We only know about some crates that their total weight is 10 tons, and the weight of no crate is greater than 1 ton. We want to transport the crates with 3-ton trucks. What is the minimum number of trucks that are always sufficient to transport the crates?
We can always load at least 2 tons of cargo onto a truck, because as long as the total weight of the boxes on the truck is less than 2 tons, we can still load any of the remaining ones. Thus, we can always load a total of at least 8 tons of cargo onto four trucks, and the remainder will always fit onto a fifth one. Therefore, five trucks are certainly enough. If we only have four trucks, it can be inconvenient if only 3 boxes fit on them, and we have more than 12 boxes. This is precisely the situation with 13 identical boxes, since $4 \cdot \frac{10}{13}>3$ means that indeed four of these will not fit onto our trucks. So there is a case where 4 trucks are not enough, but 5 are always enough.