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Project Description Prerequisites Warm up Problems Hints Resources Teaching Notes Extension Problems Results

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 two k  plus one -cent stamps, k greater than or equal to one?

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 a times b minus a minus b  is always odd.


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

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