11. Given $f_{1}(x)=|1-2 x|, x \in[0,1], f_{n}(x)=f_{1}\left(f_{n-1}(x)\right)$, then the number of solutions to the equation $f_{2005}(x)=\frac{1}{2} x$ is $\qquad$
11. $2^{2005}$ Hint: You can use the method of inductive guessing.