MathNet 2023-part-02 — 191 problems (EN–VI) Question 105

Let $n \geqslant 1$ be an integer. Morgane initially has $n$ piles, each containing one coin. She then allows herself operations of the following form: she chooses two piles, removes the same number of coins from the first pile as from the second, and forms a new pile with the coins she has removed.

Determine, as a function of $n$, the smallest number of non-empty piles that Morgane can obtain by means of such operations.