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Warm-up Problems for Postage Stamp Arithmetic

1. Suppose that you have a large source of water, like a lake.

(a) How do you measure exactly two gallons of water with 13- and 7-gallon jugs?

(b) How is this problem different from the postage stamp problem?

2. (a) What postage amounts can you not make with 2-cent and 11-cent stamps?

(b) What postage amounts can you not make with 2-cent and 13-cent stamps?

(c) What postage amounts can you not make with 2 -cent and -cent stamps, ?

3. (a) What postage amounts can you not make with 3-cent and 5-cent stamps?

(b) What postage amounts can you not make with 3 cent and 6-cent stamps?

(c) What postage amounts can you not make with 3 cent and 7-cent stamps?

(d) Can you generalize the results in (a), (b) and (c)?

4. Explain why we assume that *a* and *b* are relatively prime in Question 3 of the original problem statement. If they were not, what would you do to start working on this problem?

5. If *a* and *b* are positive integers that share no common factor greater than 1, explain why is always odd.

You can find solutions to these warm up problem in the Results section of this project.