2. The number of non-negative integer solutions to the equation $x_{1}+x_{2}+\cdots+x_{99}+2 x_{100}=3$ is $\qquad$ .
2. 166749 .

Classify by $x_{100}$:
(1) When $x_{100}=1$, there are 99 non-negative integer solutions;
(2) When $x_{100}=0$, there are
$$
\mathrm{C}_{99}^{1}+\mathrm{A}_{99}^{2}+\mathrm{C}_{99}^{3}=166 \text { 650 (solutions). }
$$

Combining (1) and (2), the total number of non-negative integer solutions is
$$
99+166650=166749 \text { (solutions). }
$$