## Monday, August 9, 2010

### KenKen and Other Goodness

Another couple of cute geometry SAT problems from David Marain:
Problem 1: Chords PQ and PR are each of length 6 and form an inscribed angle of 60°. If the area of the circle is k*pi, what is the value of k?

Problem 2: From point X, the 2 tangent segments to a circle have lengths 6 and form a 60° angle. Find the square of the least distance from X to the circle.
As a visual person, I love geometry word problems, because the first thing I do when I read problems like these is that I sketch them out quickly. (And then I tend to "see" information that I wouldn't otherwise observe from the flat phrasing of the problem.) That's a good habit I would like to instill in all of my geometry students.

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By the way, I've been incredibly addicted to the KenKen puzzles in the free daily newspaper during my latest visit to NYC. Since my friends could only meet either for lunch or dinner (or sometimes happy hour), I found myself spending a lot of quality time by myself in the city, and each time I would skim through all the gossipy news and go directly to the crossword and KenKen puzzles.

(I'm terrible with crossword puzzles, but the ones in trashy newspapers are usually very do-able for me. I guess I'm their target audience. By the way, I find it hysterical that Wyclef is running for president in Haiti; it's like South Park in real life, or something.)

Here is one KenKen puzzle I kept from the papers. I know these things have been around for a while, but I never really tried them until these last couple of weeks. I find them much, much more enjoyable (read: less repetitive -- and actually somewhat mathematical!) than Sudokus.

The rules are simple:
1. Each row and each column must contain the numbers 1 through 6 without repeating.

2. The numbers within the heavily outlined boxes, called cages, must combine using the given operation (in any order) to produce the target numbers in the top-left corners.

3. Freebies: Fill in single-box cages with the number in the top-left corner.

Try it. And tell me if you find it as addicting as I do. :)