I’ve been meaning to start a problem-solving journal and write about actual problem-solving experiences. I’d been putting it off but now that it’s the summer I have no excuse… and then this blog post at Infigons, etc. inspired me!

I just picked out a possible Algebra Problem of the Week for next year that asks, “A point is chosen at random from within a circular target board. What is the probability that the point will be closer to the center of the board than to the boundary of the region?”

Infigon’s problem changes the circular dart board to a square. To which I say, “Yikes!”

My first thought is to solve the simpler problem first. I’m going to start with the circular board. My first idea is we need to find a circle that takes up half the area of the dart board. I know every point on the boundary of the circle is as close to the boundary of the dart board as every other point on the circle…