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Imagine the United States only had two postage stamps, a 3 cent stamp and a 7 cent stamp. If you can put any number of stamps on an envelope that you want, what amounts of postage can and cannot be paid for?

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sqdancefan

Answer:

  • not possible:  1, 2, 4, 5, 8, 11
  • possible: all others

Step-by-step explanation:

Obviously, all multiples of 3 and 7 can be paid.

1 cent can be added by adding a 7-cent stamp and taking away two 3-cent stamps. 2 cents can be added by adding three 3-cent stamps and taking away one 7-cent stamp. Hence any value more than 7 +2(3) = 13 cents can always be accommodated.

Amounts that are impossible:

  1, 2, 4, 5, 8, 11 cents

All other positive integer amounts are possible.

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