Let us analyse how the recorded moves affect the sum of the digits written in a circle. Let us denote the numbers by $a_1, a_2, \dots, a_{300}$. The following numbers will be written after the move of the first type: $b_k = a_k - a_{k-1} - a_{k+1}$, $k = 1, \dots, 300$ ($a_{301} \equiv a_1$). Let $S = a_1 + a_2 + \dots + a_{300}$,

then $b_1 + b_2 + \dots + b_{300} = S - S - S = -S$. After the move of the second type, the sum becomes $S+2$ or $S-2$. Since the parity of the sum after each move does not change, it is impossible to get an even sum from the original odd sum.