# Winning Contest

Computer Science Level 5

Alice and Bob challenged each other to​ a duel. A person will win if they have won precisely 3 more than the other. If they decided to play at most 30 rounds, how many different sequence are there for Alice to win?

Denote the duel where Alice or Bob wins as A and B respectively. Some winning sequences for Alice are as follows:

 1 2 3 AAA AABAA ABABBAAAA 

Note that the sequence BBBAAAAAA is not a winning sequence for Alice because Bob already won on the third round and the game would have ended.

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