Example 13 Unload several boxes from a cargo ship, with a total weight of $10 \mathrm{t}$, and the weight of each box does not exceed $1 \mathrm{t}$. To ensure that these boxes can be transported away in one go, how many trucks with a carrying capacity of $3 \mathrm{t}$ are needed at least?
(1990, Jiangsu Province Junior High School Mathematics Competition)
First, note that the weight of each box does not exceed $1 \mathrm{t}$, so the weight of the boxes that each vehicle can carry at one time will not be less than $2 \mathrm{t}$; otherwise, another box can be added.

Let $n$ be the number of trucks needed, and the weights of the boxes they carry be $a_{1}, a_{2}, \cdots, a_{n}$. Then,
$$
2 \leqslant a_{i} \leqslant 3(i=1,2, \cdots, n) .
$$

Let the total weight of all the goods transported be $S$. Then,
$$
2 n \leqslant S=a_{1}+a_{2}+\cdots+a_{n} \leqslant 3 n,
$$

which means $2 n \leqslant 10 \leqslant 3 n$.
Thus, $\frac{10}{3} \leqslant n \leqslant 5$, i.e., $n=4$ or 5.
In fact, 4 trucks are not enough. This can be illustrated by the following special case. Suppose there are 13 boxes, each weighing $\frac{10}{13} \mathrm{t}$. Since $\frac{10}{13} \times 33$, each truck can only carry 3 boxes. Therefore, 4 trucks cannot carry all the boxes, so at least 5 trucks are needed to transport all the boxes at once.