Twin Sudoku Puzzles and Triplet Solid Sudoku Cubes From Strongly Mutually Distinct Twin Sudoku Tables

摘要

A new class of twin Sudoku tables (TSTs) is presented. These tables can be divided into both $s times d$ and $d times s$ subtables. They are constructed using the cyclotomic cosets of $Z_n$ via two distinct vectors of cyclotomic coset elements and their Kronecker product. We prove that it is possible to generate $m$ TSTs that are strongly mutually distinct (SMD), i.e., for every $0leq i, j leq m-1$ , 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 SMD TSSTs in order 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. As a result, new twin Sudoku puzzles (TSPs) and SMDTSPs are obtained that can be used to design new types of Sudoku games.