Reach 180

Logic Level 3

Dan and Sam play a game in which the first to start says the number 2, the next says 3, and the one who's next must say a number strictly between, (not including the endpoints), the previous number and the maximum possible integer number that, with the two previous said numbers, can be the sides lengths of a triangle.

For example, Dan begins saying 2, then Sam says 3, and then Dan must say 4, but can't say 5 nor 3.

The game finishes when someone reaches 180 (who is the winner). If Dan begins, who will win? This means, who has a winning strategy?

This is the seventh problem of the set Winning Strategies.

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