II. (25 points) Several containers are unloaded from a cargo ship, with a total weight of 10 tons, and the weight of each container does not exceed 1 ton. To ensure that these containers can be transported in one go, how many trucks with a carrying capacity of 3 tons are needed at least?
First, note that the weight of each container does not exceed 1 ton, so the weight of containers that each vehicle can carry at one time will not be less than 2 tons; otherwise, another container can be added.

Let $n$ be the number of vehicles, and the weights of the containers they carry be $a_{1}, a_{2}, \cdots, a_{n}$, then $2 \leqslant a_{1} \leqslant 3(i=1,2, \cdots, n)$.
Let the total weight of all the containers carried be $s$, then
$$
2 n \leqslant s=a_{1}+a_{2}+\cdots+a_{n} \leqslant 3 n \text {. }
$$

That is, $2 n \leqslant 10 \leqslant 3 n$.
Thus, $\frac{10}{3} \leqslant n \leqslant 5$, which means $n=4$ or 5.
In fact, 4 vehicles are not enough.
Suppose there are 13 containers, each weighing $\frac{10}{13}$ tons. Since $\frac{10}{13} \times 3 < 3$, each vehicle can only carry 3 containers, so 4 vehicles cannot carry all of them.
Therefore, at least 5 trucks are needed.