Exercise 11.

Suppose you have a collection of 5-cent stamps and 8-cent stamps. We saw earlier that it is possible to make any amount of postage greater than 27 cents using combinations of both these types of stamps. But, let's ask some other questions:

  1. Prove that if you only use an even number of both types of stamps, the amount of postage you make must be even.

  2. Suppose you made an even amount of postage. Prove that you used an even number of at least one of the types of stamps.

  3. Suppose you made exactly 72 cents of postage. Prove that you used at least 6 of one type of stamp.

Hint.
in-context