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.
Abstract: Sudoku is a logic-based combinatorial puzzle game which is popular among people of different ages. Due to this popularity, computer softwares are being developed to generate and solve Sudoku puzzles with different levels of difficulty. Several methods and algorithms have been proposed and used in different softwares to efficiently solve Sudoku puzzles. Various search methods such as stochastic local search have been applied to this problem. Genetic Algorithm (GA) is one of the algorithms which have been applied to this problem in different forms and in several works in the literature. In these works, chromosomes with little or no information were considered and obtained results were not promising. In this paper, we propose a new way of applying GA to this problem which uses more-informed chromosomes than other works in the literature. We optimize the parameters of our GA using puzzles with different levels of difficulty. Then we use the optimized values of the parameters to solve various puzzles and compare our results to another GA-based method for solving Sudoku puzzles.
Abstract: Sudoku is a kind of logic puzzles. Each puzzle consists
of a board, which is a 9×9 cells, divided into nine 3×3 subblocks
and a set of numbers from 1 to 9. The aim of this puzzle is to
fill in every cell of the board with a number from 1 to 9 such
that in every row, every column, and every subblock contains each
number exactly one. Sudoku puzzles belong to combinatorial problem
(NP complete). Sudoku puzzles can be solved by using a variety of
techniques/algorithms such as genetic algorithms, heuristics, integer
programming, and so on. In this paper, we propose a new approach for
solving Sudoku which is by modelling them as block-world problems.
In block-world problems, there are a number of boxes on the table
with a particular order or arrangement. The objective of this problem
is to change this arrangement into the targeted arrangement with the
help of two types of robots. In this paper, we present three models
for Sudoku. We modellized Sudoku as parameterized multi-agent
systems. A parameterized multi-agent system is a multi-agent system
which consists of several uniform/similar agents and the number of
the agents in the system is stated as the parameter of this system. We
use Temporal Logic of Actions (TLA) for formalizing our models.
Abstract: There are many approaches proposed for solving
Sudoku puzzles. One of them is by modelling the puzzles as block
world problems. There have been three model for Sudoku solvers
based on this approach. Each model expresses Sudoku solver as
a parameterized multi agent systems. In this work, we propose a
new model which is an improvement over the existing models. This
paper presents the development of a Sudoku solver that implements
all the proposed models. Some experiments have been conducted to
determine the performance of each model.