# Making N baht using only 9 baht and 10 baht coins

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.

• This is the coin problem. $71$ is the largest sum you cannot obtain. – Arthur Oct 23 '13 at 7:50

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.)
• I definitely meant $n - 9$. – Dennis Meng Oct 23 '13 at 8:03
• The number of elements for which you can not make change is:$\frac{1}{2}*(10 - 1)*(9 - 1) = 36$ – Alan Oct 23 '13 at 16:46