Looking for an intuitive solution to the following problem:
In a certain country the following coins are in circulation: 1 cent, 2 cents, 5 cents, 10 cents, 20 cents, 50 cents, and 1 dollar. It is known that you can pay A cents with B coins. Prove that you can pay B dollars with A coins.
This is a problem from the book, Mathematical circles, a Russian experience by Fomin and other authors.