Difficulty Rating of Sudoku Puzzles by a Computational Model

We discuss and evaluate metrics for difficulty rating of Sudoku puzzles. The correlation coefficient with human performance for our best metric is 0.95. The data on human performance were obtained from three web portals and they comprise thousands of hours of human solving over 2000 problems. We provide a simple computational model of human solving activity and evaluate it over collected data. Using the model we show that there are two sources of problem difficulty: complexity of individual steps (logic operations) and structure of dependency among steps. Beside providing a very good Sudoku-tuned metric, we also discuss a metric with few Sudoku-specific details, which still provides good results (correlation coefficient is 0.88). Hence we believe that the approach should be applicable to difficulty rating of other constraint satisfaction problems.