On the Method of Creating and Couting Problems of 4 × 4 Sudoku X

Takuya KITAMOTO  Norimitsu SEKI  Tadashi WATANABE  

Publication
A - Abstracts of IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences (Japanese Edition)   Vol.J103-A   No.8   pp.185-195
Publication Date: 2020/08/01
Online ISSN: 1881-0195
DOI: 
Type of Manuscript: PAPER
Category: 
Keyword: 
sudoku,  sudoku X,  4 × 4 sudoku,  couting problems,  

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Summary: 
Sudoku is a pencil puzzle that is spreading all over the world. In this paper, we focus on 4 × 4 Sudoku X, which is a variant of Sudoku where the grid size is 4 × 4 and an additional constraint on the diagonal elements of the grid is imposed (the diagonal elements must contain all of the digits from 1 to 4). We examine the property of the problem of 4 × 4 Sudoku X, and clarify necessary and sufficient conditions for 4 × 4 Sudoku X problems to be appropriate. Also, using the results obtained, we proposed a procedure to create 4 × 4 Sudoku X manually and count the total number of 4 × 4 Sudoku X problems.