We have 5 trucks with a capacity of 3 tons each. What is the maximum weight of cargo that we can always transport with these 5 trucks, if we only know that the cargo consists of parts weighing no more than 1 ton each?
The task can be interpreted in two ways. According to the majority of solvers, the trucks need to transport as many packages as possible, with each package weighing no more than 1 ton. The other interpretation is that the shipment is predefined, and all packages must be delivered.

We can also imagine the situation as a negotiation between the shipper and the client. In the first case, the shipper only knows that the shipment consists of parts weighing no more than 1 ton, so they must declare the maximum weight they are willing to transport. In the second case, the client's offer includes the total weight of the shipment, and the shipper must decide whether to accept the shipment or not. In both cases, we are looking for the maximum weight the shipper can transport despite any maneuvers by the client. The key difference between the two cases is that in the second case, the client can only divide the predefined weight, while in the first case, there is no such restriction.

If the packages weigh more than $3/4$ ton, then no more than three packages can be loaded onto one truck. We will show that according to the first interpretation, the shipper cannot always transport more than $15 \cdot 3/4 = 11.25$ tons. Suppose the shipper agrees to transport $11.25 + v$ tons, where $0 < v \leq 3.75$. If the client now prepares packages weighing $0.75 + v/30$, then the condition is met: $0.75 + v/30 = 0.75 + 3.75/30 < 1$, and at most $5 \cdot 3 = 15$ packages, or $11.25 + v/2$ tons, can fit on the trucks. It is clear that the client's countermeasure—the appropriate packaging of the boxes—depends on the driver's offer.

If the shipper agrees to transport no more than 11.25 tons, then they can indeed do so. It is sufficient to show that at least 2.25 tons of cargo can be loaded onto each truck.

Arrange the packages in descending order of weight and start loading them onto the truck until the next one in line no longer fits. If the weight of the remaining package is no more than $3/4$ ton, then it did not fit because there is already more than 2.25 tons of cargo on the truck. If, however, the weight of the remaining package is more than $3/4$ ton, then the packages already on the truck are also heavier than $3/4$ ton. No single package can be heavier than 1 ton, so there must be at least three packages on the truck, which means more than $3 \cdot 3/4 = 2.25$ tons of cargo.

This means that 11.25 tons of cargo can always fit on five trucks, but the shipper cannot take advantage of this.

In the second interpretation, however, the client is bound by the amount of cargo to be transported. According to the above reasoning, at least $4 \cdot 2.25 = 9$ tons of cargo can be placed on the first four trucks. This means that in the second case, the shipper can agree to transport 12 tons, as the remaining 3 tons can be loaded onto the fifth truck.

The shipper cannot, however, agree to transport a heavier shipment, even in the second case. Suppose the client prepares 16 packages, each weighing more than $3/4$ ton $(16 \cdot 3/4 = 12)$, each of which is of course no more than 1 ton. The five trucks can transport at most 15 of these packages.

Thus, we have found that according to the first interpretation, the maximum transportable weight is no more than 11.25 tons, and according to the second interpretation, it is 12 tons.