What is the most efficient way to find a penny in an empty field? Let's say that I'm in a rectangular field,2 miles in width and 3 in length, with a metal detector. I know that somewhere within this field lies a penny, which is equally likely to be at any point. My metal detector will detect any penny within a 30-ft radius of my location. Furthermore, this penny is the only metallic object in the field (at least as far as my metal detector is concerned). I want to minimize my metal detector's battery usage. Of course, I'll turn off my metal detector when I walk back to a place I've already been to.

I was thinking something like this. Basically we divide a rectangle into halves, eighths, etc. until we find what we're looking for.
First, I walk along each each diagonal
Second, I walk along the center lines of the rectangle and thereby divide the rectangle into smaller rectangles.
I then repeat these two steps with each rectangle until I find the penny.
