## KenKen Example Three:

Looks like we have another 3x3 puzzle. So we know we can only use the number 1, 2, and 3 to fill in the boxes. We first see that in the upper left corner the puzzle we are given that the box has to contain the number 3.

We also are given that the center box contains the number 2.

Alright now lets look at the far left column. There is a cage that subtracts to 1. Since the top box of this row contains the number 3, we know that the two boxes in the subtract to 1 cage need to be filled with the numbers 1 and 2. Since there is a 2 in the center box of this puzzle, we know that the 2 and 1 have to be placed in the first column like this.

Now lets look at the middle row. Since it already contains the numbers 1 and 2 we know that the final box in this row has to be the number 3.

Now lets look at the top row. The number in the upper left of the cage says that the two numbers in the boxes of this cage need to subtract to 1. There is already a number 3 in this row, so we know that the two boxes in the subtract to 1 cage need to be filled with the numbers 1 and 2. Since there is already a number 2 in the center box, we know that the numbers 1 and 2 have to be placed in the boxes this way.

Since there are only two boxes left to be filled in the add to 7 cage, we can look at the columns that each of these boxes are in to know what numbers have to fill them. Looking at the middle column, we know it has to be filled with the number 3 since the column already has the numbers 1 and 2. While the last column already has the numbers 2 and 3. Thus, the final box has to be filled with the number 1 like this.

Now we check through to make sure all of the rules of filling in a KenKen puzzle are satisfied. Each row and column contain only the numbers 1, 2, and 3 and each number is used only one time in each row and column. Now we check and see if the numbers all reach the goal number of each cage, and they do. Thus, we have completed this KenKen puzzle.