Shannon Meets Shortz: A Probabilistic Model of Crossword Puzzle Difficulty

This paper is concerned with the difficulty of crossword puzzles. A model is proposed that quantifies the difficulty of a puzzle P with respect to its clues. Given a clue-answer pair (c,a), we model the difficulty of guessing a based on c using the conditional probability P(a | c); easier mappings should enjoy a higher conditional probability. The model is tested by two experiments, each of which involves estimating the difficulty of puzzles taken from The New York Times. Additionally, we discuss how the notion of information implicit in our model relates to more easily quantifiable types of information that figure into crossword puzzles.