Undergraduate Honors Thesis by Radu Rosu

Definitions

colors	The set of different colors used in a mastermind code. In this paper, colors are referred to as numbers from 1 to the number of colors m.
positions	The number of different pegs that make a legal mastermind code in a specific game.
mastermind code	A set of colored pegs that are placed in a set number of positions. Order matters and repetitions of the colors are allowed, giving us colors ^positions different possible codes. For simplicity, code structures are denoted as {colors, positions}.
mastermind result	A set of black and white pegs that describes the match between two mastermind codes. A black peg corresponds to a match in color and position; a white peg corresponds to a match in color but not in position. In this paper, a mastermind result is denoted (blacks, whites). A result of (0,0) means that the two codes do not share any colors.
code set	The set of all possible codes for a chosen number of colors and positions {c, p}. By definition, a code set has size c^p .