You are a pickle fanatic and only order your pickles online from Papa Pete’s Pickle Emporium. All orders from Papa Pete’s must be in sets of either three or seven jars. For example, you could order 20...

You are a pickle fanatic and only order your pickles online from Papa Pete’s Pickle Emporium. All orders from Papa Pete’s must be in sets of either three or seven jars. For example, you could order 20 jars by doing 3 + 3 + 7 + 7 (this is two sets of three and two sets of seven).

Use strong induction to prove that you can order any number
n
of jars where
n
is a natural number and
n >=
12. Be sure to clearly show/state your base cases, inductive hypothesis, what you wish to prove using the IH, and inductive step.