A local nursery is discounting shrubs and bushes. A 1-foot diameter shrub is only $1. A ½-foot diameter shrub is $2. The ¼-foot diameter shrub is $4. (And so on… one-third foot diameter = $3, one-tenth foot diameter = $10.)

What is the cheapest way to fill the greatest area of a flowerbed that is a 4-foot square? How much of the area will be unfilled?