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?
Note that, if we have $n$ numbers as the pile numbers with common $\gcd=d, d>2.$ So we have say $da_1,~da_2,\dots, da_n.$
Then whatever moves we make, the resultant pile numbers will be divisible by $d.$
For example, say we have a pile having $$115~~100~~100 \rightarrow 115,~~50,~~50,~~50,~~50$$Then whatever move we do, we can atmost reach $$ 5,~~5\dots \dots,5~~5.$$
Now, note that $\gcd(81, 115+119=234)=9.$
So the pile number will always be divisible by $9.$ For this case we can't achieve pile numbers as $1,1,\dots 1$ $315$ times..
Now, note that $\gcd(115,81+119=200)=5.$
So the pile number will always be divisible by $5.$ For this case we can't achieve pile numbers as $1,1,\dots 1$ $315$ times..
Now, note that $\gcd(119,81+115=196)=7.$
Same reason.
Hence Ah Meng can not divide the marbles into $315$ piles, each with a single marble.