Difficulty Rating of Sudoku Puzzles: An Overview and Evaluation
This work addresses the challenge of rating puzzle difficulty for game designers and AI researchers, offering insights that could generalize to other problems, though it is incremental in building on existing metrics.
The paper tackles the problem of predicting Sudoku puzzle difficulty by evaluating various metrics on a dataset of over 1700 puzzles and hundreds of solvers, finding that a computational model of human solving activity yields the best results and identifies two key sources of difficulty: step complexity and dependency structure.
How can we predict the difficulty of a Sudoku puzzle? We give an overview of difficulty rating metrics and evaluate them on extensive dataset on human problem solving (more then 1700 Sudoku puzzles, hundreds of solvers). The best results are obtained using a computational model of human solving activity. Using the model we show that there are two sources of the problem difficulty: complexity of individual steps (logic operations) and structure of dependency among steps. We also describe metrics based on analysis of solutions under relaxed constraints -- a novel approach inspired by phase transition phenomenon in the graph coloring problem. In our discussion we focus not just on the performance of individual metrics on the Sudoku puzzle, but also on their generalizability and applicability to other problems.