What Crossword Puzzles Teach us about Information

This paper studies crossword puzzles as a vehicle for analyzing information in a rigorous yet meaningful fashion. The paper asks, how does information operate in the context 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 a corpus 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.