Suppose there are piles with stones $a_1,a_2,\cdots,a_n$. Consider the quantities $a_i \pmod{3}$. Note that since any power of 2 is not divisible by 3, this means that the new piles formed by splitting the original pile must have different remainders $\pmod{3}$. A pile with remainder 0 splits into 1 and 2 A pile with remainder 1 splits into 0 and 1 A pile with remainder 2 splits into 0 and 2 Each move, the number of zeros changes by 1. Since at the start and at the end, there are no piles with remainder zero, this means that the number of moves performed was even.