Problem

Source: Singapore Junior Math Olympiad 2019 2nd Round p2 SMO

Tags: combinatorics



There are $315$ marbles divided into three piles of $81, 115$ and $119$. In each move Ah Meng can either merge several piles into a single pile or divide a pile with an even number of marbles into $2$ equal piles. Can Ah Meng divide the marbles into $315$ piles, each with a single marble?