POTW #2 (Chris Okasaki)
The largest integer that cannot be formed as a combination of 6’s, 9’s, and/or 20’s is 43.
All larger integers can be formed as such a combination. We show that the six consecutive integers
44…49 can be formed as such combinations, and then every larger integer can be formed by adding one
or more 6’s to one of the numbers in the range 44…49.
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44 = 20 + 9 + 9 + 6
45 = 9 + 9 + 9 + 9 + 9
46 = 20 + 20 + 6
47 = 20 + 9 + 9 + 9
48 = 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6
49 = 20 + 20 + 9