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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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 Solutions – Some Helpful Tips For Beginners

Learn some of the basic rules of solving Sudoku puzzles and what makes this Japanese game so popular in different parts of the world – in our special interest article on the scope of Sudoku, its solutions and how to reach faster at them.

Primarily a logic-determined number placement puzzle, the game of Sudoku involves placing numerals 1-9 in every given cell of a 9×9 grid, which is further divided into a 3×3 region and to begin the game, the player has to focus on a set of pre-entered numbers, screen these to decide how to fit others in empty cells.

While Sudoku is not a very difficult game to play, it does have its moments of flummoxing even the most intelligent player or mathematical genius simply because sometimes their approach to the game is more academic than based on logic and reasoning, which is what is required in this clever game of abstract thinking.

Players who have moved from the light and easy stage through the moderately hard to the difficult will find that using existing techniques, revisiting some of the old solutions and challenging their brain cells about strategic number placement of the Sudoku range (1-9, appearing only once in each cell in a given timeline) works for them more than trying to figure out a formula. This is why Sudoku’s main methods – Scanning, Marking Up and Analysis are never in doubt by the more experienced players and we outline these here for your perusal.

Among the most popular and accepted techniques that simplify the game, Sudoku’s 3 methods of Scanning, Marking Up and Analysis are ideal for the beginner level player to get a basic understanding of the game.

At every level of the Sudoku game, these techniques come into use: scanning is started at the beginning of the puzzle and may be done many times when a person studies various possibilities of the number placement, including the pre-entered numbers on the 9×9 grid. It consists of cross-hatching (scanning rows and columns with an imaginary line connecting possibilities next to the ‘givens’ and eliminating frequently occurring numbers to arrive at an accurate result) and counting (where missing numbers are determined, till the last numeral is ascertained).

In the marking up stage, numbers are entered after determining there are no numerals left to be detected; it consists of 2 notations – subscript (writing possibilities in a box) and dots (to denote intended numbers and to avoid confusion – suitable for more experienced players).

Analyzing is the last stage in the Sudoku solution and has 2 techniques namely, elimination and what-if used to remove possible numbers from one cell till only one choice is remaining or using clever guess-work; it involves a fair degree of trial and error and thus is not favored by perfectionists whereas What-if leaves one with 2 options to work out the complete set of Sudoku grid numbers.

Try your hand today at this fun and fast puzzle game that stimulates your brain cells and also gives you superior logical thinking skills – the more you practice it!

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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 – Tips For Easy Play

Here we learn the best ways to play easy Sudoku, so if you are enamored by what makes every Sunday paper such a treat for the game’s enthusiasts, stick around and learn the simple strategies – you just may surprise yourself with emerging as a Sudoku champion at the end of it!

Essentially involving numbers, the game of Sudoku has left very few untouched with the excitement or pairing the grids right in the fastest time possible and Americans are all for the addiction that is easy Sudoku.

This famous puzzle involves the use of a 9 x 9 grid divided into 9 equal squares with the objective of placing numbers 1 to 9 in these squares; but, the player has to remember that each number can only be used one in every row or column and only in formation of 3×3 squares.

The easy Sudoku puzzle typically has a given set of numbers that the player needs to deduce regarding placement, which is what decides the level of complexity of the puzzle game. The various ranges of game range from easy to moderately hard to very difficult, which a player can choose based on the strength of his skills of logic.

Begin with the easy Sudoku if you are just starting to develop an interest in the game and work your way up to the next level once you’ve mastered the first; you can also purchase a Sudoku puzzle book that falls in this range if you don’t fancy the one in the daily rag.

Usually, the puzzle appearing on Monday has the easy game and once you’ve learned the strategies and techniques for playing this one right, you will find it a breeze to get to the next level. Thinking in a logical manner and clearly is very important to ensure you don’t get the same numbers in each row or column. Each 3×3 box in the game should hold a new number that should act as a clue to your getting to use the next number in the same series.

Easy Sudoku puzzles afford a better chance to start the game series easily, so are recommended for beginners.

Look around for the various possibilities for numbers when you begin at 1; you can make an imaginary line on the boxes in the rows and columns of 1’s. Once you’ve done this and see only a single box is in the 9-square block, know your possibility is strong, so stick with it.

Next, to solve the easy Sudoku, you can work on the other numbers till you reach the possibility for 9; this is more do-able after you’ve successfully fitted in a few numbers at least.

If you feel the number is not fitting in and you are trapped, you may need to go back a few steps and try other numbers. This step involves the location of the ‘missing number,’ which can be reached at by labeling each block with everything which has a chance to be on the box.

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