The numbers you can use in a puzzle depend on the size of the grid. If it’s a 3 x 3 grid, you’ll use the numbers 1–3. In a 4 x 4 grid, use numbers 1–4. In a 5 x 5 grid… well, you can probably figure it out from there.
The heavily-outlined groups of squares in each grid are called “cages.” In the upper-left corner of each cage, there is a “target number” and a math operation (+, –, x, ÷).
Fill in each square of a cage with a number. The numbers in a cage must combine—in any order, using only that cage’s math operation—to form that cage’s target number. Example: Your target number is 5, your operation is addition, you’re using the numbers 1–4, and the cage is made up of two squares. You could fill in 2 and 3 (because 2 + 3 = 5) or 1 and 4 (1 + 4 = 5). But which number goes in which square? Read the next instruction!
Important: You may not repeat a number in any row or column. You can repeat a number within a cage, as long as those repeated numbers are not in the same row or column.
There is only one solution to each KENKEN puzzle. As long as you follow the rules above, you’ll know you got it right!
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TUTORIAL
There are some simple techniques that will help you solve the easier puzzles. Let’s learn them as we walk through solving a 3 x 3 grid, step-by-step.
Every square in this grid will contain one of the numbers 1, 2, or 3. A number cannot be repeated within any row or column.
The heavily-outlined areas are called cages.
The small number in the upper-left corner of each cage is our "target number." The math symbol next to the target number tells us which operation we’ll be using in that cage. This puzzle uses addition and subtraction.
Cages that are around only one square are the easiest to solve. The target number is the number that goes in the square. Enter the number in this cell.
Now look for the cage which has the next greater number of cells. The target number for that cage is 2 and the operator is subtraction. So the possible candidates are 1 and 3 only. But we are not sure about their placement. So let’s start filling in the numbers we are completely sure about. For example, the cell just above the cage we are currently considering can have only one number in it as 1 and 3 are always used in the cells below. So let’s fill that cell up first.
Now let’s consider the first row in which two numbers 3 and 2 are already filled up. There is only one more option that can get filled in. Let’s fill that cell up.
Consider the cage with the target number 6. The operator is addition. And the other two cells in that cage are filled with 1 and 2. So what is the remaining number which would add up to give the target number 6? Let’s fill it up.
Now consider the cage with target number 2 and operator subtraction. Remember we had decided that the only two numbers that can go in that cage. They are 1 and 3. Now since the adjacent cell on the left has 3, it’s very clear where the 1 and 3 will go in the two cells in that cage. Let’s fill them up too.
Now consider the last cage. The target number is 5. And the operator is addition. And there are three cells.
Now let’s consider the second row in which two numbers as 1 and 3 are already filled up. There is only one more option that can get filled in. Let’s fill that cell up.
Repetition of any number in the row or column is not allowed. Now it is very clear what the remaining cell value will be. Let’s fill these up.