Difficulty Rating of Sudoku Puzzles: An Overview and Evaluation

Abstract

How can we predict the difficulty of a Sudoku puzzle? We give an overview of difficulty rating metrics and evaluate them on exten-sive dataset on human problem solving (more then 1700 Sudoku puzzles, hundreds of solvers). The best results are obtained using a computa-tional model of human solving activity. Using the model we show that there are two sources of the problem difficulty: complexity of individ-ual 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