My grocery store frequently has a special on pears and apples where you fill the bag for a set price and I'm never quite sure how well I've done maximizing the contents.
My restrictions and (limited) sense of etiquette:
- I prefer apples to pears, so I wouldn't want a solution of more than 1/3 pears.
- I also get bored with one fruit, so I don't want 0 pears.
- I also refuse to harm any fruit in the process (i.e. no apple sauce.)
- The bag is 2 sheets of 30x30cm plastic when laid flat. Apples are 4-6cm ~spheres, while a pear might be 4x6cm.
- I have no measuring instruments in the shop, no willingness to replace fruit already in the bag, or take an excessive amount of time, etc.
Given these restrictions, my question is how do I maximize the total volume filled and minimize the air gaps assuming these varying sphere and pear shapes?
Do I start with smaller or larger apples first, do I start with pears first? Are same size or mixed size/shaped objects easier to use to fill a space? Etc.
More about the bag:
It has plastic handles at the top which need to be closed together making a rough sphere. It is prone to ripping, particularly where the handles connect, so stretching is not practical. The bottom corners are pushed up inside about 2 cm and welded in the side welds, making it slightly more spherical when full. The offer claims that it can hold at least 3 Kg.