Abstract: Several experiments are conducted at different environments such as locations or periods (seasons) with identical treatments to each experiment purposely to study the interaction between the treatments and environments or between the treatments and periods (seasons). The commonly used designs of experiments for this purpose are randomized block design, Latin square design, balanced incomplete block design, Youden design, and one or more factor designs. The interest is to carry out a combined analysis of the data from these multi-environment experiments, instead of analyzing each experiment separately. This paper proposed combined analysis of experiments conducted via Sudoku square design of odd order with same experimental treatments.
Abstract: Samurai Sudoku consists of five Sudoku square designs each having nine treatments in each row (column or sub-block) only once such the five Sudoku designs overlaps. Two or more Samurai designs can be joint together to give an extended Samurai design. In addition, two Samurai designs, each containing five Sudoku square designs, are mutually orthogonal (Graeco). If we superimpose two Samurai designs and obtained a pair of Latin and Greek letters in each row (column or sub-block) of the five Sudoku designs only once, then we have Graeco Samurai design. In this paper, simple method of constructing Samurai designs and mutually orthogonal Samurai design are proposed. In addition, linear models and methods of data analysis for the designs are proposed.
Abstract: Sudoku is a logic-based combinatorial puzzle game
which people in different ages enjoy playing it. The challenging and
addictive nature of this game has made it a ubiquitous game. Most
magazines, newspapers, puzzle books, etc. publish lots of Sudoku
puzzles every day. These puzzles often come in different levels of
difficulty so that all people, from beginner to expert, can play the
game and enjoy it. Generating puzzles with different levels of
difficulty is a major concern of Sudoku designers. There are several
works in the literature which propose ways of generating puzzles
having a desirable level of difficulty. In this paper, we propose a
method based on constraint satisfaction problems to evaluate the
difficulty of the Sudoku puzzles. Then we propose a hill climbing
method to generate puzzles with different levels of difficulty.
Whereas other methods are usually capable of generating puzzles
with only few number of difficulty levels, our method can be used to
generate puzzles with arbitrary number of different difficulty levels.
We test our method by generating puzzles with different levels of
difficulty and having a group of 15 people solve all the puzzles and
recording the time they spend for each puzzle.