Question 11
Anna and Berta play a game in which they take turns removing marbles from the table. Anna makes the first move. If at the beginning of a move there are $n \ge 1$ marbles on the table, then the player whose turn it is removes $k$ marbles, where $k \ge 1$ is either an even number with $k \le \frac{n}{2}$ or an odd number with $\frac{n}{2} \le k \le n$. A player wins the game if she removes the last marble from the table.
Determine the smallest number $N \ge 100\,000$ such that Berta can force a win if there are exactly $N$ marbles on the table at the beginning.
(Gerhard Woeginger)
Determine the smallest number $N \ge 100\,000$ such that Berta can force a win if there are exactly $N$ marbles on the table at the beginning.
(Gerhard Woeginger)