6. At the pier, 9 trucks arrived. Each of them brought no more than 10 tons of cargo, and it is known that the weight of each individual cargo does not exceed 1 ton. At the pier, there are 10 barges with a carrying capacity of $k$ tons each. For what minimum $k$ can all the delivered cargo be guaranteed to be transported by the barges?
Answer: when $k=180 / 19=10-10 / 19$ tons. Evaluation. If all items weigh $10/19$ tons each, and there are a total of $9 \cdot 19=171$ items, then on some barge there will be no fewer than 18 items, and they will weigh no less than $180 / 19 \mathrm{~m}$.

Example. To load the barges, items weighing between $10/19$ and $20/19$ tons must be removed from each truck; then the remaining contents of each truck will fit on a separate barge, and all the removed items will weigh no more than $9 \quad 20 / 19=180 / 19$ tons, and all of this will fit on the 10th barge.

To implement this plan for a specific truck, we will remove items from it in descending order. If the first removed piece is greater than $10/19$, the process is complete: it is no more than 1 and certainly no more than $20/19$. If it is no more than $10/19$, then all subsequent pieces certainly do not exceed $10 / 19$, and when we remove them one by one (in any order), the total weight of the removed items will not jump over the interval [10/19,20/19]. If the total weight of all the cargo in this truck is less than $10/19$, then nothing needs to be removed.