How much more efficiently would you be able to pack 1cm diameter disks into the 1m square? Could you make an estimate for the efficiency of packing disks of diameter 1mm?
Whilst it might seem relatively simple, the problem of 'shape packing' is often very difficult mathematically to solve with certainty for many shapes. Intuitive visualisation often works just as well as a strict mathematical analysis, and often is the only sensible possibility with packing together complicated shapes.
You might like to consider situations in which efficient shape packing is relevant in the physical world.