# KenKen is FunFun

Following my surgery a few weeks ago, my friends Gerarda and Alan dropped by with a most excellent ‘get well soon’ gift. The gift included a hilarious card, a trashy tabloid, and the book that I’m holding in the picture to the left. That book is a book of KenKen puzzles.

What the hell is KenKen?

Think Sudoku, but better.

Like Sudoku, KenKen starts with a grid of numbers. Within this book, there are grids that are 4×4, 5×5, and 6×6, but other sizes exist.

The rules are simple; fill in the digits 1 through $n$ where $n$ is the length of one dimension of the grid (i.e., the grid is $n\times n$) in each row AND each column. The catch, you must do so while satisfying the hints that are provided in the squares, and each row and column can contain each digit only once. As you can see below, the grid is divided into several sections. One of the squares within each region will have a clue. The clue will give you the result of a mathematical formula, and the operation that is to be used ($+, -, \times, \div$)

For example, in the 6×6 grid to the right, we have 3 squares in the upper left corner that must multiply to 80 (80x). Since this is a 6×6 grid, we can only use the digits 1 through 6. I begin by trying to figure out what can’t work. Since 80 is not divided evenly by 3 or 6, I can ignore these numbers. That means I could use 1, 2, 4, and 5. If I opt to use 1, that means the other 2 digits must multiply to 80. But, we don’t have digits large enough to get to 80 with only 2 of them. Note that the largest digit available (that being a 5) when multiplied by itself, only brings us to 25. So 1 can’t be used here either. We are left with 2, 4, and 5. Clearly, I can’t use 2 either or the remaining two digits would have to multiply to 40, and as we just determined, we can’t get to that value with the digits we have available. Hence, we need to double up one of the numbers. In this case, we can use 4, 4, and 5.

Since we have the rule that each row and column must contain the digits 1 through 6 only once, we would necessarily have to separate the 4s, as illustrated in the picture. And from this, we continue to fill in each of the rows and columns using the information provided.

Cool stuff!

Anyway, these are very addictive and I’ve been playing them almost daily since Gerarda and Alan dropped off the book. So, a huge thank you to Gerarda and Alan for this. It has made the recovery process so much more tolerable.

For those that want to give it a try, check out the KenKen website. It goes up to the challenging 9×9 grid.