# Reach 200

Logic Level 3

Dan and Sam play a game in which the first to start says the number $$1$$, the next says $$2$$, and the one who's next must say an integer number between the number previously said and its double (but not including).

For example, Dan begins saying $$1$$, then Sam says $$2$$, and then Dan can say whichever number he wants between $$2$$ and $$4$$; as the only integer between $$2$$ and $$4$$ is $$3$$, he must say $$3$$. Then, Sam can choose any number between $$3$$ and $$6$$; that is, he can say either $$4$$ or $$5$$.

The game finishes when someone reaches $$200$$ (who is the winner). If Dan begins, what's the minimum quantity of numbers that the one who has a winning strategy must say, to win?

Submit $$0$$ if you think that nobody has a winning strategy.

Assumptions: Both players want to win the game.

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