2. Albert and Béatrice are playing a game. There are 2021 pebbles on a table. Taking turns and starting with Albert, they will remove a certain number of pebbles from the table, following this rule. On turn $n \geqslant 1$, the player whose turn it is, that is, Albert if $n$ is odd and Béatrice if $n$ is even, can remove a number of pebbles between 1 and $n$. On the first turn, Albert must remove 1 pebble; on the second turn, Béatrice can remove 1 or 2 pebbles; on the third turn, Albert can remove 1, 2, or 3 pebbles, and so on. The player who removes the last pebble from the table loses the game. Determine which of the two players has a strategy to win for sure.
Solution

Answer: Béatrice has a winning strategy.