Alice and Bob play the following game. Alice starts by choosing an integer between 1 and 11. Then,

Bob adds any integer between 1 and 11, and the game continues in this manner, taking turns. The first player to reach 56 wins. Who has a winning strategy?
Alice starts with 8, then each time Bob adds $x$, Alice adds $12-x$. Thus, after Alice's second move, 20 will be written, then 32 after Alice's third move, and so on. Alice will be the first to write $56=8+4 \cdot 12$.