A Statistical Study of Failures in Solving Crossword Puzzles

Abstract Crossword puzzles are the most popular form of linguistic puzzles; for the solver they are intellectually challenging and entertaining as well. An interesting exercise for this author, a keen solver of the British-style ‘cryptic’ crossword puzzles, has been the statistical distribution of the number of unsolved clues (x) in a puzzle. Data are cumulated over a decade (total number of puzzles 3404). The large sample size makes it possible to examine the tail of the distribution at large x, up to 12. It is found that the Poisson distribution with one free parameter (λ) is inadequate, but the negative binomial distribution (NBD) with two free parameters (p, k) fits the distribution well as vouched by a χ 2-test. The NBD can be interpreted as a “mixture” of Poisson and Gamma distributions. It is suggested that this is an appropriate model for the distribution of x. Surprisingly, a 3-parameter lognormal distribution (LND2) also fits the observed distribution of x equally well. The popular model for LND...