Clickomania: A Puzzle Game's Complexity Explained

Title: Clickomania: A Puzzle Game's Complexity Explained

Main Research Question: How complex is the puzzle game Clickomania, and how does it change with different parameters?

Methodology: The researchers used a combination of mathematical analysis, algorithmic techniques, and computational experiments to study the complexity of Clickomania. They focused on the decision problem (whether a puzzle is solvable) and the optimization problem (finding the maximum number of blocks that can be removed). They considered various parameters such as the number of colors, the number of rows, and the number of columns.

Results: The researchers found that the decision problem for two colors and five columns is NP-complete, meaning that it is computationally difficult and likely impossible to solve in an efficient way. On the other hand, they showed that the optimization problem for one column (or one row) can be solved in polynomial time, meaning that it can be solved efficiently for any input size.

Implications: These results provide insights into the complexity of Clickomania and the challenges involved in solving these types of puzzles. They also have implications for the design of puzzle games and the development of algorithms for solving similar problems in other fields. For example, the techniques used in this study could be adapted to analyze the complexity of other puzzle games or to solve real-world problems involving similar types of combinatorial optimization problems.

Link to Article: https://arxiv.org/abs/0107031v1 Authors: arXiv ID: 0107031v1