The Thai government decides to issue coins of 9 baht. Show that, for all sufficiently large numbers N you can make N baht using only 9 baht and 10 baht coins.
First, note that all of the values from 72 to 80 can be expressed with 8 coins.
Use that as a base case, and prove that every higher value can be achieved using induction. (Note that if $n - 9$ is expressible, then $n$ is as well.)