4. A warehouse stores 1500 tons of various goods in containers. The weight of any container is a multiple of a ton and does not exceed $k$ tons. A train consisting of 25 platforms, each with a load capacity of 80 tons, has been dispatched to the warehouse. For what maximum $k$ can this train guarantee the transportation of all goods?
Answer: 26.

Solution. If $k=27$, then it is not always possible to transport all the goods. Indeed, suppose there are 55 containers, each weighing 27 tons, and one weighing 15 tons. Only two containers of 27 tons each can fit on one platform. Therefore, to transport 55 such containers, at least 28 platforms are required.

We will show that if the weight of each container does not exceed 26 tons, then it is always possible to transport them from the warehouse. Imagine that the containers store boxes, each weighing one ton, and the containers themselves are weightless. We will sequentially load the platforms with these boxes: as soon as the current platform is full, we move to the next one. We will load the boxes starting with all the boxes from the first container, then from the second, and so on. As a result, the boxes will fit on 19 platforms, since $19 \cdot 80=1520>1500$. With such placement, boxes from no more than 18 containers can end up on two platforms. To accommodate these containers, 6 platforms are sufficient, since any three containers can fit on one platform.