11. Use 100 RMB to buy items, with the rule that you can only buy items in one of the following three ways each day: (1) buy candy for 1 RMB; (2) buy cookies for 2 RMB; (3) buy fruit for 2 RMB, and you are not allowed to buy nothing. There are $\qquad$ ways to spend all 100 RMB.
11. $\frac{1}{3}\left(2^{101}+1\right)$.

Let the number of ways to spend $n$ yuan be $x_{n}$. If on the first day, 1 yuan is spent on candy, the remaining $(n-1)$ yuan can be spent in $x_{n-1}$ ways; if on the first day, 2 yuan is spent on cookies or fruit, the remaining $(n-2)$ yuan can be spent in $x_{n-2}$ ways. Therefore, $x_{n} = x_{n-1} + 2 x_{n-2} (n \geqslant 3), x_{1} = 1, x_{2} = 3, x_{n} = \frac{1}{3}\left[2^{n+1} + (-1)^{n}\right]$. Hence, $x_{100} = \frac{1}{3}\left[2^{101} + 1\right]$.