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Proof by strong induction:
- blavigne13 December 06, 2015N=44
Basis:
44=20+6+6+6+6
45=9+9+9+9+9
46=20+20+6
47=20+9+9+9
48=9+9+9+9+6+6
49=20+20+9
Inductive hypothesis:
...actually, formal proofs are one of my weaker areas, so I'll use "plain old English" in place of a formally stated inductive hypothesis, etc.
In essence, once we have 6 consecutive base cases, we are trivially able to construct any larger number by adding some multiple of 6 to one of the base cases.
Note: This problem is commonly presented as making exact postage using only stamps of the specified values, so searching one of those solutions should provide a better explanation.