Exploring Mathematics through Game-Based Learning Mastermind Game: Colour Code Breaker

Abstract

Mastermind, a classic code-breaking game for two players, features various versions with differing numbers of code pegs (ranging from 4 to 6) and rules concerning repeated colours and blank pegs. This paper explores a simplified variant of Mastermind, where solutions are restricted to code pegs with unique colours and no blank pegs. By focusing on a subset of two code pegs, we model each attempt as a linear system. Through three attempts that satisfy the criteria of a linear system, we determine the initial colour solution for each small group. Further analysis allows for the calculation of the correct colours and their positions within each group using probability measurements. This approach provides a systematic method for solving the simplified Mastermind game and demonstrates the application of linear systems and probabilistic techniques in code-breaking. The findings offer insights into the effectiveness of these mathematical methods in deriving accurate solutions and enhancing problem-solving strategies within the game.