BucketOfQuarters

Goal: Guess the value of a 5 gallon bucket of quarters.

Solution:

Money = Value of one quarter x Number of quarters

Number of quarters = Mass of all quarters / Mass of single quarter

Mass of quarters = Density of quarters * Volume of quarters

Volume of quarters = Volume of container * packing factor

To determine packing factor, load up a container with quarters, pour in some water, pour out the water, measure its volume

Volume of water / volume of container gives packing factor

Can see if size of container affects measurements (edge effects of packing, circle packing)

There may be more elegant mathematical approaches, but this is a good old fashioned engineering approach.