(no subject)

You are hired by your favorite 3 letter government agency to find a bag of fake gold. They place you in a room with many bags of gold coins, one of the bags, however, is full of fake coins. To help you with this endeavor you have been given a penny scale, you can drop a penny in to get one measurement. Along with this you are handed a small scrap of paper which has written on it the weight of a gold coin and the weight of a fake gold coin.

As with most projects, there was an unfortunate lack of forsite in planning and you were only allocated one penny.

Two questions...

1. How do you figure out which bag has the fake gold?

2. At what point in an increasing number of either bags or coins can you no longer solve this out with only one penny?