at a second portion of the playing field border.