Conference Paper2048 without mergingAkitaya, Hugo; Demaine, Erik D; Ku, Jason S.; Lynch, Jayson; Paterson, Mike; Toth, Csaba D.nullImagine t ≤ mn unit-square tiles in an m×n rectangular box that you can tilt to cause all tiles to slide maximally in one of the four orthogonal directions. Given two tiles of interest, is there a tilt sequence that brings them to adjacent squares? We give a linear-time algorithm for this problem, motivated by 2048 endgames. We also bound the number of reachable configurations, and design instances where all t tiles permute according to a cyclic permutation every four tilts.2021-08-0510253546Proceedings of the 32nd Canadian Conference on Computational Geometryhttps://doi.org/1800734National Science Foundation