The popularity of Sudoku puzzles is evident across the US. Also gaining momentum is the logic puzzle, KenKen®, invented in 2004 by Japanese mathematics teacher Tetsuya Miyamoto. Derived from the Japanese word for cleverness, KenKen combines logical, simple arithmetic with combinatorial skills. The puzzle was first published in the London Times in March 2008 and now appears in more than 40 newspapers including the New York Times. In 2016, the National Council of Teachers of Mathematics (NCTM) launched a free App to encourage the use of KenKen in grades 1-12.
Overview & Objective of KenKen:
The objective of KenKen is to fill in a grid with the digits 1 through n, where n is the number of rows or columns (# of rows = # of columns), such that:
- Each row contains exactly one of each digit
- Each column contains exactly one of each digit
- Each bold-outlined group of cells is called a cage containing digits which achieve the specified result using the specified mathematical operation: addition (+), subtraction (−), multiplication (×), division (/ or ÷), and equal (=).
- A digit can be repeated in a cage as long as it is not in the same row or column.
Note: KenKen puzzles are commonly generated from square grid with dimensions 3x3 to 9x9. A KenKen puzzle of size 2x2 is of little value (why?). Extension of the puzzle beyond 9x9 is certainly acceptable, presenting only the “difficulty” of calculating larger numbers and the potential need to record possible values to avoid confusion. When introducing KenKen to students, it is often helpful to start with a 3x3 puzzle. (Sample 3x3 and 4x4 puzzles are located in the attached PDF.)
Adaptations for KenKen in the Classroom
Whether you are working with middle schoolers or college students, there are many ways to adapt the KenKen puzzles for a variety of ability levels. One such adaptation is called “No-Operations” (see puzzle #3 in the PDF). The “normal” KenKen rules apply to this puzzle, but the operation symbols next to the target numbers are omitted. Therefore, one must determine the mathematical operations for each cage in addition to solving the puzzle.
Another adaptation involves changing the puzzle digits. For this variation, the puzzle digits change from the traditional digits (1 to n based on the size of grid). Otherwise, the normal KenKen rules apply to the puzzle. See puzzle #4 in the attached PDF for an example.
The most challenging adapation includes a combination of two variations listed above; mathematical operations are not included in the puzzle, and the parameters of the acceptable digits are changed. This type of puzzle is especially interesting for advanced students and those at the collegiate level. Puzzle #5 is an example of such a variation.
Additional Resources for KenKen
KenKen in the Classroom:
KenKen Classroom Program Sign-Up
KenKen App (free) from NCTM
KenKen Puzzle Apps (free):
KenKen Puzzles March 2016.pdf