4. A warehouse stores 400 tons of cargo, with the weight of each being a multiple of a centner and not exceeding 10 tons. It is known that any two cargos have different weights. What is the minimum number of trips that need to be made with a 10-ton truck to guarantee the transportation of these cargos from the warehouse?
Answer: 51.

Solution. We will show that it is always possible to transport the goods in 51 trips, even if the warehouse contains all weights from 1 to 100 tons. Indeed, we can divide all the goods, except for the 50-ton and 100-ton ones, into 49 pairs as follows:

$$
(1,99), \quad(2,98), \quad(3,97), \quad \ldots, \quad(49,51)
$$

For their transportation, 49 trips are sufficient, since each pair fits into the truck. Two more trips are needed to transport the 50-ton and 100-ton goods.

Now we will show that it is not always possible to transport the goods in 50 trips. Suppose the warehouse stores goods weighing 31 and $47,48, \ldots, 100$ tons. Their total weight is $31+\frac{54 \cdot(47+100)}{2}=4000$ tons. No two
goods weighing from 50 to 100 tons can be transported together in one truck. But there are 51 such goods, so at least 51 trips are required.