## KenKen Example Two:

Just like in our last example, this is a 3x3 puzzle. Since you all now understand the rules of how to fill in the puzzle, we will just work through this one together. What should we do first? That's right, fill in the squares that tell us which number has to be in them. Those sqaures are in the bottom right corner of the puzzle, the space with the number one in the upper left corner. The other square is in the top row in the middle, with the number two in the upper left hand corner. So we now know that our puzzle has to look like this to start.

Now lets look at the add to 5 cage. So we now know how to fill in the 2 and 3 of the add to 5 cage.Since we can only use the number 1, 2, and 3 to fill in the squares. We know this cage has to be filled with 2 and 3. We see at the top of the puzzle that we have a number 2 in the same column as the right square of the add to 5 cage, so we know that the 2 and 3 have to be filled in this way.

Since every row and column has to have the digits 1, 2, and 3 so we know that the center square has to be filled with the number 1.

Also the far left column already has the number 2. So we know that the other two boxes in that column need to be the numbers 1 and 3. Since there is now a number 1 in the center box we know that the number 1 in the far left column has to be in the very top box. Which puts the number 3 right below it in the middle box of the far left column.

Now since we know that every row and column must contain the numbers 1, 2, and 3 we can fill in the last two boxes of the add to 5 cage by looking at the numbers we already have in the top two rows.

Now we have our puzzle completely filled in. We think that our answers are right since they all made sense but lets check just to make sure. First look through each of the columns and make sure that they all contain the number 1, 2, and 3 and each of those numbers is used only once. Now lets check the rows and make sure that each contain the numbers 1, 2, and 3 and each of those numbers is used only once. This KenKen rule is satisfied. So now we go through each of the cages and make sure that the numbers equal the number we want them to. For example, the add to 5 cage with three boxes in it contains the numbers 1, 3, and 1. Do these numbers add to 5? Yes they do. Go through the rest of the cages just like this. They all satisfy the goal numbers in the upper left hand corner of the boxes in each cage. So we have correctly filled in this puzzle. Remember that every KenKen puzzle is unique. So this is the one and only way in which the puzzle can be completed correctly.