Suppose that a certain currency has three coins: $1c,8c,$ and $c$ where $$ is unknown but is less than $48.$ Suppose you know that the minimum number of coins function A satisfies: Solve using min$\{..\}$ dynamic programming

$[5$ pts$]$

$A[47]=7$

$A[48]=4$

$A[40]=4$

What is the value of $A[48-]?$ Justify.

Solution: