How KenKen Puzzles can Help You Learn Math

 

KenKen is the hottest puzzle craze since Sudoku. It combines the logic of a Sudoku puzzle with arithmetic. You have to add, subtract, multiply and divide to arrive at the numbers given in KenKen puzzle. 

In KenKen, like Sudoku, there is a grid of 4×4, 6×6, 8×8, or 9×9 cells. That means the grid has 16, 36, 64 or 81 cells. The puzzle can actually be even larger, but those are for really advanced solvers. In both kinds of puzzles, you must have all the digits in one row. In other words, if a row has 4 cells, like in a 16-grid puzzle, you must use the numbers 1-4 in each row, and in each column. No digit may be left out of row or column, nor may there be duplicates in a row or a column. 

So far, that’s totally easy to understand. If you look at a puzzle, you can see what I mean in a second. 

The diabolical cleverness of KenKen, which sets it apart from Sudoku, is that:

• some adjacent groups of cells have a thick border around them. Those groups are called “cages.” Each cage has a number printed in it, along with an operation sign. 

• The cells within that cage must be filled with the digits that will amount to the number given. Let’s say the cage has two cells surrounded by a thick border, the number in it is 6, and the operation sign is multiplication (x). That tells you that you must find two numbers that multiply to 6.

 You may be tempted to say, “That’s easy. The answer is 2 x 3!” But don’t jump to conclusions! The answer could just as well be 6 x 1. Furthermore, you don’t immediately know which of the two cells the 2, 3, 6 or 1 belong in. You have to find that out from looking at the other cages and narrowing down your possibilities. 

It takes about two minutes to learn how to do KenKen, but it can take years to master. There’s something for all levels of solvers. 

Good math teachers will look into this puzzle and learn some strategy, then introduce the puzzles to their students. There are very inexpensive books of KenKen, as well as online sites where you can download free puzzles. One of them is http://kenken.com

Once you understand how KenKen really works, you will start learning all about factoring, exponents, and mathematical logic. You won’t need a workbook, and there are no grades (if the teacher is smart). The only stress is the gentle strain on your brain, and you’ll be developing that brain with every KenKen puzzle you solve. 

It’s easy to get good at KenKen with some practice. The nice thing about the practice is that you won’t be able to stop. KenKen is the most addictive puzzle around!

Imagine a student being able to hone his or her basic math skills without worksheets, flash cards, charts, rote-memorization, or quizzes. Imagine that student loving math like never before!

KenKen was invented by Tetsuya Miyamoto, a Japanese math teacher who says, “I believe that if you give children good learning materials, they will think and learn and grow on their own.” If you teach yourself, your child or your students basic math with KenKen, they will develop a lifelong love of mathematics, and you will have done them a wonderful favor. 

For free KenKen video lessons, all the way to the very advanced level, check out http://mathmojo.com/kenken

 

 

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The Rules of Sudoku

If you’re fond of playing puzzles, solving math problems, and think logic reasoning you can actually combine them all in playing the Sudoku puzzle.

For you to know, sudoku was first seen in a magazine published in New York in the late 70’s by specialist puzzle publisher Dell Magazines under the name of Number Place. “Su” means number in Japanese, and “doku” means the single place on the puzzle board so that each numeral can be fitted into. Although its name sounds like Japanese, its origins came from Europe and America in which the game shows the very best in thinking and reasoning. Sudoku initially caught Japan in 1986 and gained international prominence in 2005. Unlike many other games that were known within the span of time, nothing can beat Sudoku’s challenge.

Sudoku, commonly known as the Number Place, is a logic type placement puzzle. The aim of the puzzle is to place numerical digits from 1 to 9 in each cell of a 9×9 grids that is made up of 3×3 subgrids or regions. To start playing the game, you are given in some empty cells numerals which are called “givens”. The goal of the puzzle is to put the numbers 1-9 to which it must contain only once in each subgrids, rows, and columns.

Basic rules

Rules in playing the game are very simple:

•  Sudoku is played over a 9×9 grid, divided in 3×3 subgrid.

•  Begins the play with some given numerals from 1-9 that are placed in grid cells.

•  A number can only appear once on each row.

•  A numeral can only appear once on each column.

•  Digit can only appear once on each region.

Now you finally know the basic rules in playing the game, but you’re really just starting the process of making solutions to how finish the game. There are some solutions methods that can help you and these are:

•  Scanning- it can be performed from the very beginning and throughout the solution process. Scanning basically has two techniques, first the cross-hatching. Cross-hatching technique can identify which line in a particular region may contain a digit that can be eliminated. The second is counting the region, columns and rows in identifying missing numbers. Counting based upon the last digit discovered may actually speed up the corresponding search.

•  Marking Up- the candidate numbers are simply written in subscript in the cell. The disadvantage of this is that some first puzzles are printed in magazines and newspapers which are usually small to accommodate many preferred numbers. Unlike to some newly designed Sudoku game board, all inputs are done electronically. You can also use a pattern of dots within the cell, wherein the position of the dot corresponds a number from 1-9. Dot notation can be an advantage to a sudoku that is printed in paper. In playing sudoku in print, using a sharp pencil with an eraser is highly recommended.

•  By Analysis- you can approach the game by either “candidate elimination or “what if”. In candidate elimination, numerals from one or more cells are eliminated and leaving just one choice. After each answer is placed, another scan can be done. You can check to see the effect of the contingencies. In “what if” approach, a cell can be placed with two candidate numbers then a guess should be made.

Difficulty ratings

Published Sudoku puzzles are ranked depending of rate of difficulty. For you to understand, the numbers that are given has nothing to do on a puzzle’s difficulty. A sudoku puzzle with less number of givens may be very easy for you to solve. A sudoku puzzle with more number of givens can still be very difficult for you to solve as the difficulty rate of the puzzle depends on the relevance and positioning of the given numerals rather than the number of given placed in the grids.

Computer solvers find the range of difficulties for a human to find a certain solution, based on the complexity of the techniques needed. For in this kind of estimation allows publishers to take Sudoku puzzles to be very demanding. Some sort of publications rate their Sudoku puzzles into four levels are “easy”, “intermediate”, “hard”, and “challenging” are set.

So, by playing the “fastest growing puzzle in the world”, you can be sure to challenge your way of thinking and have fun in the process.

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The Interactive Postcard: How to Make People Respond to Postcards

The digital age has spread around the world. More and more people are turning away from printed media like marketing print postcards and going digital with online advertising. With its cheaper costs, and interactive content, this kind of advertising has probably a long life ahead of it. But this does not mean postcard printing is dead. In fact this is an opportunity to innovate your view on postcard printing.

Since interactivity is the buzz nowadays, you can apply it to a lot of marketing strategies. So why not try it on print postcards? Discover the concept of the interactive postcard. They are basically postcards that require people to respond to them in some way. This makes postcard printing interesting; making people pay more attention on the design. Also, since it encourages people to “participate” in the design or customize it in some way people will not find it boring. They may even want to send more of these kinds of postcards.

So as you can see, this new kind of postcard printing strategy is a good way to change your direction in terms of postcard making or marketing. If you are interested in this promising idea then read on. We have a few examples of typical interactive postcards below, that you may find inspiration from.

The puzzle postcard One of the first interactive postcards that appeared on the market was the puzzle postcards. These were print postcards that have some kind of puzzle or problem that you needed to solve. In most cases, it was just a neat and trivial puzzle or problem like a crossword, or those “find the object or person” games. Others had mental problems and puzzles like “Sudoku”, the Japanese number puzzle. It did not take long for people to innovate and try out a few special puzzles. One of the best examples was a simple crossword that when completed, spelled out the postcard’s special greeting in one line. This gave the receiver of the print postcard a special thrill in finally answering the solution.

With that kind of interactivity, the puzzle postcards were far from boring. Added with some creative advertising phrases and images, it became a nice platform for marketing with an interactive touch. It provided more exposure that a normal postcard and it had “replay” value as people showed the postcard to others.

Holographic or 3D postcards Another kind of interactive postcard are the holographic or 3D postcards. These kinds of postcard printing can be a bit more expensive to produce, but they do have a very eye catching property. These cards are printed with holograms that capture a 3D object within the design. A variation of this form is the puzzle 3d postcard. This kind had those “3d” puzzles where you had to look for the object or image in 3D within a seemingly abstract design. These designs of course causes people to look at the postcard design more closely as they move the postcard from left to right, trying to see the object in 3D. Along with some helpful marketing phrases and images, it is again a good platform for marketing using postcards.

So are you inspired to make interactive postcards? They are a promising medium to print for marketing. Explore the limits of your imagination and maybe you can think of another kind of interactive postcard that will promise you exposure in your target market.

For comments and inquiries about the article visit: Print Postcards

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Printable Games an Alternative to Free Offline Games

Free printable games are a revolutionary an innovative way to learn and enjoy at the same time. These Games are easily accessible in a printable form with just a touch of button. One does not need to access online to play games.  The online games are complicated and expensive where as printable games is rational being free.  It is said that games are like enigma. The main targets of these games are to attract children of any age.  Mothers who want to inculcate playing and learning habits in their growing children to enhance their ability for future. Home schooled children can benefit a lot from it because they can learn while playing without anyone’s direction. Teachers who want to teach students innovatively can take a great idea from free printable games. Parents who want to entrench learning practices in their children must opt for printable games.

Free Printable games provide fun language-building skill, reasoning skills and challenge brain of children, teens and adults. Whether you’re a teacher looking for ways to help your students build their vocabulary skills or a grownup who simply loves to play with language, reasoning and puzzle printable games provide entertainment and learning. This helps player develop facility and skill. You can print each day a game and collect a collection. Children, adolescents and adult all can find something interesting for them to play.

 The Internet is full of web sites offering hundreds of free printable games so try the following:-

Crossword puzzle enhances the ability to stimulate the mind by answering clues and vocabulary.

Brain Teasers: it challenges your mind to test your skills and helps to improve it. 

Puzzle:  jigsaw puzzle is the most famous puzzles of all.

Word Search: it helps to construct words which especially help children above the age 5 to learn new word building.

Maze: a game which is constructed like a muddle where a player sits on his seat travels from start to end with its own imagination.

Sudoku: this game is all about calculating and filling the grids in such manner that in each row, column and block the digits enter one time each.

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Improve Your Memory With These Simple Tips

Tip No1. Start playing memory games and games that involve lots of thinking.

Such games would be chess, checkers, sudoku or logic games that are to be found online. This way you will both have fun and sharpen your brain. If you like computer games, I advice you trying Myst. It is a beautiful game with very hard puzzles.

Tip No2. Use associations.

When you have to remember something specific, be sure to associate it with some funny or bizarre image or event. You can think of whatever you want as long as it stays in your mind. You should remember a funny and unique image because that way it will stay in your brain better than a common image you can see everyday.

Tip No3. Use less technology and more your brain

Try to use less calculators and mobile phone contacts. Try to do the equations in head and remember phone numbers and names using associations. The more you will use these techniques, the better your memory will become, and a good memory will always be a huge benefit.

Tip No4. Notice small details.

Pay attention to details and minor things. When you meet a friend, notice what clothing or jewelry she/he is wearing. When you enter some area, notice how many objects are there and where they are. Then close your eyes and try to recall what you saw. You can do this anywhere. For example, when you enter a parking lot, try to look at it for a few seconds, then close your eyes and recall how many cars where their, what brands where they and color of the cars.

Tip No5. Be fit and exercise.

By doing cardio exercises your body will be in good shape and more oxygen will be delivered to your brain such way improving your memory. You can choose from tons of exercises: running, climbing, playing ball, rope jumping, athletics. Choose one which you enjoy. I for example absolutely **** running, I rather swim.

 

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Solving A Sudoku – The Various Levels Involved

Sudoku is a very interesting and addicting number puzzle played in almost all parts and sections of the globe. It is an exciting and very thrilling game. But at times, Sudoku can be tricky and very difficult.

The objective of the game is to fill in all numbers from one to nine in each and every cell in the given grid. Numbers should not repeat in any column, row or three x three block.

How to start solving a Sudoku puzzle? The following steps will help a player to solve any sudoku easy or difficult.

Easy Sudoku

1. be careful while solving the puzzle. Now that you already know duplication of numbers isn’t allowed, you can use it as a hint for considering other numbers. Always remember, more difficult the given Sudoku, harder it will be to start.

2. While solving any easy Sudoku, you should first prioritize your search for possibilities. They are the numbers which are possible in the column, row or block. So if you know the possible numbers, it will be easier to choose whichever number is suitable for a particular cell.

3. Start your work from number one till you are on your way towards number nine. Since you already filled in some numbers, this will be your clue to search for other numbers to be filled.

4. If you become confused, you can go back and make sure to have a look at every number you have filled in already. This will surely help you to know if there is any number you have missed. Once everything gets settled, you can go on with the puzzle and try to complete it. If you still can’t find the problem, label each three x three box with numbers which can possibly go into the box. Example, if an empty box is left. Fill it with possible numbers to see the result of your action.

5. It is advisable to begin your play in a magazine or newspaper. There are magazines or newspapers, which have sudoku. Easy puzzles usually come out during either Monday or Tuesday. The difficult ones come out the days that follow.

Hard Sudoku

1. Start with number 1. Use the same logic used by you in the easy version to complete every empty block, column and row with all possible numbers. Put possibilities if necessary. They’ll help you at a later stage if you have 2 or 3 choices for each cell but can’t remember them all.

2. If two cells in any row, column or block is one of the two numbers, remove the other possibilities using it. Example, if in a three x three block, four empty cells are there, you have established: cell A and cell B can be one, two, three, four; cell C and cell D can be three or four, you’ll know cell A and cell B can never have three or four as they already have one or two. Cell C and cell D should be three or four. This information can be quite helpful to complete other boxes given.

3. A hard Sudoku will consume more time. It can even take few days to complete, but they can provide players more fun, contentment and enjoyment after they have solved the puzzle. It is just the same as an easy Sudoku – both of them will give you very less clues to start with. The best technique of solving the hard version is to know the possible digits which can go into each box. In case you have two numbers for a single 3 x 3 box, column or row, decide which number should fill each of the locations. Though this may be confusing, when you apply it, you’ll realize that it is simple and quite useful.

4. Visit the net. There are lots of sites that provide puzzles – easy to hard. Practice some of the sample puzzles and prepare for a more complicated puzzle.

Follow these steps to solve the Sudoku and find out that however difficult it may seem, in the end, you will feel incomparably excited and have fun.

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Sudoku Answers – The Perfect Guide To A Number Game

Do you feel bored?

Want to be entertained?

A hobby will act as a good diversion. Try answering puzzles. It keeps you from becoming word-weary and also sharpens the mind.

A puzzle is defined as a game where problems are solved which challenges different mind strategies you have. There are lots of puzzles – some are easy, others are very crucial when you are solving logic or Math based problems.

A puzzle which is more likely towards logic is called the Number Place or Sudoku.

The aim of the puzzle is to fill a nine x nine grid from three x three regions by placing numbers one to nine in each cell in the grid given. Not even a single number should repeat itself in the grid and that is the trickiest part.

At first glance, it seems to be an easy and fun game. But during the long run the player needs to have a deep thought of the strategies needed to solve it.

Sudoku can be solved in three different ways. You can use scanning to solve a puzzle or prefer marking up and come up with a puzzle that is solved or use the analysis method to solve a puzzle

In scanning, you elimination reigns above the others. Under it, you can either choose counting or cross-hatching. Cross-hatching needs a systematic action course where to scan columns or rows in any particular region may give you hints about the possibility of placing a number. Counting though, requires basic counting where you should count numbers one to nine in regions, columns and rows to find a missing number.

In your next game, try marking up. It is usually used when all possibility to solve a puzzle by scanning has been exhausted. Here, you should use notations. Commonly, notations are in the form of dots or subscript. It is best though, to use notation where you will feel comfortable using them such as codes, shapes or lines. It is good to assign a notation that would be used instead of numerals which are most likely repeated and notation which is most likely to be present in the grid said. One drawback is that when the grid is small as in magazines and newspapers, it becomes difficult to use..

Analysis is the third way. It involves two main tactics, the what-if method and candidate elimination. Candidate elimination does away with numerals from grids to come down to one option only. You can do this in tandem with scanning. The what-if method involves guessing which number will go into a cell from two numbers.

If for example, you seek answers of Sudoku from a computer program or software, there are other ways to finish it.

Firstly, try and act like a human being when solving. Use the suggested procedures given above. Also, using a computer program or software, you’ll devise the difficulty level for each game.

Secondly, you have to plan or search a good computation which will help you to solve a puzzle faster.

As a player, you can use many combinations of the methods and can even formulate various solutions which will work the best for others and you. Take the entire thing one step at a time. Learn the game’s basics. Shed the line of attacks which are boggling you. Pick pieces of information from wherever you think you can succeed; learn from wherever you fall apart. Sudoku is a game and you should learn how to take risks.

Boredom fades away if you keep thinking how sudoku works.

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Get Your Children Hooked On Sudoku Jigsaw Puzzle Books

Parents are getting very concerned with their children’s growing obsessions. Children are now spending endless hours watching television and then to sitting on the computer chatting away on emails, webcams and social network sites. So what can a parent do to distract their children?

Get Them Hooked On Sudoku

There are some addictions that are actually very helpful and educational. Take for example the present day addiction to Sudoku jigsaw puzzle books which are sweeping the globe. This is one addiction that can take your child away from the television and computer and can actually be of great help to your child’s development of problem solving and logic.

Sudoku jigsaw puzzle books offer children of all ages and even adults many advantages. Those who play Sudoku regularly find that their mind is sharper; they can solve problems easier than before and are more patient when the solution is not exactly in sight.

Puzzles are games that have always fascinated children and so for a parent it is easy to introduce the Sudoku jigsaw puzzle books to them. It is hard for a child to resist the challenge and in no time they will be addicted to these incredible puzzles. Children who play Sudoku have a greater logic and deduction skills because of the need to use logic to solve the puzzles, this opens ups other spheres of their lives.

Where Do You Find Sudoku Jigsaw Puzzle Books For Children?

Most bookstores have a good collection of Sudoku jigsaw puzzle books but when you want a wide variety to choose from you could always go on the Internet. You could choose one set or a series of Sudoku books that increase in complexity over time prompting the children to develop their skills gradually.

If you like to create your own you can find tutorials on the internet that will help you make your own puzzles. There are also software packages that can help you create the puzzles with a click of the mouse from scratch if you do not have the time to create your own.

Lastly, your local library generally have a good selection of Sudoku jigsaw puzzle books where you can borrowed and return the books once you have completed them. It is wise though to photo copy the Sudoku games before giving them to your child as you do not want them to write in the books and spoil the fun for other players.

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Solving A Sudoku – The Various Levels Involved

Sudoku is a very interesting and addicting number puzzle played in almost all parts and sections of the globe. It is an exciting and very thrilling game. But at times, Sudoku can be tricky and very difficult.

The objective of the game is to fill in all numbers from one to nine in each and every cell in the given grid. Numbers should not repeat in any column, row or three x three block.

How to start solving a Sudoku puzzle? The following steps will help a player to solve any sudoku easy or difficult.

Easy Sudoku

1. be careful while solving the puzzle. Now that you already know duplication of numbers isn’t allowed, you can use it as a hint for considering other numbers. Always remember, more difficult the given Sudoku, harder it will be to start.

2. While solving any easy Sudoku, you should first prioritize your search for possibilities. They are the numbers which are possible in the column, row or block. So if you know the possible numbers, it will be easier to choose whichever number is suitable for a particular cell.

3. Start your work from number one till you are on your way towards number nine. Since you already filled in some numbers, this will be your clue to search for other numbers to be filled.

4. If you become confused, you can go back and make sure to have a look at every number you have filled in already. This will surely help you to know if there is any number you have missed. Once everything gets settled, you can go on with the puzzle and try to complete it. If you still can’t find the problem, label each three x three box with numbers which can possibly go into the box. Example, if an empty box is left. Fill it with possible numbers to see the result of your action.

5. It is advisable to begin your play in a magazine or newspaper. There are magazines or newspapers, which have sudoku. Easy puzzles usually come out during either Monday or Tuesday. The difficult ones come out the days that follow.

Hard Sudoku

1. Start with number 1. Use the same logic used by you in the easy version to complete every empty block, column and row with all possible numbers. Put possibilities if necessary. They’ll help you at a later stage if you have 2 or 3 choices for each cell but can’t remember them all.

2. If two cells in any row, column or block is one of the two numbers, remove the other possibilities using it. Example, if in a three x three block, four empty cells are there, you have established: cell A and cell B can be one, two, three, four; cell C and cell D can be three or four, you’ll know cell A and cell B can never have three or four as they already have one or two. Cell C and cell D should be three or four. This information can be quite helpful to complete other boxes given.

3. A hard Sudoku will consume more time. It can even take few days to complete, but they can provide players more fun, contentment and enjoyment after they have solved the puzzle. It is just the same as an easy Sudoku – both of them will give you very less clues to start with. The best technique of solving the hard version is to know the possible digits which can go into each box. In case you have two numbers for a single 3 x 3 box, column or row, decide which number should fill each of the locations. Though this may be confusing, when you apply it, you’ll realize that it is simple and quite useful.

4. Visit the net. There are lots of sites that provide puzzles – easy to hard. Practice some of the sample puzzles and prepare for a more complicated puzzle.

Follow these steps to solve the Sudoku and find out that however difficult it may seem, in the end, you will feel incomparably excited and have fun.

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Get Your Children Hooked On Sudoku Jigsaw Puzzle Books

Parents are getting very concerned with their children’s growing obsessions. Children are now spending endless hours watching television and then to sitting on the computer chatting away on emails, webcams and social network sites. So what can a parent do to distract their children?

Get Them Hooked On Sudoku

There are some addictions that are actually very helpful and educational. Take for example the present day addiction to Sudoku jigsaw puzzle books which are sweeping the globe. This is one addiction that can take your child away from the television and computer and can actually be of great help to your child’s development of problem solving and logic.

Sudoku jigsaw puzzle books offer children of all ages and even adults many advantages. Those who play Sudoku regularly find that their mind is sharper; they can solve problems easier than before and are more patient when the solution is not exactly in sight.

Puzzles are games that have always fascinated children and so for a parent it is easy to introduce the Sudoku jigsaw puzzle books to them. It is hard for a child to resist the challenge and in no time they will be addicted to these incredible puzzles. Children who play Sudoku have a greater logic and deduction skills because of the need to use logic to solve the puzzles, this opens ups other spheres of their lives.

Where Do You Find Sudoku Jigsaw Puzzle Books For Children?

Most bookstores have a good collection of Sudoku jigsaw puzzle books but when you want a wide variety to choose from you could always go on the Internet. You could choose one set or a series of Sudoku books that increase in complexity over time prompting the children to develop their skills gradually.

If you like to create your own you can find tutorials on the internet that will help you make your own puzzles. There are also software packages that can help you create the puzzles with a click of the mouse from scratch if you do not have the time to create your own.

Lastly, your local library generally have a good selection of Sudoku jigsaw puzzle books where you can borrowed and return the books once you have completed them. It is wise though to photo copy the Sudoku games before giving them to your child as you do not want them to write in the books and spoil the fun for other players.

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