Fill in the numbers 1 through n in every row and in every column. Next to the puzzle the value of n is given. Numbers indicate the sum, the product, the difference or the result of the division of all the numbers in that region. Often the operator used is given. Subtraction and division can only apply to regions with two numbers. It is possible for numbers to occur more than once within a region as long as this does not violate any of the rules.


The example puzzle requires us to fill in the numbers 1, 2, 3 and 4 in every row and every column. In the rightmost column there is only one place where the 4 can be, because 4 is not an integer divisor of 6 and 2. In the same column the 3 is not an integer divisor of 2, but it is of 6, so we write the 3 above the 4.

Since 2x3=6, the cell the left of this 3 needs to be a 2. Because 3+4=7, the cell to the left of the 4 needs to be a 3.

The first row still needs to have a 1 and a 4. Although we don't know yet in what order they need to be, we do know they add up to 5 and that together with another cell they add up to 6. This means this extra cell on the second row and in the second column must be a 1. Now because there can only be one 1 in the second column, row one becomes 1423. The second row can also be completed, because only the 2 is still missing.

Now the first column can be completed to 1234, and to the right of the 4 we need to write a 3, because 4+3=7. Then the second column can be completed to 4123. The third column still needs a 1 and a 4, but there is already a 4 on the fourth row, so the order becomes 2341. The rightmost column will have to be 3412.


This type of puzzle was invented by Tetsuya Miyamoto, a Japanese math teacher. It is also known under the trademarked names KenKen(R) and KenDoku(R).

Puzzles in this genre.