Dan and Sam play a game in which the first to start says the number \(1\) and the one who's next must say an integer number between the number previously said and its triple (but not including).
For example, Dan begins saying 1, then Sam can say whichever number he wants between 1 and 3; as the only integer between 1 and 3 is 2, he must say 2. Then, Dan can choose any number between 2 and 6; that is, he can say either 3, 4 or 5.
The game finishes when someone reaches 90 (who is the winner). If Dan begins, who will win? This means, who has a winning strategy?