## Archive for September 15, 2011

### Moebius Noodles Project

My friend Maria Droujkova of the Natural Math Project has taken on the task of building a Creative Commons book and support site for parents who want to enjoy math with their young kids (ages 0 to 5 years).

As a parent who loves to play math games and talk about numbers and shapes with my twin 4-year-old sons (see my previous post), I believe this effort is laudable. I support the project, and I would like to ask for your support, too.

### Wee Wee Can-Can Doodoo KenKen

My sons love words with repeating syllables, such as…

*pee pee**poo poo**knock knock**bam bam**Pop Pop**couscous*

But, by far, their favorite word that exhibits exact reduplication is KenKen.

My friend Harold Reiter creates KenKen puzzles. His aren’t the garden-variety, generated-by-computer-algorithm type, though. His puzzles have interesting features, such as including the first initial of his name as one of the cages:

Note that the puzzle above also has a “clueless cage” in the upper right corner; to solve the puzzle, it is not necessary to know the value or operation associated with this three-square cage. (If KenKen is new to you, check out the rules for solving.)

On a recent rainy afternoon, my twin four-year-old sons Alex and Eli solved the puzzle above. On their own, they identified the set of seven numbers that could uniquely fill the H. Eli said, “I know that 8 × 6 = 48, and 8 = 4 × 2 and 6 = 3 × 2, so it’s {1, 1, 1, 2, 2, 3, 4}.” I asked if there were any other possibilities. Eli continued, “Well, 1 × 1 × 2 × 2 × 2 × 2 × 3 = 48, too, but there can’t be four 2’s, because there are only three columns in the H.” I then had to help with some of the logic about how to place those seven numbers… but once they realized that the center of the H had to be a 1, they were off to the races.

After completing the puzzle, I told Alex and Eli that my friend Harold had created the puzzle. Upon hearing this, Alex turned the paper over. “Let’s make a KenKen puzzle,” he suggested. And why not? I drew a 4 × 4 grid for them, and they proceeded to tell me where to place the digits to create a Latin square. Then, they indicated the location of the cages, as well as the values and operations to use within the cages. To prove that the solution was unique, I created a blank version of the puzzle on a different sheet of paper. When I asked the boys to solve it with me, Alex grabbed the paper on which we had originally designed the puzzle and showed me the solution. (Okay, so maybe they don’t yet understand the concept of uniqueness, but I appreciated Alex’s application of a fundamental problem-solving strategy: reduce it to a previously solved puzzle!)

For your enjoyment, I present Alex and Eli’s first-ever KenKen puzzle.

If you roll your mouse over the puzzle above, you’ll notice the alternate text reads, “Alex and Eli’s KenKen Puzzle for Grandma.” Upon completing the puzzle, the boys suggested that we send the puzzle to their grandmother. So we did. That was over a week ago… and we still haven’t heard a response.