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Expert: - 9/8/2009


Question
I have four 3-cent stamps and three 5-cent stamps. using one or more of these stamps, how many different amounts of postage can I make?

Answer
1, 2, 3, or 4 3c stamps are 3c, 6c, 9c, or 12c.
That is 4 sets of postage.

If one 5c stamp is included, we can add 0, 1, 2, 3, or 4 3c stamps to it.
That is 5 sets of postage.

If two 5c stamps are included, we can still add 0, 1, 2, 3, or 4 3c stamps to it.
That is another 5 sets of postage.

If three 5c stamps are used, once again we can add 0, 1, 2, 3 or 4 3c stams to it.
Tat is one more 5 sets of postage.

The total number of sets of postage are 4+5+5+5 = 19.

Note that the number is also (4+1)(3+1) - 1 = 5*4 - 1 = 20 - 1 = 19.

The value of the total stamps is
  0   3   6   9   12
0   0   3   6   9   12
5   5   8   11   14   17
10   10   13   16   19   22
15   15   18   21   24   27

where the top is the value of the 3 cent stamps and the left side is the value of the 5 cent stamps.

In the middle are the 20 values, all of them unique.
Not that the upper left value is 0, which means there are no stamps.
That one has to be discarded, since there is no such thing as sending a free letter.

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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