[ Algorithm Theory (Miscellaneous).]

Authors: Feerumin L.E., Feeuumina E.M.

Ponchik is in a broken Lunokhod 18 km away from the Lunar Base, where Nезнайка is sitting. There is a stable radio connection between them. The air supply in the Lunokhod will last for 3 hours, and Ponchik also has a spacesuit tank with a 1-hour air supply. Nезнайка has many tanks with a 2-hour air supply each. Nезнайка cannot carry more than two tanks at a time (one of which he uses himself). The speed of movement on the Moon in a spacesuit is 6 km/h. Will Nезнайка be able to save Ponchik and not die himself?

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Nезнайка with two balloons is walking down the road to the lunar rover. After walking 6 km, he leaves a full balloon and returns with one (it takes exactly 2 hours). At the base, he immediately takes two more balloons and heads back to the lunar rover. At a distance of 6 km, he picks up the full balloon he left and leaves the half-used one. At this moment (exactly 3 hours have passed, and the air in the lunar rover has run out), Ponchik sets out to meet him with a single balloon. An hour later, they meet 6 km from the lunar rover and 12 km from the base. Nезнайка gives Ponchik the full balloon, which will allow him to reach the base, and continues with the half-used one to the other half-used balloon he left, which is just enough for him to reach the base.

## Answer

He will be able to.

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