Year: 2025
Type: article
Abstract: This paper introduces a novel class of Latin squares that includes Sudoku squares as a subset. We define a new structure by applying a ceiling-based function to each entry of a Latin square of order n=r2 , grouping values into blocks, and requiring that each block contains each integer from 1 to r exactly r times. This defines an intermediate grid type that bridges standard Latin squares and Sudoku grids. Furthermore, we introduce a bijective mapping ϕ on the space of Latin squares, where each row in ϕA encodes the column positions of a given value in the original square A . This mapping enables a new method for generating Sudoku-like grids by transforming Latin squares in a structured way. We present mathematical foundations, formal definitions, and proofs establishing the properties of this new class of grids and their relation to classical Sudoku puzzles.
Source: Journal of High School Science
DOI: 10.64336/001c.136395
Author: Gloria S Choi
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W6977880103