Question 462282: I have 4 three cent stamps and 3 five cent stamps. Using one or more of these stamps, how many different amounts of postage can I make?
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!
1, 2, 3, or 4 3c stamps are 3c, 6c, 9c, or 12c.
That is  sets of postage.
If one 5c stamp is included, we can add 0, 1, 2, 3, or 4 3c stamps to it.
That is  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 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 sets of postage.
The total number of sets of postage are  .
Note that the number is also  .
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  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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