MathDB

Anna and Berta play a game in which they take turns in removing marbles from a table. Anna takes the first turn. At the beginning of a turn there are n ≥ 1 marbles on the table, then the player whose turn is removes k marbles, where k ≥ 1 either is 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\ge100000

which Berta has wining strategy.
proposed by Gerhard Woeginger

Problem Statement