Today,I came across this problem:
Suppose you have a currency, named miso, in three denominations, $1, 10$ and $50$. In how many ways can $107$ miso be given in this currency if you have access to infinite number of coins of the said three denominations only?
$a)15 \quad \quad \quad b)16 \quad \quad \quad \quad c)17 \quad \quad \quad d)18 \quad \quad \quad \quad e)19$
I identified that this is the coin change problem and I am aware of the dynamic programming formulation for this, and till now my solution looks like this which is not at all intended by the problem setter, I am just wondering is it possible to solve this just by pencil-paper way? Of-course I don't want to do the dynamic programming steps in pencil paper.