Discrete Mathematics Stamp problem

Question

I am very confused on how to solve.

Use the Principle of Mathematical Induction to prove that every amount of postage of 18 cents or more can be formed using just 4-cent and 7-cent stamps.

Do you have to use induction to prove? – Edward Jiang Apr 15 '16 at 03:03 — Edward Jiang, Apr 15 '16 at 03:03
Yes, this must be proved by Mathematical Induction. – Bean Apr 15 '16 at 03:04 — Bean, Apr 15 '16 at 03:04
Have you tried looking at some of these similar questions? – JMoravitz Apr 15 '16 at 03:08 — JMoravitz, Apr 15 '16 at 03:08

Seven · Answer 1 · 2016-04-15T03:17:15.790

4

You can create the first four in the following way:

$18 = 2\cdot 7 + 1 \cdot 4$

$19 = 1\cdot 7 + 3 \cdot 4$

$20 = 0\cdot 7 + 5 \cdot 4$

$21 = 3\cdot 7 + 0 \cdot 4$

Now assume that you can create all values $18, 19 , 20, 21, \cdots , k$.

Then you can create $k+1$ as $(k-3) + 1\cdot 4$. Hence, we are done by induction.

edited Apr 15 '16 at 03:17

answered Apr 15 '16 at 03:09

Seven

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Discrete Mathematics Stamp problem

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