Group values up to a threshold and minimize groups Given a threshold $t$ and a list of numbers $N$. $\forall n \in N: n \leq t$ 
Now group the numbers so that the sum of the numbers $s$ is lower or equal $t$. Minimize the amount of groups.

Example: $N={20,19,18,17,14,12,9,5,4}$ and $t = 40$

Possible Grouping: ${(20,19),(18,17,4),(14,12,9,5)}$ (Greedy)

Is greedy a strategy/algorithm, that will lead to the optimal solution? If not, are there other algorithms to solve this problem?
I just learned that this is the bin packing problem with goal of minimizing the bins. This problem is NP hard. So the greedy strategy wont guarantee an optimal solution.