Bean, RichardHelm, LouieAntal, EugenMarák, Pavol2025-05-162025-05-1620251736-6305https://hdl.handle.net/10062/109740We give solutions to the 24 letter and 22 letter Playfair challenges proposed in Dunin et al. (2022) A number of methods were tried combining successful approaches of previous solvers, introducing new ideas while using letter-level and word-level approaches. We used vanilla and positional n-gram models for n values from 6 up to 10. However, these did not greatly assist to distinguish the intended solution from other high-scoring solutions. The most effective discriminative approach involved using a multi-terabyte-scale, unpruned large language model from Buck, Heafield, and Van Ooyen (2014) which moved the solution in each case into the top 5,000 ranked possibilities.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttps://creativecommons.org/licenses/by/4.0/Playfair ciphersimulated annealingtabu searchlarge language modelsArticle