jmc

Let the $x$-coordinates of the vertices of $P_1$ be $x_1,x_2,\dots ,x_{33}$. Then, by the midpoint formula, the $x$-coordinates of the vertices of $P_2$ are $\frac{x_1+x_2}{2},\frac{x_2+x_3}{2},\dots ,\frac{x_{33}+x_1}{2}$. The sum of these equals $\frac{2x_1+2x_2+\cdots +2x_{33}}{2}=x_1+x_2+\cdots +x_{33}$. Similarly, the sum of the $x$-coordinates of the vertices of $P_3$ equals the sum of the $x$-coordinates of the vertices of $P_2$. Thus the desired answer is $\boxed{99}$.