Mathematics for Scalable Tic - Tac - Toe (I) : Arithmetic Progression Edt.
Year: 2026
Type: preprint
Abstract: This paper presents a mathematical approach for indexing elements in a two-dimensional grid using arithmetic progressions. Each row and column of the grid is represented as an arithmetic sequence, allowing their general terms to be expressed in a structured algebraic form. Formulas are derived for row-wise and column-wise indexing, followed by an analysis of diagonal and anti-diagonal elements. These derivations provide a systematic method for identifying positions within an N × N grid. The proposed framework can be applied to grid-based problems such as Tic-Tac-Toe, matrix indexing, board-game analysis, and computational grid systems.
Author: RAI, SURAJ
Institution: Dong-Eui University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165756918
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