Construction of Standard Solid Sudoku Cubes and 3D Sudoku Puzzles

Abstract

In this paper, 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. The structure of these cubes is based on cyclotomic cosets of Z n , and we make use of a design vector Z and a basic table T to construct SSSCs. We obtain m tables by multiplying all entries of T with 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 the SSSC is presented as standard solid Sudoku puzzles (SSSPs).

Sudoku sequences, Costas sequences, and random permutations in a multi-sub-FDA radar

“…9 In the case of Sudoku, this elevated Shannon Entropy occurs because the rules of Sudoku place constraints on where numerical values can be placed, leading to 'better randomness.' Additional instances of 10,11,12,13,14 The rules of a Sudoku game are simple: a player must completely fill an N × N gameboard using only the numbers 1 to N ; however, there can be no repeated integer in any row, column or any of the n × n sub-matrices, where n 2 = N . A typical solved 9 × 9 Sudoku game is shown in Figure 1.…”