Hercules and the Hydra
Hercules is fighting with the Hydra, which has 2018 heads. In each round, at most three heads can be cut off. If he cuts off one head, it immediately grows back. If he cuts off two heads, nine heads grow. If three heads are cut off, the further development depends on whether the remaining number of heads is divisible by seven. If yes, the number of heads is reduced to one seventh; if not, the number of heads is increased 10 000 times. What is the minimum number of rounds in which Hercules is able to defeat the Hydra and cut off the last head?
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