Two-State Alien Tiles: A Coding-Theoretical Perspective

Hoover H. F. Yin (), Ka Hei Ng, Shi Kin Ma, Harry W. H. Wong and Hugo Wai Leung Mak ()
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Hoover H. F. Yin: Institute of Network Coding, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
Ka Hei Ng: Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
Shi Kin Ma: Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
Harry W. H. Wong: Department of Information Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
Hugo Wai Leung Mak: Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

Mathematics, 2022, vol. 10, issue 16, 1-30

Abstract: Most studies on the switching game Lights Out and its variants focus on the solvability of given games or the number of solvable games, but when the game is viewed in a coding-theoretical perspective, more interesting questions with special symbolizations in coding theory will naturally pop up, such as finding the minimal number of lit lights among all solvable games apart from the solved game, or finding the minimal number of lit lights that the player can achieve from a given unsolvable game, etc. However, these problems are usually hard to solve in general from the perspective of algorithmic complexity. This study considers a Lights Out variant called two-state Alien Tiles, which toggles all the lights in the same row and those in the same column of the clicked light. We investigate its properties, discuss several coding-theoretical problems about this game, and explore this game as an error-correcting code and investigate its optimality. The purpose of this paper is to propose ways of playing switching games in a think-outside-the-box manner, which benefits the recreational mathematics community.

Keywords: alien tiles; coding theory; Lights Out; recreational mathematics; abstract algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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