KenKen and Number Sense

KenKen is a self-motivating puzzle that builds number sense. As an added bonus, using this teaching and learning tool builds creative logical thinking and patterns of self-reliance. It also develops strong focus for an extended period of time, a necessary skill in mathematical problem solving. This article spotlights some of the prime factorization, number trees, and number combinations found in KenKen.

KenKen and Sudoku share two of the same rules, which makes an easy transition for teachers and students: numbers in each row and column must not repeat. The third rule sets KenKen apart as being more mathematical than Sudoku. In KenKen there are Cages, which are heavily outlined areas with specific numerical properties.

The most commonly used puzzles for classroom use are 4×4, 5×5, and 6×6. As with Sudoku, KenKen comes in several levels of difficulty. This allows the instructor to introduce the puzzle at the elementary level, and then gradually ramp up the challenge level as students are ready.

Here is a 6×6 KenKen from the 3-7-12 issue of the NY Times at the Medium difficulty level:

What I suggest solvers do is write the possible numbers at the top or bottom as on a number line. This gives a sense of number magnitude and provides a great help when solving.

A. Look at the 9+ cage: How many different sets of three numbers add up to nine? Hint: there is more than one way.

B. Check out the 4+ cage: How many different sets of three numbers multiply to 4? Again, there is more than one way.

C. Now let your eyes rest on a similar region, the 24+ cage, with even more possibilities. Hint: what is the prime factorization of 24, and how many ways can you make a factor tree for 24?

By looking at numerical possibilities, along with other clues from rows and columns, it’s possible to solve this KenKen by logic and reasoning alone, with no guesswork. This is the hallmark of great mathematical thinking!

Every teacher that has talked/emailed me after using KenKen with students is enthusiastic in support of this methodology. Students always look forward to doing KenKens, and it’s always a great addition to a Friday workday, or useful as extra credit. Give it a try, and you will be a hero with your students!

KenKen puzzles can be found for free on several websites. Here are my two favorites, which publish six new puzzles daily: www.nytimes.com/ref/crosswords/kenken  and  www.kenken.com

The second site also has allows participants to receive regularly via email a nine page PDF file with KenKen puzzles in sizes from 3×3 through 6×6, including answers – something for everybody!