1. Call a non-empty subset of $\{1,2,3,4,5,6,7,8,9\}$ an odd subset: if the sum of all numbers in it is odd, then the number of odd subsets is $\qquad$ .
Let $A=\{1,2,3,4,5,6,7,8,9\}$, map the subset $S$ of $A$ containing 1 to $S \backslash\{1\}$. One of the two subsets must be odd, and the odd subset is non-empty, so the number of odd subsets is $\frac{1}{2} \cdot 2^{9}=256$.