Sudoku Solver

Introduction to Sudoku, Creative and Impressive Lego Mindstorms NXT 2.0 Builds As Seen on YouTube

Sudoku Solver - Introduction to Sudoku, Creative and Impressive Lego Mindstorms NXT 2.0 Builds As Seen on YouTube

Introduction to Sudoku Puzzles

Sudoku is an abbreviation of the Japanese phrase “Su-ji wa dokushin ni kagiru” which means that the “number should remain single or unmarried”. The complete name was used when the puzzle was first released in 1984 by Nikoli, the company who popularized the game in Japan. Later on, they felt that the name was too long and settled for the abbreviated version which we now use today.A first time Sudoku solver will have to first understand the basics of the puzzle before attempting to solve one. Technically speaking, a Sudoku puzzle contains a number of grids. To make it easier to understand though, let’s simply put that a Sudoku puzzle is a 9 x 9 board.The spaces that form a vertical series are the columns while the ones that form a horizontal series are the rows. There are a total of 9 columns and 9 rows that the Sudoku solver needs to fill with the numbers 1 to 9. You’ll also notice that a Sudoku board has bolder black lines and these delineate 3 x 3 boxes which have 9 spaces and there are 9 of those boxes.How to Play Sudoku?The Sudoku puzzle is derived from the Latin Squares invented by the Swiss Mathematician, Leonard Euler. It has been used for statistical treatment and other mathematical operations. However, Sudoku does not require the use of any mathematical operations, not even any of the four basic mathematical equations which include addition, subtraction, multiplication and division.One should note that numbers are only being used for the solver’s convenience not because they are necessary. Numbers are easier to track since they already come in a series. Any 9 different symbols or characters can actually be used for the puzzles, e. g. the letters of the alphabet from A to I or 9 different shapes, etc.
The only thing that a Sudoku solver should focus on when learning how to do Sudoku is the use of Logic. Each of the numbers 1 to 9 can only appear once in each row, column and smaller 3 x 3 box. The puzzle will have some of its spaces supplied with numbers already and you just have to complete the rest. Some may think that the more numbers you are given, the easier it is to solve the puzzle. However, the locations of the pre-filled spaces on the board has as much to do with the difficulty as the number of pre-filled cells

You don’t have to worry about figuring the difficulty level yourself because normally, you will see the puzzle’s difficulty level or rating printed next to the puzzle in the book or newspaper. However, make sure that you buy puzzle books from reputable puzzle makers or publishers in order to get accurate difficulty ratings.Furthermore, an indicator that you are solving a properly constructed puzzle is its restriction for having only a single solution. If you find that there are 2 or more solutions to the puzzle, then you got a poorly constructed one, and it’s best to look for other, more credible puzzle sources.

Introduction to Sudoku

Have you ever played with a Rubik’s Cube? You may have mastered the Rubik’s cube and are looking for a greater challenge. Try the puzzle game called Sudoku. Sudoku is a number placement puzzle that requires logic skills and patience. It is a fantastic puzzle game that can be found in newspapers, books and on puzzles and games websites.How do you play Sudoku?The Sudoku puzzle consists of a series of grids. The grids include one large 9 x 9 grid that houses, nine 3 x 3 smaller grids. The purpose of the game is to place a number from 1-9 in each of the grid cells. You don’t have to worry about finding the sum of the numbers of the rows, columns, like in Magic Squares.No addition is involved; however there are three conditions that rely on each other and must be followed. Each number 1-9 can appear only once in each column, once in each row, and once in each small 3 x 3 grid. Mathematically, Sudoku puzzles are a derivation of Latin Squares.The famous mathematician Leonard Euler created Latin Squares. They are a prevalent part of discrete math. Basically, a Latin Square consists of an n x n table filled with numbers, letters, or symbols. Each symbol can only appear exactly once in each row and exactly once in each column. Sudoku puzzles take the Latin Square one step further with the 3 x 3 smaller grid constraints. The fact that you have to make sure that each small 3 x 3 grid contains each number 1-9 only once significantly increases the complexity of the puzzle.Sudoku puzzles come in varying levels of difficulty. The amount of numbers given initially in the 9 x 9 matrix varies. One would think that the more numbers you are given initially, the easier the puzzle would be to solve. This is not always the case because the “placement” of the numbers has a profound effect on the complexity of the puzzle.

Where did Sudoku puzzles originate?Sudoku is the Japanese word for “placement puzzle”. Sudoku swept Japan in the mid-1980′s. Before that, however, a puzzle constructor in the United States named Howard Garnes created the first puzzle of this type in 1979. It was called “Number Place” instead of Sudoku. It was published in the Dell Magazine Math Puzzles and Logic Problems.How do you solve a Sudoku puzzle?Good question! The key is to have patience and use your logic skills. Don’t just use a trial and error method. Many players construct their own puzzle solving techniques and methods, which they share in Sudoku player online forums.You can start anywhere in the puzzle, but as a beginner start by focusing on the top three smaller 3 x 3 grids. Look at the initial numbers and start with the number “1″. Check to see if a “1″ appears in the other two smaller 3 x 3 grids. Then find cells in these smaller grids where you can possibly place a “1″ while still adhering to the rules. You will also need to take into consideration 3 x 3 grids that are attached to the given grid. It is like dancing on eggshells, but the key is to look for patterns. Logically, you need to prove why a number should go in a certain cell.Sudoku is a clever puzzle game that will sometimes make you feel like you are going around in circles. However, practicing on different puzzles will help you to understand certain techniques that work and those that lead you to a dead end. The beauty of the game is that there are a great number of Sudoku puzzles to solve. Time yourself. Many puzzle solvers can finish a puzzle in 10 to 30 minutes. Get out your stopwatch and see how fast you can solve a Sudoku puzzle.

Creative and Impressive Lego Mindstorms NXT 2.0 Builds As Seen on YouTube!

With Lego Mindstorms NXT 2.0, there are many people that have created some amazing project over the past few years. Lego has released the Mindstorms NXT product since 2006, and the technology has only improved along with the possibilities when the second version was released three years later. Aside from the regular mechanical builds and construction style assembly toys children had been making for the past decade, many eager students and robotics fans have been showing off their projects to the world. There are many videos available online that show what is possible with the Lego Robotics, but there are a few that really stick out and have drawn tremendous hits. In other words, they have gone viral.The Sudoku Solving robot built using Lego Mindstorms NXT 2.0 is one amazing example that illustrates the limitless potential of this pragmatic education tool and entertaining hobby kit. This particular bot does exactly what the name implies; it can actually solve a Sudoku puzzle. Sudoku is a number puzzle where a person is to fill in numbers in squares to finish the nine by nine square that has some of the little squares already filled out to begin with. The nine by nine squares are sectioned off in three by three squares. The puzzle is printed on regular paper and placed on the ground, and the autonomous vehicle built using Lego Robotics NXT 2.0 utilized its sensors and motors to drive a pencil. It uses a pencil to fill in the squares with the appropriate numbers where only digits one through nine can be used, and each digit can only be used once in three by three squares.Another one of the Lego Mindstorms NXT 2.0 examples is the Rubik’s cube solver that also does exactly what it says. This Lego Mindstorms robot uses an optical sensor to detect the different colored squares in its field of vision, and it then flips the cube to take an initial record of each face of the cube. After it has indexed the original, random configuration of each side of the cube, it then begins to use its actuators to manipulate the cube to begin solving it. Its optical sensors tell the NXT Intelligent Brick what colors are where and keeps track of them as the motors or actuators turn the sides of the cube. It takes nearly ten minutes for this robot to solve the cube which is shorter than some human beings.

There is also a way for a person to use Lego Mindstorms to interact with an iPhone. It is possible to use a Safari Web App on the iPhone to control a robot built using the Lego Mindstorms NXT. Everything works wirelessly, and the phone and robot are synced together by placing the phone right next to the optical sensor of the robot. This type of application is not as impressive as other Lego Mindstorms creations, but it does demonstrate one of the many powerful features of the NXT development platform. When something is controlled remotely like in this instance, it is not truly considered a robot, because in the other applications the robots are fully autonomous. This means a computer controls everything, and there is no human control.Because Lego robots can be programmed with a huge diversity of programming languages, there are literally unlimited possibilities of what can be built. Some fanatics have even forgone using the NXT Intelligent Brick and opted to use more powerful microntrollers. The versatility of Lego Robotics is what drives many people from around the world to implement this platform in their robotic building hobbies, and Lego Mindstorms NXT 2.0 will definitely be followed by a third version scheduled to be released by Lego very soon.