MathNet 2024-part-02 — 168 problems (EN–VI) Question 84

Aline and Elsa play the following game. They have 100 stones, which they split into two piles (not necessarily of the same size) at the beginning of the game. Then, taking turns and starting with Aline, they make the following move: they choose a pile, then a strictly positive integer less than or equal to half the size of the chosen pile, and remove that number of stones from the pile. The first player who can no longer make a move loses.

Determine all initial configurations for which Elsa has a winning strategy.