Generalizing Sudoku to three dimensions

The well-known logic puzzle Sudoku can be generalized from two to three dimensions by designing a puzzle that is played on the faces of a cube. One variation, already introduced as a puzzle by Dion Church, uses three adjacent faces. Another variation uses all six faces. We have developed a set of rules and constraints for both three-dimensional Sudoku variations and have studied the properties using the method of simulated annealing.