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The Mathematics of Various Entertaining SubjectsResearch in Recreational Math$
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Jennifer Beineke and Jason Rosenhouse

Print publication date: 2015

Print ISBN-13: 9780691164038

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691164038.001.0001

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Analysis of Crossword Puzzle Difficulty Using a Random Graph Process

Analysis of Crossword Puzzle Difficulty Using a Random Graph Process

(p.105) 8 Analysis of Crossword Puzzle Difficulty Using a Random Graph Process
The Mathematics of Various Entertaining Subjects

John K. McSweeney

Princeton University Press

This chapter quantifies the dynamics of a crossword puzzle by using a network structure to model it. Specifically, the chapter determines how the interaction between the structure of cells in the puzzle and the difficulty of the clues affects the puzzle's solvability. It first builds an iterative stochastic process that exactly describes the solution and obtains its deterministic approximation, which gives a very simple fixed-point equation to solve for the final solution proportion. The chapter then shows via simulation on actual crosswords from the Sunday edition of The New York Times that certain network properties inherent to actual crossword networks are important predictors of the final solution size of the puzzle.

Keywords:   crossword puzzles, crossword puzzle difficulty, random graph process, network structure, iterative stochastic process, The New York Times, network properties, crossword networks

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