Abstract:
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...View moreMetadata
Abstract:
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
0\leq 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.
Published in: IEEE Transactions on Games ( Volume: 14, Issue: 4, December 2022)