Abstract: A game is described involving operations on a six-sided cube. Each of the six sides of the cube has four corners which are identified by a different symbol; and the order of the symbols on each of the six sides of the cube is rotationally distinct. The cube has eight vertices each formed by three corners of three different sides. The symbols may be ordered in two ways: the same symbol may be found at each of the three corners that form a vertex, or the same symbol may be found at adjacent vertices on opposite side of a common edge. The object of the game is for the player to begin with a first orientation of the cube which defines a first sequence of symbols and to obtain a second sequence of symbols by performing a series of manipulations on the six sided cube. Preferably the game is played as a baseball game with two players alternating turns and with scoring of runs, hits and outs depending on the number of cube rotations required to turn the cube to match the second sequence.

Abstract: A game is described involving operations on a permutation group (X,*) where X is a set of symbols, illustratively the alphabet, and * is a two argument operation on the symbols of said set, said group having closure, associativity, an identity element and an inverse for each element of the set. A series of plaintext symbols of the set X is encoded by replacing each plaintext symbol with a symbol pair comprising two of the three symbols x, y, z in the relation x*y=z and where x, y, and z are each elements of the set X and one of x, y and z is the plaintext symbol to be encoded. The encoded symbol pairs are then decoded to recover the series of plaintext symbols.