Reach 216000000

Logic Level 2

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 cube (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 8; that is, he can reply 3, 4, 5, 6 or 7.

The game finishes when someone reaches 216000000 (who is the winner). If Dan begins, who will win? This means, who has a winning strategy?

This is the ninth problem of the set Winning Strategies.

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