Puzzles vs. Games

In the strictest sense, games require multiple participants.

While many puzzles are considered games, particularly in the electronic context (Tetris, Candy Crush, etc.) they are nevertheless solo endeavors.

[M] games are doubly interesting because they present a competitive endeavor of pure strategic skill, and maintain the pattern-recognition puzzle qualities of Sudoku.

The transformation of Sudoku into a game expands its dimensionality in a profound way, the introduction of sequence as the dimension of time.

In the Sudoku puzzle, the order the integers are filled in has no significance. In [M] games, the sequence in which the integers are placed is of utmost importance.

While the number of strategically viable choices is greatly limited in [M], reducing the number of possible games, it is factorially expanded by the number of possible sequences in which the gameboard may be filled.

Because a game is a contest against an opponent, scoring may be utilized, and it becomes possibly to apply values to the integers which are merely symbols in the Sudoku puzzle. The application of a quantitative value in place of a one merely qualitative has the added benefit of eliminating reduction by relabelling, which maintains the size of the game tree.

The application of value, or magnitude, in a second method in which [M] games expands the dimensionality of the Sudoku construct.