**Reference**:- Hugo Akitaya, Erik D. Demaine, Jason S. Ku, Jayson Lynch, Mike Paterson, and Csaba D. Tóth, “2048 Without Merging”, in
*Proceedings of the 32nd Canadian Conference in Computational Geometry (CCCG 2020)*, Saskatchewan, Saskatoon, Canada, August 5–7, 2020. **Abstract**:-
Imagine
*t*≤*m**n*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. **Comments**:- Hugo Akitaya's presentation is available on YouTube.
**Availability**:- The paper is available in PDF (774k).
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Last updated September 20, 2023 by Erik Demaine.