[ Processes and Operations ]

When organizing an expedition to Everest, the participants set up four high camps (not counting the base camp), each a day's journey apart from each other, after which everyone descended. After recounting the supplies, the leader decided that one more oxygen cylinder needed to be brought to the fourth camp, and then everyone would go down again.

1) can carry no more than three cylinders uphill,
2) consumes exactly one cylinder of oxygen per day.

What is the minimum number of cylinders that will need to be taken from the camp to achieve the set goal?

(Leaving cylinders is only allowed in the camps.)
Note that to move one cylinder from one high-altitude camp to the next, it requires 3 cylinders: one to be moved, and another two that the expedition member uses on the way there and back. Therefore, to accomplish the task, no less than three cylinders need to be delivered to the third camp; for this, no less than $3 * 3=9$ cylinders need to be delivered to the second camp; reasoning similarly, we get that no less than 81 cylinders need to be taken from the base camp. It is easy to show that with 81 cylinders in the base camp, the task can be accomplished.

## Answer

81 cylinders.