Event Details
Construction of twin Sudoku tables and their extension to triplet and standard solid Sudoku cubes
Presenter: Mehrab Najafian
Supervisor:
Date: Tue, July 8, 2025
Time: 14:00:00 - 00:00:00
Place: Zoom - see below.
ABSTRACT
Zoom Link:
Meeting ID: 890 4872 8223
Password: 370127
Abstract:
In this seminar a new class of twin Sudoku tables (TSTs) is presented. These tables can be divided into both s×d and d×s subtables. They are constructed using the cyclotomic cosets of Zn via two distinct vectors of cyclotomic cosets elements and their Kronecker product. We prove that it is possible to generate m twin Sudoku tables that are strongly mutually distinct (SMD), i.e. for every 0 ≤ i, j ≤ m-1, the (i, j)-th entry of the tables contains different symbols. We also provide a method to construct m different TSTs that can be converted into twin solid Sudoku tables (TSSTs) as a perfect set of strongly mutually distinct TSSTs to make triplet solid Sudoku cubes (TSSCs). These TSSCs are symmetric cubes so that a cut from any of the six faces is a TSST.
Standard solid Sudoku cubes (SSSCs), a three-dimensional (3D) extension of Sudoku tables, are introduced, and a method to construct these cubes is presented. This is the first class of standard solid Sudoku cubes. An SSSC of order m is a solid Latin cube of order m with solid subcubes of order x×y×z in which each element occurs exactly once in each row, column, depth, and subcube. We make use of a vector Z and a basic table T to construct SSSCs. We obtain m tables by multiplying all entries of T by a number from the vector Z. Then, these tables are converted to an SSSC by stacking them in order. Based on this method of construction, a perfect set of strongly mutually distinct standard solid Sudoku cubes is designed. We also provide a two-dimensional (2D) representation of these SSSCs in a table with numbers placed on the main diagonal of its subtables. Finally, a new class of 3D Sudoku puzzles based on SSSCs is presented as standard solid Sudoku puzzles (SSSPs).