Assume we have the following denominations of coins (1, 3, 6, and 10). How can we use dynamic programming to figure how the minimum number of coins to arrive at n? Let F(n) be the minimum number of coins need to make n.

Would a greedy approach in which you always select the largest possible denomination always provide an optimal solution (e.g., A greedy solution to find F(24) would be to select 10, followed by another 10, followed by 3 and then 1)? If not, provide a counter-example.