KenKen is a puzzle game that trains memory and logical thinking

Where KenKen Came From

These puzzles can be called new at a stretch: Yokohama math teacher Tetsuya Miyamoto formulated the principle of playing KenKen back in 2004. Many progressive ideas created in Japan remain there. But KenKen has successfully spread to the West: it is played not only in Korea, Thailand or China, but also in Western Europe and America. New Japanese puzzles were published in the British edition of The Times and the American New York Times.

In more than ten years, the puzzle has evolved from a Japanese teacher's initiative into a large-scale game played by the whole world. Thousands of teachers use KenKen in teaching, international tournaments are held in this discipline.

How to play KenKen

The KenKen puzzle is a square grid with empty blocks. In the upper left corner of each block there is a number and an arithmetic sign. It is necessary to fill the grid so that the numbers in rows and columns do not repeat themselves, while the numbers inside the block as a result of the specified arithmetic operation should give the answer to the left of the sign. The number of different numbers is equal to the number of rows or columns. This means that numbers from 1 to 4 will be located in a 4 × 4 square.

Even the simplest rules become very complex when explained without examples. Therefore, we will try to tell you step by step how to solve KenKen. Let's consider a simple 4x4 square.

First, fill in a block with a single digit without an arithmetic sign by writing one in it.

Consider the block below this unit. The mark "2 ÷" means that the numbers in this block, when dividing, will give the number 2. There can be two such combinations in the range from 1 to 4: 4 ÷ 2 = 2 and 2 ÷ 1 = 2. The second option does not suit us, because we have already used the unit in this column. We do not yet know the location of the numbers in this block, but remember that there must be 2 and 4. By the elimination method, we get 3 in the first line (1, 2 and 4 in this column are already taken).

Consider the "16 ×" block. What are the three numbers when multiplied by 16? Option one: 4 × 4 × 1 = 16. Remember that the numbers in the rows and columns are not repeated, so we enter fours on the sides of the block and one in the middle. The four that appears in the third line excludes the appearance of such in the block "2 ÷", which we considered earlier. We fill it with numbers as well.

Let's consider two blocks "1 -". In the one below, we put a three - the only number not used in the third line. Based on the condition of the block "1 -", a two or a four can be adjacent to a three (3 - 2 = 1 or 4 - 3 = 1). There is already a four in the second row, so we put 2. In the block on the first row, we stand in front of the same choice, but since we have already entered a two in this column, we put 4.

We look at the block "6 ×". In the second line, write 3, since the rest of the numbers have already been used in it. When filling out the block, only one combination of numbers is suitable for us: 1 × 2 × 3 = 6. There is already a unit in the first column, the variant of the arrangement of the numbers is one.

Fill in the last block "6 +" with numbers. This can be done without resorting to calculations, but simply by entering the missing numbers in the columns. The puzzle has been solved.

Will Shorts, columnist and crossword editor for the New York Times, has a particular love for Japanese puzzles. He is not only an avid and gambler at KenKen, but also an active promoter of this game. For those who are only confused by our explanations, we offer his video explaining the solution to the simplest KenKen 3 × 3.

KenKen examples

Here are some examples of KenKen of varying complexity for an independent solution.

KenKen 4 × 4. Below average difficulty

KenKen 5 × 5. Medium difficulty

KenKen 5 × 5. High difficulty

Why you should pay attention to KenKen

The main advantage of this puzzle is that it is interesting to solve. If you are into crossword puzzles and you like to challenge yourself intellectually, you will definitely like KenKen.

The principle of filling the grid with numbers is used in the much more popular Sudoku. But KenKen bypasses the famous fellow in a number of characteristics. First, the brain works more actively when solving KenKen. The fact is that the player here must not only exclude inappropriate options, but also make calculations, and also keep many alternative solutions in his head. If Sudoku of average difficulty level is easy to solve using a template, then KenKen leaves no choice but to think and guess.

Puzzles That Make You Smarter - such an inscription flaunts on the covers of books with KenKen-puzzles for a reason. Mathematics teachers in many countries have noted the positive effects of these logic puzzles. Sometimes such puzzles can not only improve the general level of arithmetic and logic skills in the class, but also reveal hidden potential in individual students. It has also been proven that intellectual activity contributes to the prevention of senile dementia. KenKen is perfect for this too: it captivates both children and adults.

Last but not least, KenKen is great to compete. The simplest puzzles are easy even for children, and adults can break their heads over some. And new tasks motivate both of them, forcing them to break their own and others' records.

If you are interested in these Japanese puzzles, you can find them on the Internet or even download a special application for your smartphone. But if you think that solving them electronically is terribly inconvenient, then pay attention to the book versions of “KenKen. Japanese Brain Training System from Eksmo Publishing House. In four editions, you can find hundreds of puzzles of varying difficulty, and special time-stamping fields will help you fix records.