There may be a mathematical reason why crossword puzzles seem to get easier as you solve them. Credit: Deposit Photos / Jordan FeegShareWhats a 11-letter concept shared by crossword puzzles and avalanches, and starts with the letter P? According to one physicist, the answer is simple: Percolation.When a statistical physicist looks at a partially solved crossword puzzle, she or he sees immediately a percolation problem: Is there a spanning path consisting of fully solved words? writes the University of Oldenburgs Alexander Hartmann in a recent paper published in Physical Review E.Percolation is ubiquitous in all fields of sciences like physics, mathematics, computer science, social sciences, or biology, he adds.Percolation, in this sense, relates to what is known as percolation theory. In mathematics and statistical physics, percolation theory concerns the behavior of a network model as additional points, nodes, or links are added to the overall system. At a certain point, these interconnected frameworks undergo a geometric version of a phase transition, suddenly becoming a much larger, new formation with novel properties.Think of it like a tea bag so saturated by water droplets that it begins to leak out of its mesh container, the snowflake that shifts a mound of frozen powder into an avalanche. Or, as Hartmann describes, the letters and words that suddenly make a formerly difficult crossword puzzle much easier to solve.Hartmann, a crossword fan, was recently curious if he could generate a single block of letters that created words in every direction, minus the puzzles trademark black spacer squares. He soon realized, however, that he was encountering a variation on a percolation problem. In mathematics and statistical physics, percolation theory concerns the behavior of a network model as additional points, nodes, or links are added to the overall system. Hartmann then devised percolation-based calculations to illustrate the concept.In the present work, crossword-puzzle percolation is introduced, where letters or words are occupied with independent or neighbor-dependent probabilities. In the model, letters correspond to sites and words to segments of sites, bordered by black sites, he explains. But Hartmann noticed something after graphing his crossword-centric formula. Get the Popular Science newsletter Breakthroughs, discoveries, and DIY tips sent every weekday. By signing up you agree to our Terms of Service and Privacy Policy.[I]t appears that crossword-puzzle percolation comprises a new type of universal behavior, he writes. This means Hartmanns new formula is unique among all other known percolation problems.The physicist theorizes one potential explanation may be that the uncertainty one feels while staring at a largely blank crossword puzzle changes as you make progress.Since solving a word leads to an increase of the probability of solving neighboring words, this leads to further iterations, i.e., avalanches of solving words, writes Hartmann.Hartmann believes this concept can be studied further to explore relations between these abstract phase transition concepts and their physical counterparts. In the meantime, crossword puzzlers can be comforted that physics now implies that as difficult a puzzle may seem, its often darkest before the dawn. All it often takes is one letter or word to bring a puzzle to its percolation point.